Keywords: Control of networks
Abstract: Recent radical evolution in distributed sensing, computation, communication, and actuation has fostered the emergence of cyber-physical network systems. Examples cut across a broad spectrum of engineering and societal fields. Regardless of the specific application, one central goal is to shape the network collective behavior through the design of admissible local decision-making algorithms. This is nontrivial due to various challenges such as the local connectivity, imperfect communication, model and environment uncertainty, and the complex intertwined physics and human interactions. In this talk, I will present our recent progress in formally advancing the systematic design of distributed coordination in network systems. We investigate the fundamental performance limit placed by these various challenges, design fast, efficient, and scalable algorithms to achieve (or approximate) the performance limits, and test and implement the algorithms on real-world applications.

Keywords: Learning, Control of networks, Large-scale systems
Abstract: We study reinforcement learning (RL) in a setting with a network of agents whose states and actions interact in a local manner where the objective is to find localized policies such that the (discounted) global reward is maximized. A fundamental challenge in this setting is that the state-action space size scales exponentially in the number of agents, rendering the problem intractable for large networks. In this paper, we propose a Scalable Actor Critic framework that exploits the network structure and finds a localized policy that is an O(rho^{kappa+1})-approximation of a stationary point of the objective for some rhoin(0,1), with complexity that scales with the local state-action space size of the largest kappa-hop neighborhood of the network.

Keywords: Fluid power control, Mechanical systems/robotics, Discrete event systems
Abstract: Conventional off-highway vehicles in agricultural, construction industries have used hydraulics for power transmission and throttling as a means for control which reduced system efficiency. The goal to increase system efficiency and reap the benefits of electrification have led to the creation of a novel Hybrid Hydraulic-Electric Architecture (HHEA) which could significantly increase efficiency and decrease electrical component sizes also maintaining control performance. A set of common pressure rails provide majority of power via power dense hydraulics to drive the actuators and power modulation is done by the electric components for precise control.

This paper presents the strategy for motion control of the actuators present in the HHEA. A non-linear control strategy has been implemented as a nominal controller for the system. The energy optimization creates frequent pressure rail switches that increases error in trajectory tracking during the switch. In order to reduce the tracking error and improve control performance during the switch, this paper talks about a transition controller that uses Least Norm Control technique and a valve switching strategy to reduce the tracking error during the switch.

The transition controller is able to reduce the maximum tracking error during a pressure rail switch from 3.8mm to 0.26mm and also reduce the control input (motor torque), to enable better control performance with smaller electrical components.

Keywords: Autonomous robots, Decentralized control, Intelligent systems
Abstract: Multi-robot learning has been extensively studied in the recent years. Developing sample-efficient and tractable multi-robot learning algorithms for decentralized control policies remains challenging. In this work, we propose a novel multi-robot learning method based on guided policy search (GPS) to learn decentralized control policies. The proposed method exploits distributed trajectory optimization to provide guiding trajectory samples for policy learning. In turn, the currently learned policy plays a part in the trajectory optimization to update the guiding trajectory samples such that the guiding trajectories are reproducible by the current policy. A guided search algorithm is designed to alternate between the distributed trajectory optimization and policy learning using the Alternating Direction Method of Multipliers (ADMM) to find the optimal policy that exhibits good long-term performance. We demonstrate the effectiveness of our method in a robotic swarm control problem and the experimental results show that our method efficiently learns the decentralized control policy with considerably less samples.

The main contribution of this work is the multi-robot guided policy search method. Specifically, a distributed trajectory optimization method based on linear-quadratic-regulator (LQR) is designed to solve for the guiding trajectories used to train the policy. The distributed trajectory optimization extends the single-robot guided policy search to multi-robot systems. The learned decentralized policy accomplishes the robotic swarm control task using each robot’s local observation only and does not require inter-robot communication. The proposed method provides a new framework for learning decentralized multi-robot control policies, which demonstrates superior performance with regard to sample-efficiency. To the best of our knowledge, this is the first time that the multi-robot guided policy search method is proposed.

Keywords: Constrained control, Optimal control, Optimization algorithms
Abstract: This work presents an in-depth investigation of the stability of Time-distributed Optimization (TDO) for real-time model predictive control for the specific case of linear systems subject to input constraints. When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. We prove that if enough optimizer iterations are performed, the plant-optimizer interconnection is asymptotically stable using small gain arguments. In this work, we investigate how the problem formulation affects the minimum number of optimizer iterations required to stabilize the plant dynamics. Using the input-to-state stability framework, we show that closed-loop stability of real-time model predictive control can be guaranteed using multiple mechanisms including selecting suitable cost matrices, pre-conditioning the optimal control problem, increasing the number of solver iterations, and reducing the length of the receding horizon. Although we prove these results in a simplified setting, the insight they represent is valuable when studying the stability of more complex real-time MPC formulations.

Keywords: Decentralized control, Control of networks
Abstract: The major contribution of this work is to accelerate transport of flexible object using a decentralized robot network. This is implemented by formulating the consensus based approach as a gradient descent, and improve the convergence rate using an accelerated Delayed Self Reinforcement (A-DSR) method, which leads to decrease in deformation during transport. The advantage of this method is that it does not require any additional network information. The result shows a significant improvement in deformation and completion time with A-DSR compare to without A-DSR case.

Keywords: Decentralized control, Control of networks
Abstract: Rapid transitions in consensus-based, multi-agent networks are necessary for quick response to external stimuli. The response speed can be improved with high-gain, however stability bounds tend to limit the maximum possible gain, and therefore, limit the maximum convergence rate to consensus during transitions [1]. The main contributions of this work are to i) extend the accelerated-gradient approach [2], [3] to more general networks with directed graph topology (whose Laplacians have real eigenvalues) using DSR, and ii) Accelerated delayed self reinforcement (A-DSR) is used to improve robustness and convergence rate of a robotic network. Experimental results are presented that show a similar 37% faster convergence with the A-DSR when compared to the case without the A-DSR.

Keywords: Autonomous systems, Estimation, Vision-based control
Abstract: This poster introduces Bayesian fusion of unlabeled camera and Radio Frequency (RF) measurements, for aerial tracking of ground targets. Sensor fusion is used to ensure reliable and robust tracking, in the case of occlusion of the camera or signal interference in the RF sensor. A small Unmanned Aircraft System(sUAS) is fitted with an RF receiver and a camera, to track a moving RF emitter on the ground. The RF sensor receives signals from the RF emitter and processes them using a non-linear, region-based, sensor model. The camera detects objects of interest(OOIs) (in this case, cars) that could potentially contain the RF emitter, using an object detection algorithm. To identify and differentiate the car with the emitter from the other cars, an Emitter Association Variable, 'L', is introduced. A probabilistic graphical model for data association and fusion helps outline dependencies between the measurements, 'L', and the target state. The fusion of multi-sensor data is performed through Bayesian inference using a Sequential Monte Carlo filter with the addition of the 'L' to perform data association in clutter. To localize and track the target, we obtain the posterior RF emitter target state probability distribution, given information from the RF sensor and OOIs described by the camera sensor, coupled with 'L'. Simulation results show the utility of the fusion filter by comparing it with the camera measurement-only filter. Monte Carlo simulations of the particle filter were run to derive unbiased performance metrics that account for the uncertainty due to random variables.

Keywords: Traffic control, Automotive control
Abstract: In this paper we demonstrate that the velocity controller, FollowerStopper, is safe and string unstable. The FollowerStopper controller is a velocity supervisory controller for a connected automated vehicle system, which was shown to dampen emergent traffic waves in the Arizona Ring Experiment in 2016. Through mathematical proof, simulation in Simulink, and hardware in the loop implementation on a real autonomous vehicle through Robot Operating System (ROS) and Gazebo, several results are achieved with respect to analysis of this controller as it was implemented for the experiments. It is found that an autonomous vehicle controlled by FollowerStopper will not crash into the vehicle in front of it, as long as the control vehicle has more powerful braking than the vehicle in front. FollowerStopper will dissipate larger traffic waves from human-driven vehicles but will amplify smaller velocity perturbations that are created within the controller. Given the maximum LiDAR range of 81 m, FollowerStopper will never command a velocity greater than 13.69 m/s.

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Abstract: We envision a future of zero crashes, zero emissions and zero congestion, and we have committed ourselves to leading the way toward this future. General Motors has been pushing the limits of transportation and technology for over 100 years. Today, we are in the midst of a transportation revolution. And we have the ambition, the talent and the technology to realize the safer, better and more sustainable world we want. As an open, inclusive company, we’re also creating an environment where everyone feels welcomed and valued for who they are. One team, where all ideas are considered and heard, where everyone can contribute to their fullest potential, with a culture based in respect, integrity, accountability and equality. Our team brings wide-ranging perspectives and experiences to solving the complex transportation challenges of today and tomorrow. At General Motors, innovation is our north star. As the first automotive company to mass-produce an affordable electric car, and the first to develop an electric starter and air bags, GM has always pushed the limits of engineering. We are General Motors. We transformed how the world moved through the last century. And we’re determined to do it again as we redefine mobility to serve our customers and shareholders and solve societal challenges.

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Abstract: The MATLAB and Simulink product families are fundamental applied math and computational tools at the world's educational institutions. Adopted by more than 5000 universities and colleges, MathWorks products accelerate the pace of learning, teaching, and research in engineering and science. MathWorks products also help prepare students for careers in industry worldwide, where the tools are widely used for data analysis, mathematical modeling, and algorithm development in collaborative research and new product development. Application areas include data analytics, mechatronics, communication systems, image processing, computational finance, and computational biology.

For additional information see https://www.mathworks.com/

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Abstract: Mitsubishi Electric Research Laboratory (MERL), located in Cambridge, MA, is the North American R&D organization for Mitsubishi Electric Corporation, a 40B global manufacturer of electrical products including elevator and escalators, HVAC systems, electrical power systems, satellites, factory automation equipment, automotive electronics and visual information systems. Controls researchers at MERL collaborate with corporate R&D laboratories, business units in Japan and academic partners around the world to develop new control algorithms and control technologies that extend the performance envelope of these systems.

For students who are interested in pursuing an exciting summer of research, please check out our internship program and learn more at facebook, google, or @MERL_news.

MERL interns work closely with top researchers, and gain valuable industry experience – an impressive 1:1 intern to researcher ratio.

Internships are expected to lead to publications in major conferences and journals.

We offer competitive compensation and relocation assistance.

Boston is a fantastic student-oriented city, home to some of the best universities in the world. The summer season is especially lively as MERL and Boston are teeming with interns and visitors from all over the world.

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Abstract: Quanser is the world leader in mechatronics, robotics, and control platforms optimized for the academic setting. Our leadership in producing innovative lab solutions makes us a trusted partner with academic institutions to help strengthen their reputation with transformative research and teaching labs. The Quanser approach of innovation, collaboration and education has produced a number of notable technology firsts that pioneered many critical contemporary trends, including efficient validation platform for control research, and high-performance real-time control on common microcomputers.

For additional information see https://www.quanser.com/

Keywords:
Abstract: Quanser is the world leader in mechatronics, robotics, and control platforms optimized for the academic setting. Our leadership in producing innovative lab solutions makes us a trusted partner with academic institutions to help strengthen their reputation with transformative research and teaching labs. The Quanser approach of innovation, collaboration and education has produced a number of notable technology firsts that pioneered many critical contemporary trends, including efficient validation platform for control research, and high-performance real-time control on common microcomputers.

For additional information see https://www.quanser.com/

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Abstract: Silver Sponsor: Cancelled

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Abstract: dSPACE offers universities and research institutions flexible systems that provide all the options necessary for the model-based development of mechatronic controllers in an academic environment. From architecture-based system design and block-diagram-based function prototyping to automatic production code generation and hardware-in-the-loop (HIL) tests, dSPACE products are successfully being used in the classroom and in research projects at internationally renowned universities. To actively support high-end research at universities and the high-quality education of young talents, dSPACE offers its hardware and software products in special kits for universities at a very attractive price. Learn more at dspaceinc.com / offers for universities.

For additional information see https://www.dspace.com/en/inc/home.cfm

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Abstract: At Springer Nature, our aim is to advance discovery. For over 175 years, we’ve dedicated ourselves to the academic community, creating value across the publishing process. We deliver an unmatched breadth and depth of quality information which spans top research publications (Nature), outstanding scientific journalism (Scientific American), highly specialized subject-specific journals across all the sciences and humanities, professional publications, databases, and the most comprehensive portfolio of academic books. We use our position and our influence to champion the issues that matter most to the research community – standing up for science, taking a leading role in open research, and being powerful advocates for the highest quality and ethical standards in research.

For additional information see https://www.springer.com/gp/authors-editors

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Abstract: Processes (ISSN 2227-9717) provides an advanced forum for process/systems related research in chemistry, biology, materials and allied engineering fields. The journal publishes regular research papers, communications, letters, short notes and reviews. Our aim is to encourage researchers to publish their experimental, theoretical and computational results in as much detail as necessary. There is no restriction on paper length or number of figures and tables.

Experimental, theoretical and computational research on process development and engineering

Chemical and biochemical reaction processes

Mass transfer, separation and purification processes

Mixing, fluid processing and heat transfer systems

Integrated process design and scaleup

Process modeling, simulation, optimization and control

For additional information see https://www.mdpi.com/journal/processes

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Abstract: Founded in 1919, Halliburton is one of the world's largest providers of products and services to the energy industry. With 60,000 employees, representing 140 nationalities in more than 80 countries, the company helps its customers maximize value throughout the lifecycle of the reservoir – from locating hydrocarbons and managing geological data, to drilling and formation evaluation, well construction and completion, and optimizing production throughout the life of the asset. Halliburton’s technology organization provides cutting edge research and innovative solutions to maximize asset value for our customers.

For additional information see https://www.halliburton.com/en-US/default.html  

Keywords: Nonlinear output feedback, Robotics, Autonomous robots
Abstract: Autonomous underwater gliders have become valuable, energy-efficient tools for a myriad of applications including ocean exploration, fish tracking, and environmental sampling. Many applications, such as, exploring a large area of underwater ruins or navigating through a coral reef, would benefit from fine trajectory tracking. However, trajectory tracking control of underwater gliders is particularly challenging due to their under-actuated, nonlinear dynamics. Taking gliding robotic fish as an example, in this work we propose a backstepping-based controller for the gliding motion to track a desired reference for the pitch angle and position in the 3D space. In particular, the challenge of under-actuation is addressed by exploiting the coupled dynamics and introducing a new modified error term that combines pitch and horizontal position tracking errors. The effectiveness of the proposed control scheme is demonstrated via simulation and its advantages are shown via comparison with a PID controller.

Keywords: Biological systems, Biomolecular systems, Stochastic systems
Abstract: Macromolecular complexes have important roles in cellular functions. These complexes are formed via multimerization of either a single component (homomers) or multiple components (heteromers). Often, production and degradation of the components as well as their assembly to form the complex are stochastic. How fluctuations (or noise) in abundances of individual components affect fluctuations in abundance of the complex remains little understood. Here we consider two simple models of complex formation, one for homomer and another for heteromer of two components, and analyze effect of important model parameters on the noise in complex level. In particular, we study the effect of (i) sensitivity of the complex formation rate with respect to components' abundance, and (ii) relative stability of the complex as compared with that of its components. Using an approximate moment analysis, we find that for a given steady state level, there is an optimal sensitivity that minimizes noise (quantified by fano-factor; variance/mean) in the complex level. Furthermore, the noise becomes smaller if the complex is less stable than its components. Finally, for the heteromer case, our findings show that noise is enhanced if the complex is comparatively more sensitive to one component. We briefly discuss implications of our result for general complex formation processes.

Keywords: Biological systems, Networked control systems
Abstract: We study the influence of heterogeneous mobility patterns in a population on the SIS epidemic model. In particular, we consider a patchy environment in which each patch comprises individuals belonging the different classes, e.g., individuals in different socio-economic strata. We model the mobility of individuals of each class across different patches through an associated Continuous Time Markov Chain (CTMC). The topology of these multiple CTMCs constitute the multi-layer network of mobility. At each time, individuals move in the multi-layer network of spatially-distributed patches according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS epidemic model. We derive a deterministic continuum limit model describing these mobility-epidemic interactions. We establish the existence of a Disease-Free Equilibrium (DFE) and an Endemic Equilibrium (EE) under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We derive simple sufficient conditions that highlight the influence of the multi-layer network on the stability of DFE. Finally, we numerically illustrate that the derived model provides a good approximation to the stochastic model with a finite population and also demonstrate the influence of the multi-layer network structure on the transient performance.

Keywords: Biological systems, Learning, Computational methods
Abstract: In this paper, we consider the problem of learninga predictive model for population cell growth dynamics as afunction of the media conditions. We first introduce a genericdata-driven framework for training operator-theoretic modelsto predict cell growth rate. We then introduce the experimentaldesign and data generated in this study, namely growth curvesofPseudomonas putidaas a function of casein and glucoseconcentrations. We use a data driven approach for modelidentification, specifically the nonlinear autoregressive (NAR)model to represent the dynamics. We show theoretically thatHankel DMD can be used to obtain a solution of the NARmodel. We show that it identifies a constrained NAR model andto obtain a more general solution, we define a causal state spacesystem using 1-step, 2-step,...,τ-step predictors of the NARmodel and identify a Koopman operator for this model usingextended dynamic mode decomposition. The hybrid schemewe call causal-jump dynamic mode decomposition, which weillustrate on a growth profile or fitness prediction challenge asa function of different input growth conditions. We show thatour model is able to recapitulate training growth curve datawith 96.6% accuracy and predict test growth curve data with 91% accuracy.

Keywords: Machine learning, Aerospace, Computational methods
Abstract: We propose a data-driven supervisory method to determine actions, in real-time, for systems with a binary success/failure outcome. This approach consists of two steps. First, a high-fidelity system model is used offline to train a classifier, which acts as a quick-to-evaluate approximation of the system. Then, the classifier is used online to select an action based on the scenario encountered. The method also returns an approximate probability of success which can then be used to inform follow-on decisions. We apply this method to problems where an interceptor missile engages a threat headed towards an asset. The interceptor's supervisory actions may include selecting parameters in the guidance and control laws, setting tunable initial conditions, and determining other details about how the interceptor will engage the threat. Specifically, the proposed method is demonstrated using the case study of a planar engagement between an interceptor and a threat, with the interceptor launch angle and autopilot crossover frequency as actionable parameters. For this case study, the proposed method outperforms an alternative baseline action.

Keywords: Lyapunov methods, Stability of nonlinear systems, Biological systems
Abstract: The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuous-time nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finite-time Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.

Keywords: Stability of linear systems, Mechanical systems/robotics, Biomedical
Abstract: In this paper we develop a method to find the passivating parameter space for transfer function matrices with symbolic parameters. The method is subsequently applied to the mechanical-rotary variable impedance actuator (MeRIA), which belongs to the class of variable impedance actuators. The impedance control framework of MeRIA consists of cascaded control-loops guaranteeing a passive (positive real) load transfer function. We therefore focus on finding a robust impedance controller space by employing recursive parameter space testing with respect to the corresponding transfer function. Computed parameter spaces for the corresponding port function and simulations underline the performance of the algorithm.

Keywords: Aerospace, Variable-structure/sliding-mode control, Lyapunov methods
Abstract: This paper proposes several nonlinear impact time control guidance strategies against maneuvering targets, based on Lyapunov and sliding mode control theories. These strategies correspond to different quanta of information available to the interceptor, about the target’s maneuver. The use of deviated pursuit paradigm in the guidance design enables the use of exact time-to-go expression for intercepting moving but nonmaneuvering targets, without any small-angle approximations in heading angles. In deriving the guidance commands, the time-to-go is estimated by assuming a non-maneuvering target at each instant. Due to the inherent robustness of the proposed strategies, maneuvering targets can also be successfully intercepted at desired impact times, despite this assumption. Numerical simulations are presented to validate the efficacy of proposed guidance strategies for different initial engagement geometries and levels/types of target maneuvers.

Keywords: Aerospace, Control applications, Variable-structure/sliding-mode control
Abstract: This work addresses the problem of designing an impact time constrained guidance strategy for three-dimensional engagements, without decoupling the engagement dynamics in two mutually orthogonal planes. The guidance command is derived while considering nonlinear engagement dynamics, and with a time-to-go prediction that accounts for the interceptor's heading error. Power rate reaching law is used while designing sliding mode guidance strategy, since this law offers inherent robustness, smooth control and finite-time convergence to the sliding manifold. Further, the interceptor lateral acceleration components are obtained using a control allocation technique, that minimizes the instantaneous lateral acceleration, which aids in minimizing the total drag during interceptor's flight. Conditions for the interceptor to reach the collision course are derived and analyses are presented. Finally, simulations are provided to demonstrate the efficacy of the proposed guidance scheme.

Keywords: Aerospace, Flight control, Lyapunov methods
Abstract: A non-singular hierarchical controller using Integral Barrier Lyapunov Function (iBLF) is proposed in this paper for attitude tracking of a pitch-constrained quad- rotorcraft system. The integral function mixes the original pitch constraint with pitch error and removes the use of purely error based barrier Lyapunov function (BLF) with transformed error constraint. The design is a nonlinear hierarchical control where backstepping is used to develop an iBLF based attitude controller without any initial condition constraint on pitch error. A rigorous stability analysis proves that the tracking error of the overall closed-loop system is asymptotically converging and the signals are bounded in the cascaded control structure. Simulation results illustrate the efficacy of the proposed controller in contrast to authors’ earlier work on BLF-based tracking control of quadrotors.

Keywords: Aerospace, Cooperative control, Control applications
Abstract: This work focuses on achieving cooperative simultaneous interception against moving targets using the concepts of deviated pursuit guidance strategy. Unlike most existing salvo guidance strategies which use estimates of time-to-go, based on proportional navigation guidance, the present strategy uses exact expression for time-to-go to ensure simultaneous interception. The guidance command is derived considering nonlinear engagement kinematics. Weighted consensus in time-to-go over a pseudo-undirected graph is used to intercept a moving target cooperatively. It has been shown that through a judicious choice of these weights, the achievable set of interception times expands. Simulations are provided to vindicate the effectiveness of the proposed strategy.

Keywords: Aerospace, Control applications
Abstract: In this paper, we propose a guidance strategy that enables the interceptor to control the time of interception against stationary targets, while also respecting the field-of-view (FOV) constraints of the seeker. Such a guidance strategy always keeps the target within its field-of-view, using its seeker. Guidance command is derived using a barrier Lyapunov function, and an expression for lead angle of interceptor is obtained analytically, which further facilitates the computation and control of the impact time. The guidance comprises two stages, one of which is deviated pure pursuit, while during the latter stage, the deviation angle or lead angle decreases to zero thereby ensuring zero terminal lateral acceleration. Simulations across different engagement scenarios and tuning parameters vindicate the effectiveness of the proposed strategy.

Keywords: Aerospace, Flight control, Robust control
Abstract: In this paper, a robust disturbance observer based controller is presented for glideslope regulation of aircraft in turbulence and with uncertainties in the aerodynamic model. A significant challenge in designing disturbance observers for such system arises from the nonlinear disturbance to state coupling. This state dependent coupling limits the application of disturbance observer based control without resorting to system approximation. Instead of model simplification, this work explicitly accounts for the disturbance to state coupling and leverages the polynomial nature of the system dynamics to design an exponentially convergent disturbance observer. The underlying principle behind synthesis of stable disturbance observers is based on sum-of-squares (SOS) optimization and in particular, polynomial matrix inequalities (PMI). Through exponential convergence of disturbance estimate, the wind components and aerodynamic uncertainties can be rapidly estimated and then compensated by deploying control surfaces. The efficacy of the proposed approach is demonstrated using the disturbance observer with a nominal dynamic inversion controller for glideslope regulation of an aircraft based on the F/A-18 High Angle of Attack (HARV) model.

Keywords: Constrained control, Lyapunov methods, Flight control
Abstract: Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n leq 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.

Keywords: Control applications, Aerospace, Stability of hybrid systems
Abstract: In this paper, we present the design of trajectory tracking controllers for multirotor aerial vehicles that have the ability to operate both with and without thrust reversal. We follow a hierarchical control approach, in the sense that we start by designing a common saturated controller for the position subsystem and use it to provide a reference to an attitude tracking controller. The controllers for each operating mode are able to achieve global asymptotic stability as well as semiglobal exponential stabilization of the zero tracking error set. We demonstrate the capabilities of the proposed controllers in a simulation that performs a throw-and-catch maneuver.

Keywords: Flight control, Robotics, PID control
Abstract: In this paper, we present an autonomous flight controller for a quadcopter with thrust vectoring capabilities. This UAV falls in the category of multirotors with tilt-motion enabled rotors. Since the vehicle considered is over-actuated in nature, the dynamics and control allocation have to be analysed carefully. Moreover, the possibility of hovering at large attitude maneuvers of this novel vehicle requires singularity-free attitude control. Hence, quaternion state feedback is utilized to compute the control commands for the UAV motors while avoiding the gimbal lock condition experienced by Euler angle based controllers. The quaternion implementation also reduces the overall complexity of state estimation due to absence of trigonometric parameters. The quadcopter dynamic model and state space is utilized to design the attitude controller and control allocation for the UAV. The control allocation, in particular, is derived by linearizing the system about hover condition. This mathematical method renders the control allocation more accurate than existing approaches. Lyapunov stability analysis of the attitude controller is shown to prove global stability. The quaternion feedback attitude controller is commanded by an outer position controller loop which generates rotor-tilt and desired quaternions commands for the system. The performance of the UAV is evaluated by numerical simulations for tracking attitude step commands and for following a waypoint navigation mission.

Keywords: Flight control, Stability of nonlinear systems, Lyapunov methods
Abstract: This paper investigates a dual loop quaternion-based nonlinear control scheme for a quadrotor: the inner feedback loop controls the attitude of the quadrotor while the outer control loop aims to control the linear velocity, and/or position, of the quadrotor. The paper shows that global exponential stability of a quadrotor can be achieved with the proposed control scheme. The presented controller includes feedback and feedforward compensation of the nonlinear dynamics of the quadrotor and gyroscopic torques to guarantee global stability of the attitude controller. The outer velocity control loop uses a PI feedback structure, where the proportional action is primarily used to control linear velocity, and the integral action can either be used for linear position and/or eliminating velocity steady-state error. The inner attitude control includes a PD feedback loop, where the proportional action is in terms of the vector part of the quaternion and the derivative action is in terms of the aircraft angular velocity. The proposed controller has been both simulated and tested experimentally with a commercial quadrotor.

Keywords: LMIs, Adaptive control, Aerospace
Abstract: Occupation measures and linear matrix inequality (LMI) relaxations (called the moment sums of squares or Lasserre hierarchy) are state-of-the-art methods for verification and validation (VV) in aerospace. In this document, we extend these results to a full F-16 closed-loop nonlinear dutch roll polynomial model complete with model reference adaptive control (MRAC). This is done through a new technique of approximating the reference trajectory by exploiting sparse ordinary differential equations (ODEs) with parsimony. The VV problem is then solved directly using moment LMI relaxations and off-the-shelf-software. The main results are then compared to their numerical counterparts obtained using traditional Monte-Carlo simulations.

Keywords: Robotics, Energy systems, Control applications
Abstract: In this paper, the problem of take-off and landing of an airborne wind energy system is addressed. The solution explored is to equipe the airborne wing of the system with a multicopter drone in order to perform the take-off and land maneuvers, even in the absence of wind. The proposed model with the proposed control strategy is implemented and tested in a numerical environment. The results show efficiency of the proposed control law and its robustness with respect to modelling errors and wind gusts.

Keywords: Sampled-data control, Stability of hybrid systems, Aerospace
Abstract: This paper presents an event-triggered controller that solves the problem of trajectory tracking for an aerial vehicle with a thrust actuation in a single body-fixed direction and full angular velocity actuation. Under the framework of hybrid dynamical systems, we first design a globally stabilizing hybrid control law and then derive an appropriate event-triggering mechanism for sampling of actuation signals. We prove that bounded reference trajectories are rendered globally asymptotically stable for the closed-loop system. To enable practical implementation of the proposed event-triggered controller on digital platforms, we provide a modified event-triggering mechanism that achieves practical stability while avoiding Zeno solutions. The results are illustrated by numerical simulations and further verified by experiments.

Keywords: Variable-structure/sliding-mode control, Fault tolerant systems, Flight control
Abstract: This paper presents a novel concept for active fault-tolerant control (FTC) of dual system hybrid unmanned aerial vehicles (UAVs) based on analytical redundancy to increase the operational safety in the face of primary actuator faults. The proposed scheme exploits the inherent over-actuation property of hybrid UAVs when in addition to the aerodynamic surfaces four lift rotors are used to control the aircraft during long range fixed-wing flight mode. Fault tolerance is achieved by utilizing an integral sliding mode based model reference control law combined with control allocation techniques to reallocate control signals among healthy effectors in the face of actuator faults and maintain nominal closed-loop performance. After introducing the modelling procedure of the UAV, including the identification of aerodynamical cross-couplings between lift rotors and airframe dynamics, Hardware-in-the-loop (HIL) simulation results are presented to demonstrate the efficiency of the proposed scheme in a realistic hardware setup.

Keywords: Machine learning, Adaptive control, Nonlinear systems identification
Abstract: Control schemes that learn using measurement data collected online are increasingly promising for the control of complex and uncertain systems. However, in most approaches of this kind, learning is often viewed as a side effect that passively improves control performance, e.g., by updating a model of the system dynamics. Moreover, determining how improvements in control performance due to learning can be actively exploited in the control synthesis is still an open research question. In this paper, we present AntLer, a design algorithm for learning-based control laws that anticipates learning, i.e., that takes the impact of future learning in uncertain dynamic settings explicitly into account. AntLer expresses system uncertainty using a non-parametric probabilistic model. Given a cost function that measures control performance, AntLer chooses the control parameters such that the expected cost of the closed-loop system is minimized approximately. We show that the solution computed by AntLer approximates an optimal solution arbitrarily accurately. Furthermore, we apply AntLer to a nonlinear system, and compare the results to the case where learning is not anticipated.

Keywords: Autonomous systems, Learning, Robotics
Abstract: This paper presents an online kinodynamic motion planning scheme for dynamically evolving environments, by employing Q-learning. The methodology addresses the finite horizon continuous-time optimal control problem with completely unknown system dynamics. An actor-critic structure is employed along with a buffer of previous experiences, to approximate the optimal policy and alleviate the learning signal requirements. The methodology is equipped with a terminal state evaluation to achieve fast navigation. The path planning is assigned to the RRTX. An obstacle augmentation and a local replanning strategy are responsible for collision-free navigation. Rigorous Lyapunov-based proofs are provided to guarantee closed-loop stability of the equilibrium point. We evaluate the efficacy of the methodology with simulations.

Keywords: Building and facility automation, Fault detection, Machine learning
Abstract: Faults in HVAC systems degrade thermal comfort and energy efficiency in buildings and have received significant attention from the research community, with data driven methods gaining in popularity. Yet the lack of labeled data, such as normal versus faulty operational status, has slowed the application of machine learning to HVAC systems. In addition, for any particular building, there may be an insufficient number of observed faults over a reasonable amount of time for training. To overcome these challenges, we present a transfer methodology for a novel Bayesian classifier designed to distinguish between normal operations and faulty operations. The key is to train this classifier on a building with a large amount of sensor and fault data (for example, via simulation or standard test data) then transfer the classifier to a new building using a small amount of normal operations data from the new building. We demonstrate a proof-of-concept for transferring a classifier between architecturally similar buildings in different climates and show few samples are required to maintain classification precision and recall.

Keywords: Computational methods, Machine learning, Learning
Abstract: Certifying or enforcing performance and stability guarantees for controllers based on deep learning is challenging. This paper aims to provide conditions to verify nominal stability of a system controlled by a deep learning based controller. We focus on a special form of neural network as the controller, called non-autonomous deep networks. The training is performed using data from a baseline controller, which does not need to be known mathematically, e.g. it may be a human operating the system. We provide an emph{explicit} formula for computation of the number of hidden layers such that the resulting learning-based closed-loop system is stable. We furthermore outline how this condition can be integrated in the learning. The results are illustrated by a simulation study considering control of a continuously stirred tank reactor.

Keywords: Formal verification/synthesis, Learning, Modeling
Abstract: We propose a novel framework to differentiate between vehicle trajectories originating from human and non-human drivers by constructing a data-driven boundary using parametric signal temporal logic. Such a construction allows us to evaluate the trajectories, detect rare events, and reduce the uncertainty of driver behaviors when it assumes the form of a disturbance in control synthesis and evaluation problems. We train a classifier that separates admissible (i.e. human) examples - which arise from real-world demonstrations - and inadmissible (i.e. non-human) examples that are generated by falsifying specifications synthesized from the same real-world driving data. Proceeding in this fashion allows for finding a reasonable boundary of human behavior exhibited in real-world driving records. The framework is demonstrated using a case study involving a human-driven vehicle approaching a signalized intersection.

Keywords: Formal verification/synthesis, Learning, Cooperative control
Abstract: This paper investigates the problem of deploying a multi-robot team to satisfy a syntactically co-safe Truncated Linear Temporal Logic (scTLTL) task specification via multi-agent Reinforcement Learning (MARL) technique. Due to the heterogeneous agents considered here, typical approaches cannot avoid the task assignment problem, which is inherently difficult and can sacrifice optimality (e.g., shortest path) through manual manipulation. MARL is exploited here to eliminate the task assignment as part of the learning process. Moreover, MARL usually requires some direct or indirect coordination among agents to promote convergence and a tracker is needed to track the process of satisfying the scTLTL given its temporal nature. We use the Finite State Automaton (FSA) to address these two issues. An FSA augmented Markov Decision Process (MDP) is constructed for each agent, which share the FSA state carrying the global information. Moreover, a metric called robustness degree is employed to replace the Boolean semantics and quantify the reward of gradually satisfying the scTLTL. Consequently, a language guided semi-decentralized Q-learning algorithm is proposed to maximize the return over the FSA augmented MDP. Simulation results demonstrate the effectiveness of the semi-decentralized multi-agent Q-learning while the complexity is significantly reduced.

Keywords: Learning, Robotics, Nonlinear systems identification
Abstract: This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear state- space model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.

Keywords: Learning, Optimal control, Robust control
Abstract: We present a robust design for reinforcement learning (RL) based optimal control of continuous-time linear time-invariant singularly perturbed (SP) dynamic systems in the presence of dynamic uncertainties. We consider the dynamic model of both the plant and the uncertainty to be unknown. Assuming that the uncertainty satisfies an input-to-state stability (ISS) condition, we propose a variant of the adaptive dynamic programming (ADP) method that learns a sub-optimal controller using measurements of only the slow states of the plant. The resulting RL controller is, therefore, significantly reduced-dimensional, and enjoys reduced learning time. We illustrate our design with simulations of a SP system and of a clustered multi-agent consensus network.

Keywords: Learning, Stochastic optimal control, Markov processes
Abstract: This paper concerns approximate solutions to the optimal stopping problem for a geometrically ergodic Markov chain on a continuous state space. The starting point is the Galerkin relaxation of the dynamic programming equations that was introduced by Tsitsikilis and Van Roy in the 1990s, which motivated their Q-learning algorithm for optimal stopping. It is known that the convergence rate of Q-learning is in many cases very slow. The reason for slow convergence is explained here, along with a variant of ``Zap-Q-learning" algorithm, designed to achieve the optimal rate of convergence. The main contribution is to establish consistency of Zap-Q-learning algorithm for a linear function approximation setting. The theoretical results are illustrated using an example from finance.

Keywords: Learning, Decentralized control, Stochastic optimal control
Abstract: We consider a multi-agent Linear-Quadratic (LQ) reinforcement learning problem consisting of three systems, an unknown system and two known systems. In this problem, there are three agents -- the actions of agent 1 can affect the unknown system as well as the two known systems while the actions of agents 2 and 3 can only affect their respective co-located known systems. Further, the unknown system's state can affect the known systems' state evolution. In this paper, we are interested in minimizing the infinite-horizon average cost. We propose a Thompson Sampling (TS)-based multi-agent learning algorithm where each agent learns the unknown system's dynamics independently. Our result indicates that the expected regret of our algorithm is upper bounded by tilde{O}(sqrt{T}) under certain assumptions, where tilde{O}(cdot) hides constants and logarithmic factors. Numerical simulations are provided to illustrate the performance of our proposed algorithm.

Keywords: Learning, Robust control
Abstract: Reinforcement learning (RL) and other AI methods are exciting approaches to data-driven control design, but RL's emphasis on maximizing expected performance contrasts with robust control theory (RCT), which puts central emphasis on the impact of model uncertainty and worst case scenarios. This paper argues that these approaches are potentially complementary, roughly analogous to that of a driver and an engineer in, say, formula one racing. Each is indispensable but with radically different roles. If RL takes the driver seat in safety critical applications, RCT may still play a role in plant design, and also in diagnosing and mitigating the effects of performance degradation due to changes or failures in component or environments. While much RCT research emphasizes synthesis of controllers, as does RL, in practice RCT's impact has perhaps already been greater in using hard limits and tradeoffs on robust performance to provide insight into plant design, interpreted broadly as including sensor, actuator, communications, and computer selection and placement in addition to core plant dynamics. More automation may ultimately require more rigor and theory, not less, if our systems are going to be both more efficient and robust. Here we use the simplest possible toy model to illustrate how RCT can potentially augment RL in finding mechanistic explanations when control is not merely hard, but impossible, and issues in making them more compatibly data-driven. Despite the simplicity, questions abound. We also discuss the relevance of these ideas to more realistic challenges.

Keywords: Learning, Kalman filtering, Robust control
Abstract: In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular, we consider a control problem where the state of the system is estimated from measurements extracted from a high-dimensional sensor, such as a camera. We assume that a map between the camera’s readings and the state of the system has been learned from a set of training data of finite size, from which the noise statistics are also estimated. We show that algorithms that maximize the estimation accuracy (as measured by the mean squared error) using the learned perception map tend to perform poorly in practice, where the sensor’s statistics often differ from the learned ones. Conversely, increasing the variability and size of the training data leads to robust performance, however limiting the estimation accuracy, and thus the control performance, in nominal conditions. Ultimately, our work proves the existence and the implications of a fundamental trade-off between accuracy and robustness in perception-based control, which, more generally, affects a large class of machine learning and data-driven algorithms.

Keywords: Machine learning, Stochastic systems, Statistical learning
Abstract: Due to the growing amount of data and processing capabilities, machine learning techniques are increasingly applied for the identification of dynamical systems. Especially probabilistic methods are promising for learning models, which in turn are frequently used for simulations. Although confidence regions around predicted trajectories are of crucial importance in many control approaches, few rigorous mathematical analysis methods are available for learned probabilistic models. Therefore, we propose a novel method to estimate confidence regions for predicted trajectories, and assign them a confidence level based on Monte Carlo random trajectory sampling. Since the confidence level has a strongly nonlinear dependence on the number of Monte Carlo samples, we derive a lower bound on the number of samples that ensures a desired minimum confidence level. The efficiency and flexibility of the proposed method is demonstrated in simulations of a Bayesian hidden Markov model and a Gaussian process state space model.

Keywords: Agents-based systems, Cooperative control, Learning
Abstract: This paper considers a distributed reinforcement learning problem in the presence of Byzantine agents. The system consists of a central coordinating authority called ``master agent'' and multiple computational entities called ``worker agents''. The master agent is assumed to be reliable, while, a small fraction of the workers can be Byzantine (malicious) adversaries. The workers are interested in cooperatively maximize a convex combination of the honest (non-malicious) worker agents' long-term returns through communication between the master agent and worker agents. A distributed actor-critic algorithm is studied which makes use of entry-wise trimmed mean. The algorithm's communication-efficiency is improved by allowing the worker agents to send only a scalar-valued variable to the master agent, instead of the entire parameter vector, at each iteration. The improved algorithm involves computing a trimmed mean over only the received scalar-valued variable. It is shown that both algorithms converge almost surely.

Keywords: Machine learning, Robust control, Optimization algorithms
Abstract: Adoption of machine learning (ML)-enabled cyber-physical systems (CPS) are becoming prevalent in various sectors of modern society such as transportation, industrial, and power grids. Recent studies in deep reinforcement learning (DRL) have demonstrated its benefits in a large variety of data-driven decisions and control applications. As reliance on ML-enabled systems grows, it is imperative to study the performance of these systems under malicious state and actuator attacks. Traditional control systems employ resilient/fault-tolerant controllers that counter these attacks by correcting the system via error observations. However, in some applications, a resilient controller may not be sufficient to avoid a catastrophic failure. Ideally, a robust approach is more useful in these scenarios where a system is inherently robust (by design) to adversarial attacks. While robust control has a long history of development, robust ML is an emerging research area that has already demonstrated its relevance and urgency. However, the majority of robust ML research has focused on perception tasks and not on decision and control tasks, although the ML (specifically RL) models used for control applications are equally vulnerable to adversarial attacks. In this paper, we show that a well-performing DRL agent that is initially susceptible to action space perturbations (e.g. actuator attacks) can be robustified against similar perturbations through adversarial training.

Keywords: Machine learning, Autonomous systems, Pattern recognition and classification
Abstract: Understanding multi-vehicle interactive behaviors with temporal sequential observations is crucial for autonomous vehicles to make appropriate decisions in an uncertain traffic environment. On-demand similarity measures are significant for autonomous vehicles to deal with massive interactive driving behaviors by clustering and classifying diverse scenarios. This paper proposes a general approach for measuring spatiotemporal similarity of interactive behaviors using a multivariate matrix profile technique. The key attractive features of the approach are its superior space and time complexity, real-time online computing for streaming traffic data, and possible capability of leveraging hardware for parallel computation. The proposed approach is validated through automatically discovering similar interactive driving behaviors at intersections from sequential data.

Keywords: Machine learning, Hierarchical control, Intelligent systems
Abstract: Poor sample efficiency is a major limitation of deep reinforcement learning in many domains. This work presents an attention-based method to project neural network inputs into an efficient representation space that is invariant under changes to input ordering. We show that our proposed representation results in an input space that is a factor of m! smaller for inputs of m objects. We also show that our method is able to represent inputs over variable numbers of objects. Our experiments demonstrate improvements in sample efficiency for policy gradient methods on a variety of tasks. We show that our representation allows us to solve problems that are otherwise intractable when using naive approaches.

Keywords: Machine learning, Optimization
Abstract: This paper considers the problem of multi-agent distributed optimization. In this problem, there are multiple agents in the system, and each agent only knows its local cost function. The objective for the agents is to collectively compute a common minimum of the aggregate of all their local cost functions. In principle, this problem is solvable using a distributed variant of the traditional gradient-descent method, which is an iterative method. However, the speed of convergence of the traditional gradient-descent method is highly influenced by the conditioning of the optimization problem being solved. Specifically, the method requires a large number of iterations to converge to a solution if the optimization problem is ill-conditioned.

In this paper, we propose an iterative pre-conditioning approach that can significantly attenuate the influence of the problem's conditioning on the convergence-speed of the gradient-descent method. The proposed pre-conditioning approach can be easily implemented in distributed systems and has minimal computation and communication overhead. For now, we only consider a specific distributed optimization problem wherein the individual local cost functions of the agents are quadratic. Besides the theoretical guarantees, the improved convergence speed of our approach is demonstrated through experiments on a real data-set.

Keywords: Machine learning, Learning, Optimization algorithms
Abstract: In this paper, we propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate O(1/T) or O(frac{1}{log T}) under some mild assumptions. To handle the high dimensional nonlinear dynamical systems, we present the first-ever distributed Koopman operator learning algorithm. We show that the distributed Koopman operator learning has the same convergence properties as a centralized Koopman operator learning problem, in the absence of optimal tracker, so long as the basis functions satisfy a set of state-based decomposition conditions. Experiments are provided to complement our theoretical results.

Keywords: Network analysis and control, Identification for control, Learning
Abstract: In this paper we study the problem of learning minimum-energy controls for linear systems from heterogeneous data. Specifically, we consider datasets comprising input, initial and final state measurements collected using experiments with different time horizons and arbitrary initial conditions. In this setting, we first establish a general representation of input and sampled state trajectories of the system based on the available data. Then, we leverage this data-based representation to derive closed-form data-driven expressions of minimum-energy controls for a wide range of control horizons. Further, we characterize the minimum number of data required to reconstruct the minimum-energy inputs, and discuss the numerical properties of our expressions. Finally, we investigate the effect of noise on our data-driven formulas, and, in the case of noise with known second-order statistics, we provide corrected expressions that converge asymptotically to the true optimal control inputs.

Keywords: Statistical learning, Machine learning, Stochastic optimal control
Abstract: Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with fewer data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty.

Keywords: Switched systems, Optimal control, Learning
Abstract: This paper studies Q-learning for quadratic regulation problem of switched linear systems. Inspired by the analytical results from classical model-based optimal control, a structured Q-learning algorithm is developed. The proposed algorithm consists of a carefully designed parametric approximator that respects the analytical structure of the exact Q-function and an associated parameter training algorithm. Based on a geometric insight gained from the analysis of the exact Q-function structure, training of approximation parameters is formulated as a matrix identification problem. Probabilistic guarantee on successful identification of all matrices using the proposed algorithm is rigorously proved under moderate conditions. Several numerical studies are conducted to demonstrate the effectiveness of the overall proposed Q-learning algorithm.

Keywords: Nonlinear output feedback, Robotics, Autonomous robots
Abstract: Autonomous underwater gliders have become valuable, energy-efficient tools for a myriad of applications including ocean exploration, fish tracking, and environmental sampling. Many applications, such as, exploring a large area of underwater ruins or navigating through a coral reef, would benefit from fine trajectory tracking. However, trajectory tracking control of underwater gliders is particularly challenging due to their under-actuated, nonlinear dynamics. Taking gliding robotic fish as an example, in this work we propose a backstepping-based controller for the gliding motion to track a desired reference for the pitch angle and position in the 3D space. In particular, the challenge of under-actuation is addressed by exploiting the coupled dynamics and introducing a new modified error term that combines pitch and horizontal position tracking errors. The effectiveness of the proposed control scheme is demonstrated via simulation and its advantages are shown via comparison with a PID controller.

Keywords: Biological systems, Biomolecular systems, Stochastic systems
Abstract: Macromolecular complexes have important roles in cellular functions. These complexes are formed via multimerization of either a single component (homomers) or multiple components (heteromers). Often, production and degradation of the components as well as their assembly to form the complex are stochastic. How fluctuations (or noise) in abundances of individual components affect fluctuations in abundance of the complex remains little understood. Here we consider two simple models of complex formation, one for homomer and another for heteromer of two components, and analyze effect of important model parameters on the noise in complex level. In particular, we study the effect of (i) sensitivity of the complex formation rate with respect to components' abundance, and (ii) relative stability of the complex as compared with that of its components. Using an approximate moment analysis, we find that for a given steady state level, there is an optimal sensitivity that minimizes noise (quantified by fano-factor; variance/mean) in the complex level. Furthermore, the noise becomes smaller if the complex is less stable than its components. Finally, for the heteromer case, our findings show that noise is enhanced if the complex is comparatively more sensitive to one component. We briefly discuss implications of our result for general complex formation processes.

Keywords: Biological systems, Networked control systems
Abstract: We study the influence of heterogeneous mobility patterns in a population on the SIS epidemic model. In particular, we consider a patchy environment in which each patch comprises individuals belonging the different classes, e.g., individuals in different socio-economic strata. We model the mobility of individuals of each class across different patches through an associated Continuous Time Markov Chain (CTMC). The topology of these multiple CTMCs constitute the multi-layer network of mobility. At each time, individuals move in the multi-layer network of spatially-distributed patches according to their CTMC and subsequently interact with the local individuals in the patch according to an SIS epidemic model. We derive a deterministic continuum limit model describing these mobility-epidemic interactions. We establish the existence of a Disease-Free Equilibrium (DFE) and an Endemic Equilibrium (EE) under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We derive simple sufficient conditions that highlight the influence of the multi-layer network on the stability of DFE. Finally, we numerically illustrate that the derived model provides a good approximation to the stochastic model with a finite population and also demonstrate the influence of the multi-layer network structure on the transient performance.

Keywords: Biological systems, Learning, Computational methods
Abstract: In this paper, we consider the problem of learninga predictive model for population cell growth dynamics as afunction of the media conditions. We first introduce a genericdata-driven framework for training operator-theoretic modelsto predict cell growth rate. We then introduce the experimentaldesign and data generated in this study, namely growth curvesofPseudomonas putidaas a function of casein and glucoseconcentrations. We use a data driven approach for modelidentification, specifically the nonlinear autoregressive (NAR)model to represent the dynamics. We show theoretically thatHankel DMD can be used to obtain a solution of the NARmodel. We show that it identifies a constrained NAR model andto obtain a more general solution, we define a causal state spacesystem using 1-step, 2-step,...,τ-step predictors of the NARmodel and identify a Koopman operator for this model usingextended dynamic mode decomposition. The hybrid schemewe call causal-jump dynamic mode decomposition, which weillustrate on a growth profile or fitness prediction challenge asa function of different input growth conditions. We show thatour model is able to recapitulate training growth curve datawith 96.6% accuracy and predict test growth curve data with 91% accuracy.

Keywords: Machine learning, Aerospace, Computational methods
Abstract: We propose a data-driven supervisory method to determine actions, in real-time, for systems with a binary success/failure outcome. This approach consists of two steps. First, a high-fidelity system model is used offline to train a classifier, which acts as a quick-to-evaluate approximation of the system. Then, the classifier is used online to select an action based on the scenario encountered. The method also returns an approximate probability of success which can then be used to inform follow-on decisions. We apply this method to problems where an interceptor missile engages a threat headed towards an asset. The interceptor's supervisory actions may include selecting parameters in the guidance and control laws, setting tunable initial conditions, and determining other details about how the interceptor will engage the threat. Specifically, the proposed method is demonstrated using the case study of a planar engagement between an interceptor and a threat, with the interceptor launch angle and autopilot crossover frequency as actionable parameters. For this case study, the proposed method outperforms an alternative baseline action.

Keywords: Lyapunov methods, Stability of nonlinear systems, Biological systems
Abstract: The main result of the paper is a new converse theorem for finite-time Lyapunov functions. We show the existence of a finite-time Lyapunov function for an autonomous continuous-time nonlinear dynamical system if the origin of the system is asymptotically stable. Our proof extends the recent results in finite-time Lyapunov function theory by providing an alternative converse proof for the existence of finite-time Lyapunov functions. In particular, we show that given asymptotic stability of the origin, the linearized dynamics satisfy global finite-time Lyapunov function conditions hence proving the converse theorem. Using our results, we present a consolidated theory for using and constructing Lyapunov functions to certify system stability properties. We also propose a constructive algorithm to efficiently compute non-conservative estimates of the domain of attraction for nonlinear dynamical systems.

Keywords: Stability of linear systems, Mechanical systems/robotics, Biomedical
Abstract: In this paper we develop a method to find the passivating parameter space for transfer function matrices with symbolic parameters. The method is subsequently applied to the mechanical-rotary variable impedance actuator (MeRIA), which belongs to the class of variable impedance actuators. The impedance control framework of MeRIA consists of cascaded control-loops guaranteeing a passive (positive real) load transfer function. We therefore focus on finding a robust impedance controller space by employing recursive parameter space testing with respect to the corresponding transfer function. Computed parameter spaces for the corresponding port function and simulations underline the performance of the algorithm.

Keywords: Aerospace, Variable-structure/sliding-mode control, Lyapunov methods
Abstract: This paper proposes several nonlinear impact time control guidance strategies against maneuvering targets, based on Lyapunov and sliding mode control theories. These strategies correspond to different quanta of information available to the interceptor, about the target’s maneuver. The use of deviated pursuit paradigm in the guidance design enables the use of exact time-to-go expression for intercepting moving but nonmaneuvering targets, without any small-angle approximations in heading angles. In deriving the guidance commands, the time-to-go is estimated by assuming a non-maneuvering target at each instant. Due to the inherent robustness of the proposed strategies, maneuvering targets can also be successfully intercepted at desired impact times, despite this assumption. Numerical simulations are presented to validate the efficacy of proposed guidance strategies for different initial engagement geometries and levels/types of target maneuvers.

Keywords: Aerospace, Control applications, Variable-structure/sliding-mode control
Abstract: This work addresses the problem of designing an impact time constrained guidance strategy for three-dimensional engagements, without decoupling the engagement dynamics in two mutually orthogonal planes. The guidance command is derived while considering nonlinear engagement dynamics, and with a time-to-go prediction that accounts for the interceptor's heading error. Power rate reaching law is used while designing sliding mode guidance strategy, since this law offers inherent robustness, smooth control and finite-time convergence to the sliding manifold. Further, the interceptor lateral acceleration components are obtained using a control allocation technique, that minimizes the instantaneous lateral acceleration, which aids in minimizing the total drag during interceptor's flight. Conditions for the interceptor to reach the collision course are derived and analyses are presented. Finally, simulations are provided to demonstrate the efficacy of the proposed guidance scheme.

Keywords: Aerospace, Flight control, Lyapunov methods
Abstract: A non-singular hierarchical controller using Integral Barrier Lyapunov Function (iBLF) is proposed in this paper for attitude tracking of a pitch-constrained quad- rotorcraft system. The integral function mixes the original pitch constraint with pitch error and removes the use of purely error based barrier Lyapunov function (BLF) with transformed error constraint. The design is a nonlinear hierarchical control where backstepping is used to develop an iBLF based attitude controller without any initial condition constraint on pitch error. A rigorous stability analysis proves that the tracking error of the overall closed-loop system is asymptotically converging and the signals are bounded in the cascaded control structure. Simulation results illustrate the efficacy of the proposed controller in contrast to authors’ earlier work on BLF-based tracking control of quadrotors.

Keywords: Aerospace, Cooperative control, Control applications
Abstract: This work focuses on achieving cooperative simultaneous interception against moving targets using the concepts of deviated pursuit guidance strategy. Unlike most existing salvo guidance strategies which use estimates of time-to-go, based on proportional navigation guidance, the present strategy uses exact expression for time-to-go to ensure simultaneous interception. The guidance command is derived considering nonlinear engagement kinematics. Weighted consensus in time-to-go over a pseudo-undirected graph is used to intercept a moving target cooperatively. It has been shown that through a judicious choice of these weights, the achievable set of interception times expands. Simulations are provided to vindicate the effectiveness of the proposed strategy.

Keywords: Aerospace, Control applications
Abstract: In this paper, we propose a guidance strategy that enables the interceptor to control the time of interception against stationary targets, while also respecting the field-of-view (FOV) constraints of the seeker. Such a guidance strategy always keeps the target within its field-of-view, using its seeker. Guidance command is derived using a barrier Lyapunov function, and an expression for lead angle of interceptor is obtained analytically, which further facilitates the computation and control of the impact time. The guidance comprises two stages, one of which is deviated pure pursuit, while during the latter stage, the deviation angle or lead angle decreases to zero thereby ensuring zero terminal lateral acceleration. Simulations across different engagement scenarios and tuning parameters vindicate the effectiveness of the proposed strategy.

Keywords: Aerospace, Flight control, Robust control
Abstract: In this paper, a robust disturbance observer based controller is presented for glideslope regulation of aircraft in turbulence and with uncertainties in the aerodynamic model. A significant challenge in designing disturbance observers for such system arises from the nonlinear disturbance to state coupling. This state dependent coupling limits the application of disturbance observer based control without resorting to system approximation. Instead of model simplification, this work explicitly accounts for the disturbance to state coupling and leverages the polynomial nature of the system dynamics to design an exponentially convergent disturbance observer. The underlying principle behind synthesis of stable disturbance observers is based on sum-of-squares (SOS) optimization and in particular, polynomial matrix inequalities (PMI). Through exponential convergence of disturbance estimate, the wind components and aerodynamic uncertainties can be rapidly estimated and then compensated by deploying control surfaces. The efficacy of the proposed approach is demonstrated using the disturbance observer with a nominal dynamic inversion controller for glideslope regulation of an aircraft based on the F/A-18 High Angle of Attack (HARV) model.

Keywords: Constrained control, Lyapunov methods, Flight control
Abstract: Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n leq 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.

Keywords: Control applications, Aerospace, Stability of hybrid systems
Abstract: In this paper, we present the design of trajectory tracking controllers for multirotor aerial vehicles that have the ability to operate both with and without thrust reversal. We follow a hierarchical control approach, in the sense that we start by designing a common saturated controller for the position subsystem and use it to provide a reference to an attitude tracking controller. The controllers for each operating mode are able to achieve global asymptotic stability as well as semiglobal exponential stabilization of the zero tracking error set. We demonstrate the capabilities of the proposed controllers in a simulation that performs a throw-and-catch maneuver.

Keywords: Flight control, Robotics, PID control
Abstract: In this paper, we present an autonomous flight controller for a quadcopter with thrust vectoring capabilities. This UAV falls in the category of multirotors with tilt-motion enabled rotors. Since the vehicle considered is over-actuated in nature, the dynamics and control allocation have to be analysed carefully. Moreover, the possibility of hovering at large attitude maneuvers of this novel vehicle requires singularity-free attitude control. Hence, quaternion state feedback is utilized to compute the control commands for the UAV motors while avoiding the gimbal lock condition experienced by Euler angle based controllers. The quaternion implementation also reduces the overall complexity of state estimation due to absence of trigonometric parameters. The quadcopter dynamic model and state space is utilized to design the attitude controller and control allocation for the UAV. The control allocation, in particular, is derived by linearizing the system about hover condition. This mathematical method renders the control allocation more accurate than existing approaches. Lyapunov stability analysis of the attitude controller is shown to prove global stability. The quaternion feedback attitude controller is commanded by an outer position controller loop which generates rotor-tilt and desired quaternions commands for the system. The performance of the UAV is evaluated by numerical simulations for tracking attitude step commands and for following a waypoint navigation mission.

Keywords: Flight control, Stability of nonlinear systems, Lyapunov methods
Abstract: This paper investigates a dual loop quaternion-based nonlinear control scheme for a quadrotor: the inner feedback loop controls the attitude of the quadrotor while the outer control loop aims to control the linear velocity, and/or position, of the quadrotor. The paper shows that global exponential stability of a quadrotor can be achieved with the proposed control scheme. The presented controller includes feedback and feedforward compensation of the nonlinear dynamics of the quadrotor and gyroscopic torques to guarantee global stability of the attitude controller. The outer velocity control loop uses a PI feedback structure, where the proportional action is primarily used to control linear velocity, and the integral action can either be used for linear position and/or eliminating velocity steady-state error. The inner attitude control includes a PD feedback loop, where the proportional action is in terms of the vector part of the quaternion and the derivative action is in terms of the aircraft angular velocity. The proposed controller has been both simulated and tested experimentally with a commercial quadrotor.

Keywords: LMIs, Adaptive control, Aerospace
Abstract: Occupation measures and linear matrix inequality (LMI) relaxations (called the moment sums of squares or Lasserre hierarchy) are state-of-the-art methods for verification and validation (VV) in aerospace. In this document, we extend these results to a full F-16 closed-loop nonlinear dutch roll polynomial model complete with model reference adaptive control (MRAC). This is done through a new technique of approximating the reference trajectory by exploiting sparse ordinary differential equations (ODEs) with parsimony. The VV problem is then solved directly using moment LMI relaxations and off-the-shelf-software. The main results are then compared to their numerical counterparts obtained using traditional Monte-Carlo simulations.

Keywords: Robotics, Energy systems, Control applications
Abstract: In this paper, the problem of take-off and landing of an airborne wind energy system is addressed. The solution explored is to equipe the airborne wing of the system with a multicopter drone in order to perform the take-off and land maneuvers, even in the absence of wind. The proposed model with the proposed control strategy is implemented and tested in a numerical environment. The results show efficiency of the proposed control law and its robustness with respect to modelling errors and wind gusts.

Keywords: Sampled-data control, Stability of hybrid systems, Aerospace
Abstract: This paper presents an event-triggered controller that solves the problem of trajectory tracking for an aerial vehicle with a thrust actuation in a single body-fixed direction and full angular velocity actuation. Under the framework of hybrid dynamical systems, we first design a globally stabilizing hybrid control law and then derive an appropriate event-triggering mechanism for sampling of actuation signals. We prove that bounded reference trajectories are rendered globally asymptotically stable for the closed-loop system. To enable practical implementation of the proposed event-triggered controller on digital platforms, we provide a modified event-triggering mechanism that achieves practical stability while avoiding Zeno solutions. The results are illustrated by numerical simulations and further verified by experiments.

Keywords: Variable-structure/sliding-mode control, Fault tolerant systems, Flight control
Abstract: This paper presents a novel concept for active fault-tolerant control (FTC) of dual system hybrid unmanned aerial vehicles (UAVs) based on analytical redundancy to increase the operational safety in the face of primary actuator faults. The proposed scheme exploits the inherent over-actuation property of hybrid UAVs when in addition to the aerodynamic surfaces four lift rotors are used to control the aircraft during long range fixed-wing flight mode. Fault tolerance is achieved by utilizing an integral sliding mode based model reference control law combined with control allocation techniques to reallocate control signals among healthy effectors in the face of actuator faults and maintain nominal closed-loop performance. After introducing the modelling procedure of the UAV, including the identification of aerodynamical cross-couplings between lift rotors and airframe dynamics, Hardware-in-the-loop (HIL) simulation results are presented to demonstrate the efficiency of the proposed scheme in a realistic hardware setup.

Keywords: Machine learning, Adaptive control, Nonlinear systems identification
Abstract: Control schemes that learn using measurement data collected online are increasingly promising for the control of complex and uncertain systems. However, in most approaches of this kind, learning is often viewed as a side effect that passively improves control performance, e.g., by updating a model of the system dynamics. Moreover, determining how improvements in control performance due to learning can be actively exploited in the control synthesis is still an open research question. In this paper, we present AntLer, a design algorithm for learning-based control laws that anticipates learning, i.e., that takes the impact of future learning in uncertain dynamic settings explicitly into account. AntLer expresses system uncertainty using a non-parametric probabilistic model. Given a cost function that measures control performance, AntLer chooses the control parameters such that the expected cost of the closed-loop system is minimized approximately. We show that the solution computed by AntLer approximates an optimal solution arbitrarily accurately. Furthermore, we apply AntLer to a nonlinear system, and compare the results to the case where learning is not anticipated.

Keywords: Autonomous systems, Learning, Robotics
Abstract: This paper presents an online kinodynamic motion planning scheme for dynamically evolving environments, by employing Q-learning. The methodology addresses the finite horizon continuous-time optimal control problem with completely unknown system dynamics. An actor-critic structure is employed along with a buffer of previous experiences, to approximate the optimal policy and alleviate the learning signal requirements. The methodology is equipped with a terminal state evaluation to achieve fast navigation. The path planning is assigned to the RRTX. An obstacle augmentation and a local replanning strategy are responsible for collision-free navigation. Rigorous Lyapunov-based proofs are provided to guarantee closed-loop stability of the equilibrium point. We evaluate the efficacy of the methodology with simulations.

Keywords: Building and facility automation, Fault detection, Machine learning
Abstract: Faults in HVAC systems degrade thermal comfort and energy efficiency in buildings and have received significant attention from the research community, with data driven methods gaining in popularity. Yet the lack of labeled data, such as normal versus faulty operational status, has slowed the application of machine learning to HVAC systems. In addition, for any particular building, there may be an insufficient number of observed faults over a reasonable amount of time for training. To overcome these challenges, we present a transfer methodology for a novel Bayesian classifier designed to distinguish between normal operations and faulty operations. The key is to train this classifier on a building with a large amount of sensor and fault data (for example, via simulation or standard test data) then transfer the classifier to a new building using a small amount of normal operations data from the new building. We demonstrate a proof-of-concept for transferring a classifier between architecturally similar buildings in different climates and show few samples are required to maintain classification precision and recall.

Keywords: Computational methods, Machine learning, Learning
Abstract: Certifying or enforcing performance and stability guarantees for controllers based on deep learning is challenging. This paper aims to provide conditions to verify nominal stability of a system controlled by a deep learning based controller. We focus on a special form of neural network as the controller, called non-autonomous deep networks. The training is performed using data from a baseline controller, which does not need to be known mathematically, e.g. it may be a human operating the system. We provide an emph{explicit} formula for computation of the number of hidden layers such that the resulting learning-based closed-loop system is stable. We furthermore outline how this condition can be integrated in the learning. The results are illustrated by a simulation study considering control of a continuously stirred tank reactor.

Keywords: Formal verification/synthesis, Learning, Modeling
Abstract: We propose a novel framework to differentiate between vehicle trajectories originating from human and non-human drivers by constructing a data-driven boundary using parametric signal temporal logic. Such a construction allows us to evaluate the trajectories, detect rare events, and reduce the uncertainty of driver behaviors when it assumes the form of a disturbance in control synthesis and evaluation problems. We train a classifier that separates admissible (i.e. human) examples - which arise from real-world demonstrations - and inadmissible (i.e. non-human) examples that are generated by falsifying specifications synthesized from the same real-world driving data. Proceeding in this fashion allows for finding a reasonable boundary of human behavior exhibited in real-world driving records. The framework is demonstrated using a case study involving a human-driven vehicle approaching a signalized intersection.

Keywords: Formal verification/synthesis, Learning, Cooperative control
Abstract: This paper investigates the problem of deploying a multi-robot team to satisfy a syntactically co-safe Truncated Linear Temporal Logic (scTLTL) task specification via multi-agent Reinforcement Learning (MARL) technique. Due to the heterogeneous agents considered here, typical approaches cannot avoid the task assignment problem, which is inherently difficult and can sacrifice optimality (e.g., shortest path) through manual manipulation. MARL is exploited here to eliminate the task assignment as part of the learning process. Moreover, MARL usually requires some direct or indirect coordination among agents to promote convergence and a tracker is needed to track the process of satisfying the scTLTL given its temporal nature. We use the Finite State Automaton (FSA) to address these two issues. An FSA augmented Markov Decision Process (MDP) is constructed for each agent, which share the FSA state carrying the global information. Moreover, a metric called robustness degree is employed to replace the Boolean semantics and quantify the reward of gradually satisfying the scTLTL. Consequently, a language guided semi-decentralized Q-learning algorithm is proposed to maximize the return over the FSA augmented MDP. Simulation results demonstrate the effectiveness of the semi-decentralized multi-agent Q-learning while the complexity is significantly reduced.

Keywords: Learning, Robotics, Nonlinear systems identification
Abstract: This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear state- space model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.

Keywords: Learning, Optimal control, Robust control
Abstract: We present a robust design for reinforcement learning (RL) based optimal control of continuous-time linear time-invariant singularly perturbed (SP) dynamic systems in the presence of dynamic uncertainties. We consider the dynamic model of both the plant and the uncertainty to be unknown. Assuming that the uncertainty satisfies an input-to-state stability (ISS) condition, we propose a variant of the adaptive dynamic programming (ADP) method that learns a sub-optimal controller using measurements of only the slow states of the plant. The resulting RL controller is, therefore, significantly reduced-dimensional, and enjoys reduced learning time. We illustrate our design with simulations of a SP system and of a clustered multi-agent consensus network.

Keywords: Learning, Stochastic optimal control, Markov processes
Abstract: This paper concerns approximate solutions to the optimal stopping problem for a geometrically ergodic Markov chain on a continuous state space. The starting point is the Galerkin relaxation of the dynamic programming equations that was introduced by Tsitsikilis and Van Roy in the 1990s, which motivated their Q-learning algorithm for optimal stopping. It is known that the convergence rate of Q-learning is in many cases very slow. The reason for slow convergence is explained here, along with a variant of ``Zap-Q-learning" algorithm, designed to achieve the optimal rate of convergence. The main contribution is to establish consistency of Zap-Q-learning algorithm for a linear function approximation setting. The theoretical results are illustrated using an example from finance.

Keywords: Learning, Decentralized control, Stochastic optimal control
Abstract: We consider a multi-agent Linear-Quadratic (LQ) reinforcement learning problem consisting of three systems, an unknown system and two known systems. In this problem, there are three agents -- the actions of agent 1 can affect the unknown system as well as the two known systems while the actions of agents 2 and 3 can only affect their respective co-located known systems. Further, the unknown system's state can affect the known systems' state evolution. In this paper, we are interested in minimizing the infinite-horizon average cost. We propose a Thompson Sampling (TS)-based multi-agent learning algorithm where each agent learns the unknown system's dynamics independently. Our result indicates that the expected regret of our algorithm is upper bounded by tilde{O}(sqrt{T}) under certain assumptions, where tilde{O}(cdot) hides constants and logarithmic factors. Numerical simulations are provided to illustrate the performance of our proposed algorithm.

Keywords: Learning, Robust control
Abstract: Reinforcement learning (RL) and other AI methods are exciting approaches to data-driven control design, but RL's emphasis on maximizing expected performance contrasts with robust control theory (RCT), which puts central emphasis on the impact of model uncertainty and worst case scenarios. This paper argues that these approaches are potentially complementary, roughly analogous to that of a driver and an engineer in, say, formula one racing. Each is indispensable but with radically different roles. If RL takes the driver seat in safety critical applications, RCT may still play a role in plant design, and also in diagnosing and mitigating the effects of performance degradation due to changes or failures in component or environments. While much RCT research emphasizes synthesis of controllers, as does RL, in practice RCT's impact has perhaps already been greater in using hard limits and tradeoffs on robust performance to provide insight into plant design, interpreted broadly as including sensor, actuator, communications, and computer selection and placement in addition to core plant dynamics. More automation may ultimately require more rigor and theory, not less, if our systems are going to be both more efficient and robust. Here we use the simplest possible toy model to illustrate how RCT can potentially augment RL in finding mechanistic explanations when control is not merely hard, but impossible, and issues in making them more compatibly data-driven. Despite the simplicity, questions abound. We also discuss the relevance of these ideas to more realistic challenges.

Keywords: Learning, Kalman filtering, Robust control
Abstract: In this paper we prove the existence of a fundamental trade-off between accuracy and robustness in perception-based control, where control decisions rely solely on data-driven, and often incompletely trained, perception maps. In particular, we consider a control problem where the state of the system is estimated from measurements extracted from a high-dimensional sensor, such as a camera. We assume that a map between the camera’s readings and the state of the system has been learned from a set of training data of finite size, from which the noise statistics are also estimated. We show that algorithms that maximize the estimation accuracy (as measured by the mean squared error) using the learned perception map tend to perform poorly in practice, where the sensor’s statistics often differ from the learned ones. Conversely, increasing the variability and size of the training data leads to robust performance, however limiting the estimation accuracy, and thus the control performance, in nominal conditions. Ultimately, our work proves the existence and the implications of a fundamental trade-off between accuracy and robustness in perception-based control, which, more generally, affects a large class of machine learning and data-driven algorithms.

Keywords: Machine learning, Stochastic systems, Statistical learning
Abstract: Due to the growing amount of data and processing capabilities, machine learning techniques are increasingly applied for the identification of dynamical systems. Especially probabilistic methods are promising for learning models, which in turn are frequently used for simulations. Although confidence regions around predicted trajectories are of crucial importance in many control approaches, few rigorous mathematical analysis methods are available for learned probabilistic models. Therefore, we propose a novel method to estimate confidence regions for predicted trajectories, and assign them a confidence level based on Monte Carlo random trajectory sampling. Since the confidence level has a strongly nonlinear dependence on the number of Monte Carlo samples, we derive a lower bound on the number of samples that ensures a desired minimum confidence level. The efficiency and flexibility of the proposed method is demonstrated in simulations of a Bayesian hidden Markov model and a Gaussian process state space model.

Keywords: Agents-based systems, Cooperative control, Learning
Abstract: This paper considers a distributed reinforcement learning problem in the presence of Byzantine agents. The system consists of a central coordinating authority called ``master agent'' and multiple computational entities called ``worker agents''. The master agent is assumed to be reliable, while, a small fraction of the workers can be Byzantine (malicious) adversaries. The workers are interested in cooperatively maximize a convex combination of the honest (non-malicious) worker agents' long-term returns through communication between the master agent and worker agents. A distributed actor-critic algorithm is studied which makes use of entry-wise trimmed mean. The algorithm's communication-efficiency is improved by allowing the worker agents to send only a scalar-valued variable to the master agent, instead of the entire parameter vector, at each iteration. The improved algorithm involves computing a trimmed mean over only the received scalar-valued variable. It is shown that both algorithms converge almost surely.

Keywords: Machine learning, Robust control, Optimization algorithms
Abstract: Adoption of machine learning (ML)-enabled cyber-physical systems (CPS) are becoming prevalent in various sectors of modern society such as transportation, industrial, and power grids. Recent studies in deep reinforcement learning (DRL) have demonstrated its benefits in a large variety of data-driven decisions and control applications. As reliance on ML-enabled systems grows, it is imperative to study the performance of these systems under malicious state and actuator attacks. Traditional control systems employ resilient/fault-tolerant controllers that counter these attacks by correcting the system via error observations. However, in some applications, a resilient controller may not be sufficient to avoid a catastrophic failure. Ideally, a robust approach is more useful in these scenarios where a system is inherently robust (by design) to adversarial attacks. While robust control has a long history of development, robust ML is an emerging research area that has already demonstrated its relevance and urgency. However, the majority of robust ML research has focused on perception tasks and not on decision and control tasks, although the ML (specifically RL) models used for control applications are equally vulnerable to adversarial attacks. In this paper, we show that a well-performing DRL agent that is initially susceptible to action space perturbations (e.g. actuator attacks) can be robustified against similar perturbations through adversarial training.

Keywords: Machine learning, Autonomous systems, Pattern recognition and classification
Abstract: Understanding multi-vehicle interactive behaviors with temporal sequential observations is crucial for autonomous vehicles to make appropriate decisions in an uncertain traffic environment. On-demand similarity measures are significant for autonomous vehicles to deal with massive interactive driving behaviors by clustering and classifying diverse scenarios. This paper proposes a general approach for measuring spatiotemporal similarity of interactive behaviors using a multivariate matrix profile technique. The key attractive features of the approach are its superior space and time complexity, real-time online computing for streaming traffic data, and possible capability of leveraging hardware for parallel computation. The proposed approach is validated through automatically discovering similar interactive driving behaviors at intersections from sequential data.

Keywords: Machine learning, Hierarchical control, Intelligent systems
Abstract: Poor sample efficiency is a major limitation of deep reinforcement learning in many domains. This work presents an attention-based method to project neural network inputs into an efficient representation space that is invariant under changes to input ordering. We show that our proposed representation results in an input space that is a factor of m! smaller for inputs of m objects. We also show that our method is able to represent inputs over variable numbers of objects. Our experiments demonstrate improvements in sample efficiency for policy gradient methods on a variety of tasks. We show that our representation allows us to solve problems that are otherwise intractable when using naive approaches.

Keywords: Machine learning, Optimization
Abstract: This paper considers the problem of multi-agent distributed optimization. In this problem, there are multiple agents in the system, and each agent only knows its local cost function. The objective for the agents is to collectively compute a common minimum of the aggregate of all their local cost functions. In principle, this problem is solvable using a distributed variant of the traditional gradient-descent method, which is an iterative method. However, the speed of convergence of the traditional gradient-descent method is highly influenced by the conditioning of the optimization problem being solved. Specifically, the method requires a large number of iterations to converge to a solution if the optimization problem is ill-conditioned.

In this paper, we propose an iterative pre-conditioning approach that can significantly attenuate the influence of the problem's conditioning on the convergence-speed of the gradient-descent method. The proposed pre-conditioning approach can be easily implemented in distributed systems and has minimal computation and communication overhead. For now, we only consider a specific distributed optimization problem wherein the individual local cost functions of the agents are quadratic. Besides the theoretical guarantees, the improved convergence speed of our approach is demonstrated through experiments on a real data-set.

Keywords: Machine learning, Learning, Optimization algorithms
Abstract: In this paper, we propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate O(1/T) or O(frac{1}{log T}) under some mild assumptions. To handle the high dimensional nonlinear dynamical systems, we present the first-ever distributed Koopman operator learning algorithm. We show that the distributed Koopman operator learning has the same convergence properties as a centralized Koopman operator learning problem, in the absence of optimal tracker, so long as the basis functions satisfy a set of state-based decomposition conditions. Experiments are provided to complement our theoretical results.

Keywords: Network analysis and control, Identification for control, Learning
Abstract: In this paper we study the problem of learning minimum-energy controls for linear systems from heterogeneous data. Specifically, we consider datasets comprising input, initial and final state measurements collected using experiments with different time horizons and arbitrary initial conditions. In this setting, we first establish a general representation of input and sampled state trajectories of the system based on the available data. Then, we leverage this data-based representation to derive closed-form data-driven expressions of minimum-energy controls for a wide range of control horizons. Further, we characterize the minimum number of data required to reconstruct the minimum-energy inputs, and discuss the numerical properties of our expressions. Finally, we investigate the effect of noise on our data-driven formulas, and, in the case of noise with known second-order statistics, we provide corrected expressions that converge asymptotically to the true optimal control inputs.

Keywords: Statistical learning, Machine learning, Stochastic optimal control
Abstract: Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with fewer data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty.

Keywords: Switched systems, Optimal control, Learning
Abstract: This paper studies Q-learning for quadratic regulation problem of switched linear systems. Inspired by the analytical results from classical model-based optimal control, a structured Q-learning algorithm is developed. The proposed algorithm consists of a carefully designed parametric approximator that respects the analytical structure of the exact Q-function and an associated parameter training algorithm. Based on a geometric insight gained from the analysis of the exact Q-function structure, training of approximation parameters is formulated as a matrix identification problem. Probabilistic guarantee on successful identification of all matrices using the proposed algorithm is rigorously proved under moderate conditions. Several numerical studies are conducted to demonstrate the effectiveness of the overall proposed Q-learning algorithm.

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Abstract: ACC Awards Ceremony

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Abstract: Hybrid Systems TC meeting Friday 11:30 AM to 1:00 PM, Session FrLuT4 https://cuboulder.zoom.us/j/96466444912

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Abstract: ASME DSCD Energy Systems TC Meeting

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Abstract: Room 60: MARC TC Meeting Time: Jul 3, 2020 12:00 PM Mountain Time (US and Canada)

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Keywords: Emerging control applications, Learning, Adaptive control
Abstract: The resilient output feedback control of linear networked control (NCS) system with uncertain dynamics in the presence of Gaussian noise is presented under the denial of service (DoS) attacks on communication networks. The DoS attacks on the sensor-to-controller (S-C) and controller-to-actuator (C-A) networks induce random packet losses. The NCS is viewed as a jump linear system, where the linear NCS matrices are a function of induced losses that are considered unknown. A set of novel correlation detectors is introduced to detect packet drops in the network channels using the property of Gaussian noise. By using an augmented system representation, the output feedback Q-learning based control scheme is designed for the jump linear NCS with uncertain dynamics to cope with the changing values of the mean packet losses. Simulation results are included to support the theoretical claims.

Keywords: Intelligent systems, Machine learning, Neural networks
Abstract: Although parking space detection is a classic application in the field of image processing, most of commonly used methods can only guarantee their accuracy of detecting standard parking spaces due to the limitation of environmental diversity. Inspired by the close connection between vehicles and parking spaces in the parking environment, we believe that well-trained vehicle detection method can help improve the environmental adaptability of the parking space detection method. In this paper, we propose an environment-adaptive available parking space detection method. Based on the detection results obtained by vehicle detection and orientation estimation, our method enables the vision-only autonomous vehicle to learn environmental information near parked cars, and to detect available parking spaces accordingly. Results from real-world experiments have shown the functionality of the presented approach.

Keywords: Learning, Biological systems
Abstract: Controlling a population of neurons with one or a few control signals is challenging due to the severely underactuated nature of the control system and the inherent nonlinear dynamics of the neurons that are typically unknown. Control strategies that incorporate deep neural networks and machine learning techniques directly use data to learn a sequence of control actions for targeted manipulation of a population of neurons. However, these learning strategies inherently assume that perfect feedback data from each neuron at every sampling instant are available, and do not scale gracefully as the number of neurons in the population increases. As a result, the learning models need to be retrained whenever such a change occurs. In this work, we propose a learning strategy to design a control sequence by using population-level aggregated measurements and incorporate reinforcement learning techniques to find a (bounded, piecewise constant) control policy that fulfills the given control task. We demonstrate the feasibility of the proposed approach using numerical experiments on a finite population of nonlinear dynamical systems and canonical phase models that are widely used in neuroscience.

Keywords: Learning, Biomedical, Biological systems
Abstract: Despite recent advancements in understanding the mechanisms underlying sudden cardiac death due to cardiac fibrillation, new defibrillation techniques have been slow to manifest. The reasons for this are manifold, but from a controls perspective, the spatiotemporal behavior exhibited by the electrical activity of the heart during fibrillation is high-dimensional, chaotic, and fundamentally nonlinear making standard control techniques difficult to implement. In this work, we investigate the use of a reinforcement learning framework to identify a control strategy to eliminate reentrant spiral waves that are associated with cardiac fibrillation. We propose a reduced order model that replicates the behavior of an idealized spiral wave core traveling in an excitable medium. We implement the Q-learning method with function approximation using a neural network to learn a control strategy that actively drives a spiral core to the boundary of the domain where it can be absorbed. Results indicate that the reinforcement learning algorithm is able to rapidly learn an effective control strategy for use in the reduced order model. Continued development of this framework for implementation in more realistic models could inform the design of active control strategies to achieve low-energy control of spatiotemporal chaos in the heart associated with cardiac arrest.

Keywords: Learning, Neural networks, Automotive control
Abstract: We consider real-time origin-destination transportation requests in, e.g., ride-hailing, and for each request, provide a context-aware route recommendation. To overcome the difficulty of estimating uncertain user preferences toward multiple route features, we design and implement an approach via a combination of the weighted shortest path problem and deep learning, and evaluate it using real-world transportation data. Specifically, the proposed approach learns weights from historical choices of drivers through a deep neural network by minimizing the total weighted costs of historical routes and maximizing those of the non-chosen routes. We evaluate our method and two benchmarks with 4 million requests received by Didi Chuxing in Beijing. Based on the results, we demonstrate that distinguishing request scenarios helps provide preferable context-aware route recommendations.

Keywords: Modeling, Learning
Abstract: In this paper, we present a data driven approach for approximating dynamical systems. A system of governing equations is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly from the data provided. This approach has advantages over other methods, where a dictionary of basis functions has to be provided by the user, which is non trivial in some applications. We compare the accuracy of the proposed data-driven modeling approach to existing methods in the literature, and demonstrate that for some applications, the maximum entropy basis functions provide significantly more accurate models.

Keywords: Energy systems, Uncertain systems, Simulation
Abstract: Wind farm wake steering is an active topic in the wind community. Yaw-induced wake steering in wind farms has shown significant increases in total wind farm power output. Unfortunately, sensor uncertainty and model uncertainty often make pure model-driven approaches less effective. Due to the mechanical and financial downsides associated with experimental wake steering, collecting useful data to verify model-based approaches is often viewed as too risky. However, electric grid curtailment periods offer the opportunity to experiment with minimal mechanical and financial risks. A novel data acquisition process utilizing grid curtailment periods for wake steering experimentation is presented. This method curtails the total wind farm power output while yaw sweeping the upstream turbine to discover the optimal yaw angle for wake-steering. The optimal yaw angle can then be used in regular non-curtailment periods to increase total power output.

Keywords: Optimal control, Learning, Large-scale systems
Abstract: This article investigates optimization of wind farms using a modifier adaptation scheme based on Gaussian processes. In this scheme measurements are used to identify plant-model mismatch using Gaussian process regression, which are then used to find the optimal plant control inputs. However, for systems with many agents and a large control input space, the identification of the input-output map of the plant is challenging. Therefore, the paper proposes a distributed learning approach, in which sub-parts of the plant are identified with individual GP regression models. Afterwards, all of these are used to build a model of the overall plant-model mismatch, which is then used in the optimization. In the wind farm case the sub-parts are the individual turbines. The distributed learning approach clearly outperforms the original central learning approach in numerical illustrations of wind farm test cases.

Keywords: Control applications, Energy systems
Abstract: In this paper, we present a reinforcement-learning-based distributed approach to wind farm energy capture maximization using yaw-based wake steering. In order to maximize the power output of a wind farm, individual turbines can use yaw misalignment to deflect their wakes away from downstream turbines. Although using model-based methods to achieve yaw misalignment is one option, a model-free method might be better suited to incorporate changing conditions and uncertainty. We propose an algorithm that adapts concepts of temporal difference reinforcement learning distributed to a multiagent environment that empowers individual turbines to optimize overall wind farm output and react to unforeseen disturbances.

Keywords: Autonomous systems, Energy systems, Simulation
Abstract: This paper introduces a novel approach for estimating the wind field over an entire wind farm using a mobile sensor to collect limited amounts of data. The proposed method estimates the boundary conditions of a simplified turbine wake model by computing the model sensitivity matrix and using a recursive least-squares algorithm to recover the model parameters from the wind field measurements. To address the fact that it is not practical to take measurements across the entire wind farm, the proposed method classifies each area on the map based on its sensitivity to parameter variations. This classification is then used to generate a suitable path for a mobile sensor, which is charged with collecting data for the recursive least-squares algorithm. The proposed framework can successfully estimate the model boundary conditions using just the measurements collected along the path of the mobile sensor. This preliminary result paves the way for using real-time wind field estimates for the coordinated control of all the turbines within a wind farm.

Keywords: Fault accomodation, Energy systems, Subspace methods
Abstract: Individual Pitch Control (IPC) is a well-known and, in normal operating conditions, effective approach to alleviate blade loads in wind turbines. However, in the case of a Pitch Actuator Stuck (PAS) type of fault, conventional IPC is not beneficial since its action is disturbed by the failed pitch actuator. In this paper, a Subspace Predictive Repetitive Control (SPRC)-based IPC is proposed to implement a Fault Tolerant Control (FTC) strategy for Floating Offshore Wind Turbines (FOWTs) affected by PAS faults. In particular, an online subspace identification step is first carried out to obtain a linearized model of the FOWT system in faulty condition. The identified FOWT system is then used to develop a repetitive control law. Consequently, the adaptive repetitive control solution is implemented on the remaining healthy pitch actuators, in order to accommodate the PAS fault. Results show the developed SPRC approach allows to accommodate the PAS faults, achieving a considerable reduction of the blade loads in combination with lower pitch activities for the healthy actuators. This allows to continue power production and postpone maintenance operations, thus reducing the O&M costs.

Keywords: Energy systems, Electrical machine control, Fuzzy systems
Abstract: In this paper, a signed-distance fuzzy logic controller (SDFLC) adaptation mechanism is proposed to improve the permanent-magnet synchronous generator (PMSG) speed estimation performance of a model reference adaptive speed (MRAS) observer. In the conventional MRAS observer, a constant gain PI controller is used to drive the output error vector between the reference and the adaptive model to zero. One of the improvement noted in literature is the two-input fuzzy logic controller (FLC), this latter have greatly improved the speed estimation performance of the MRAS observer. The major drawback of the two-input fuzzy logic controller is the high fuzzy rules number, the thing that increase significantly the tuning and the control complexity. In the proposed adaptation mechanism, the two-input FLC are converted into single input named signed distance. This variable contains knowledge of all process state variables of the conventional FLC, and instead of creating and designing the fuzzy rules using a two-dimensional space of the phase plane, the new fuzzy rules will be designed only in one-dimensional rule table, this method allows greatly reducing the number of fuzzy rules and easily tuning the controller. A detailed comparison between the PI, FLC and SDFLC MRAS observer in open loop mode has been performed under step wind speed variation. As a second test, the MRAS observer based on SDFLC adaptation mechanism has been used in a vector super-twisting algorithm (STA) control strategy for a direct-drive PMSG wind turbines.

Keywords: Traffic control, Cooperative control, Optimal control
Abstract: A complete solution to a decentralized optimal merging problem for Connected and Automated Vehicles (CAVs) was provided in earlier work, based on a First In First Out (FIFO) assumption over a given Control Zone (CZ). In this paper, we relax the FIFO assumption and propose a decentralized Optimal Dynamic Resequencing (ODR) algorithm to further improve the performance of all merging CAVs in terms of time and energy. Specifically, we introduce a Resequencing Zone (RZ) prior to the CZ within which every CAV can execute the ODR algorithm. We determine the latest possible time for triggering ODR so as to minimally affect the CAV's operation. Simulation results show significant ODR benefits in CAV travel times and energy consumption over the merging and main roads, outperforming earlier results under different resequencing schemes.

Keywords: Traffic control, Modeling, Optimization
Abstract: We present a platoon-based bus dispatching strategy and passenger boarding strategy which utilizes a platoon of vehicles to improve capacity flexibility in response to dynamically changing demands, and controls passenger boarding flows to minimize the networkwise passengers’ perceived delay time. The released buses in the same platoon are allowed to separate when approaching the stop station, which makes our strategy more flexible and data-driven. A Mixed Integer Linear Programming (MILP) model is firstly developed to formulate the problem with the linear cost, in which both the passengers’ actual delay time and the operating bus vacancy are minimized subject to the volume dynamic constraints on both buses and stops. With the computational complexity as a concern, the Genetic Algorithm (GA) is adopted to solve the problem in real time. Comparison between MILP and GA on the computational time and result quality is conducted to show the efficiency of our method. Also, the optimization model with the nonlinear cost considering the passengers’ perceived delay time and the operating bus vacancy is directly solved by the GA. Finally, the performance of our method and the traditional bus schedule strategies under two different objectives is discussed in the case study, which indicates the potential of the platoon dispatching in mitigating the passenger’s perceived delay.

Keywords: Traffic control, Distributed parameter systems
Abstract: In this paper, we focus on cyber attacks in the context of macroscopic transportation network models. For our studies, we consider a strip of freeway traffic network that is actuated on the upstream boundary by ramp-metering, which are controlled remotely from a centralized command center. In our framework, we first formulate analytical conditions for generating stealthy cyber-attacks using Aw-Rascle-Zhang (ARZ) macroscopic traffic model. Such conditions elucidate the capability of attackers and theoretical limitations of attack detection algorithms. Subsequently, we propose a design framework for cyber attack detection algorithms that considers several desirable detection characteristics such as stability, robustness and attack sensitivity. Finally, we illustrate the effectiveness of our framework via simulation studies.

Keywords: Game theory, Automotive systems, Autonomous systems
Abstract: A new game theory based framework is proposed for path tracking and stabilization of autonomous vehicles. In the developed framework, vehicle body and corner traction control strategies are formulated in terms of players in a differential game. An integrated stability and path tracking control based on a non-cooperative differential game is developed. It includes bidirectional slip effect and wheel dynamics, which reflect more accurate longitudinal and lateral dynamics in harsh maneuvers and scenarios with sudden changes in the path planner’s trajectories. The open-loop and closed-loop Nash equilibrium control strategies are obtained by solving a two-player linear-quadratic differential game for the dynamical system of the overall tracking error. The performance of the proposed control strategy is validated with software simulations in various driving conditions.

Keywords: Traffic control, Simulation, Modeling
Abstract: Autonomous vehicles (AVs) will significantly affect road traffic management and control in the near future. In particular, AVs change the traffic flow characteristics of roads when mixed with human-driven vehicles (HVs). The penetration rate of AVs and their arrangement in a platoon of vehicles can influence the saturation flow of the traffic. Therefore, optimal lane management and signal timing design for arterials become crucial and challenging. We propose an integrated lane management and signal control (ILMSC) algorithm that minimizes the vehicle delay at an isolated and undersaturated intersection. Analytical models are proposed for estimating the saturation flow of the mixed traffic and the vehicle delay of a two-lane cyclic interrupted flow. Two alternative lane management policies are adopted: (i) dedicated lanes, and (ii) mixed-mixed lanes. Comprehensive microsimulation experiments emphasize the effectiveness of the proposed traffic control algorithm.

Keywords: Traffic control, Transportation networks, Networked control systems
Abstract: This paper offers a new physics-based approach to model and resiliently control traffic congestion. We model the traffic congestion as a mass conservation problem and provide discussions and proofs for the feasibility of the conservation based traffic dynamics. The paper spatially discretizes the governing continuity equation by using a directed graph with the nodes classified as (i) interior nodes, (ii) boundary inlet nodes, (iii) boundary outlet nodes, and (iv) anomalous nodes. At the interior nodes, the traffic dynamics is modeled as a probabilistic process. At the inlet boundary nodes, the traffic inflow rates can be planned and controlled but they must satisfy certain equality and inequality constraints. This paper assumes that the traffic inflow and outflow rates are identical at the outlet boundary nodes, which in turn implies that outlet boundary nodes have no dynamics. Furthermore, the traffic coordination cannot be controlled at the anomalous nodes and they are modeled as disturbance sources. We apply the model predictive control approach to effectively control the traffic congestion through the inlet boundary nodes in the presence of anomalies. The objective of the control problem is to assign the boundary traffic inflow rate such that traffic density is uniformly distributed across the traffic nodes. The boundary control inputs are assigned as the solution of a constrained quadratic programming problem.

Keywords: Hierarchical control, Predictive control for linear systems, Optimization
Abstract: The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism.

Keywords: Autonomous robots, Energy systems, Maritime control
Abstract: This paper examines the control of an autonomous underwater vehicle (AUV) with a deployable energy-harvesting kite for oceanographic observation and surveillance. The proposed design and control strategies specifically address objectives of achieving high-payload, long-endurance AUV operation through the deployment of an energy-harvesting kite while the AUV is anchored to the seabed, followed by the retraction of the kite for continued operation of the AUV. While deployed, the kite executes power-augmenting cross-current flight motions, using a hierarchical controller. When the AUV is in motion and the kite is retracted, a dynamic programming-based controller is used to select charging locations that minimize total charging time when traversing a prescribed mission path. Focusing on oceanographic observation along a Gulf Stream transect, using a hindcast model of the Gulf Stream current resource, the paper demonstrates the efficacy of the proposed control approach, as compared to several non-optimized alternatives.

Keywords: Power systems, Energy systems, Predictive control for linear systems
Abstract: Many mobile platforms and small power systems utilize a set of loads, which consume some resource, to accomplish a task. If there are inadequate resources available to accomplish the system's task, load requests must be modified in some way. This paper considers the case where loads with a specific power profile may be supplied with reduced resources, shifted in time, or substituted for one another. This extends the capability of previous works where loads could only be shifted in time. The problem is solved using a model predictive controller and an auxiliary system with binary inputs to represent the time delay and substitution variables. The proposed method is applied to a representative electric warship power system. The results demonstrate the flexibility enabled with this method: not only can the power sources be controlled, but loads can be curtailed, delayed, or substituted for each other to accomplish the same task.

Keywords: Energy systems, Hierarchical control, Hybrid systems
Abstract: A rapid increase in the electrical power on board vehicles has presented significant challenges to their thermal management. One proposed solution for large vehicles is the use of thermal energy storage (TES) modules containing phase change material (PCM) to quickly absorb large thermal loads, buffering fast thermal transients to reduce peak cooling requirements. However, the inherent nonlinearity and multi-timescale nature of vehicles with phase change energy storage must be addressed in control design. This paper presents a hierarchical hybrid model predictive control (MPC) framework to meet this need. A hierarchical control framework coordinates between the relatively slow phase change dynamics of the TES and relatively fast temperature dynamics elsewhere, excited by highly transient loading. Switched linear models are used to approximate nonlinearities across a wide range of operating conditions, resulting in hybrid MPC formulations that balance model accuracy and computational burden. The proposed approach is demonstrated in simulation on a candidate thermal management system with multiple TES modules.

Keywords: Power systems, Energy systems, Aerospace
Abstract: An inherent modular and scalable design framework has made unmanned aerial vehicles (UAV's) popular for various applications across many industries. The hybridization of UAV's facilitates higher performing and more efficient aircraft but necessitates new control designs. At a vehicle level, most efforts thus far have focused on the modeling and development of novel controllers in simulation. However, validating these controllers on experimental hardware is necessary before testing these algorithms on expensive flight-ready hardware. This paper seeks to address this research gap by experimentally validating a system-level hybrid UAV model. Using the validated system model, a baseline and predictive controller are developed in simulation and experimentally validated using a series hybrid UAV powertrain testbed.

Keywords: Automotive control, Optimal control, Automotive systems
Abstract: Predictive control strategies are state of the art in hybrid vehicles today. In this contribution, an optimal control strategy for a 48V powernet of a heavy-duty long-haul truck is investigated. A holistic approach is presented to control the power supply of actuatable electrified auxiliaries along with the common hybrid-electric driving functions. As a consequence, numerous state-control-combinations have to be calculated. To handle this computational effort the presented method utilizes heuristic information about the driven route. Thereby, the route is segmented into classes of related power demand. Subsequently, Dynamic Programming is applied to solve the optimal control problem. As example for an electrified auxiliary the compressor of the air-condition is chosen. A baseline control strategy for a reactive 48V system is compared to the optimal solution based on simulations. The features and use cases of the optimal control are discussed. It will be shown that applying the optimal control approach for the 48V system with knowledge about the whole route results in additional benefit in fuel consumption.

Keywords: Aerospace, Flight control, Adaptive control
Abstract: Control surface or actuator faults or failures in any flight lead to system-induced loss of control in-flight (LOC-I) and the result can be fatal. In this paper, to prevent these accidents, an active fault-tolerant flight control (FTFC) is proposed. The system consists of the nonlinear control technique, state-dependent Riccati equation (SDRE) and a linear controller technique. In this paper, control surface damage is studied. To prevent LOC-I, a Reconfiguration Mechanism (RM) sends signals in real-time to the SDRE controller to slow down or accelerate the control surface movement, reconfigures controller with respect to damage or changes to Linear Quadratic Regulator/tracking (LQR/LQT) control due to uncontrollability and unobservability problem. Comparative figures are given to illustrate the effectiveness of the hybrid (SDRE/LQR-LQT+PID) controller architecture.

Keywords: Aerospace, Flight control, Linear systems
Abstract: This paper develops a control scheme capable of controlling a tilt-rotor unmanned aerial vehicle during nominal hover and fixed-wing flight as well as through transitions between flight modes. The control scheme consists of two parts: a low-level angular rate controller and variable mixer, and a trajectory tracking state-dependent LQR controller. In developing this controller we also present an aerodynamic model of a tilt-rotor with parameters for the Convergence aircraft by E-Flite. Finally we present simulation results for a representative trajectory consisting of vertical takeoff and landing as well as fixed-wing flight.

Keywords: Aerospace, Optimal control, Variational methods
Abstract: Application of traditional indirect optimization methods to optimal control problems (OCPs) with control and state path constraints is not a straightforward task. However, recent advances in regularization techniques and numerical continuation methods have enabled application of indirect methods to very complex OCPs. This study demonstrates the utility and application of an advanced indirect method, the Uniform Trigonometrization Method (UTM), to a Mars Science Laboratory type entry problem. The objective is to maximize the parachute deployment altitude for a free-time, fixed-final-velocity entry trajectory. For entry vehicles, in addition to the bank angle that is characterized by bang-bang control profiles, there are typically three state path constraints that have to be considered, namely, the dynamic pressure, heat-rate, and g-load. This study shows that the UTM enables simultaneous regularization of the bang-bang control and satisfaction of the state path constraints. Two scenarios with and without state path constraints are considered. The results obtained using the UTM for both of these cases are found to be in excellent agreement with a direct optimization method. Furthermore, an interesting feature emerges in the optimal control profile of the UTM during the initial high-altitude part of the resulting optimal trajectory for the scenario with state path constraints, which has an appealing practical implication.

Keywords: Aerospace, Robust control, Linear parameter-varying systems
Abstract: In this paper, an LPV longitudinal flight controller design is presented, which takes variations of mass and mass distribution into account without the need for additional measurements or estimation of the current loadcase (a certain combination of mass, center of gravity and inertia tensor). This means the loadcase variation is included in the LPV model, but the obtained controller depends on the measurable variations of altitude and airspeed only. Therefore, a technique based on LPV systems with partly-measurable parameters is used. This approach is applied to the control of the short-period dynamic on a model of a small regional aircraft. The obtained controller is evaluated on a more detailed linear model, which takes parts of the real control system into account, as well as within a 6DOF high-fidelity nonlinear simulation environment, which is used to analyze flight controllers before real-life flight tests.

Keywords: Aerospace, Uncertain systems, Estimation
Abstract: In this paper, the polynomial chaos based Kriging (PC-Kriging) is utilized as a surrogate model for orbital uncertainty propagation. The polynomial chaos can represent the global trend of the uncertainty distribution whereas the Kriging captures the local uncertainty variations. A new learning strategy is proposed to incrementally build and improve the PC-Kriging model. This new PC-Kriging scheme only requires a small number of sampling points while achieving close performance to the Monte-Carlo based propagation. It is also more accurate than the random sampling based Kriging model. An orbital uncertainty propagation example is used to demonstrate the effectiveness of the proposed algorithm.

Keywords: Numerical algorithms, Aerospace, Optimization
Abstract: This paper presents a Laguerre function based method for solving Linear Quadratic Regulator (LQR) problems with disturbance, with particular focus on interconnected large-scale dynamic systems. In the proposed method, estimating the states and the control inputs by Ritz method is used to obtain an iterative solver for the nonlinear two-point boundary value problem derived from Pontryagins maximum principle. Numerical comparisons are made between the available Ordinary Differential Equations (ODE) solver for the same class of problems and the presented method for a standard benchmark problem. This paper extends the work presented in [1] that provided the Ritz Method and Laguerre Function based method for solving LQR problems to the new class of problems represented by large-scale interconnected systems. The results show that the presented method is superior in both accuracy and efficiency.

Keywords: Building and facility automation, Adaptive control, Distributed control
Abstract: Half of a building's energy needs is consumed by Heating, Ventilation and Air Conditioning (HVAC) systems in order to provide indoor thermal comfort for occupants. The complexity of such systems along with their high energy usage makes the design of sophisticated control algorithms to be an imperative need. In this paper we proposed an adaptive algorithm for temperature regulation in multi-zone buildings. By exploiting the building architecture as well as the structure of Air Handling Unit (AHU) systems, the proposed scheme assigns a local valve flow controller to each thermal coil that brings heat load to a zone to regulate its temperature considering the zone's needs. The scheme takes into account the network structure of thermal zones of the building and the heat exchange that occurs between them. In addition, its performance does not depend on accurate knowledge of system parameters, precise calibration or historical data, and thus it can overcome changes that happen due to human activity or wear and tear as well as disturbances due to unknown heat loads, due to solar gains, weather conditions or electrical equipment. The proposed algorithm is shown to be scalable and provide stability for the overall system. Its performance is evaluated by a simulation example where it is applied to a primary school building model.

Keywords: Building and facility automation, Control applications, Optimization
Abstract: Model Predictive Control (MPC) is a promising technique for energy efficient control of Heating, Ventilation, and Air Conditioning (HVAC) systems. However, the need for human involvement limits current MPC strategies from widespread deployment, since (i) model identification algorithms require re-tuning of hyper parameters, and (ii) optimizers may fail to converge within the available control computation time, or get stuck in a local minimum. In this work we propose an autonomous MPC scheme to overcome these issues. Two major features are embedded in this architecture to enable autonomy: (i) a convex identification algorithm with adaptation to time-varying building dynamics, and (ii) a convex optimizer. The model identification algorithm re-runs periodically so as to handle changes in the building’s dynamics. The estimated model is guaranteed to be stable and has desirable physical properties. The optimizer uses a descent and convergent algorithm, with the underlying optimization problem being feasible and convex. Numerical results show that the proposed convex formulation is more reliable in control computation compared to the non- convex one, and the proposed autonomous MPC architecture reduces energy consumption significantly over a conventional controller.

Keywords: Building and facility automation, Power systems, Smart grid
Abstract: This paper presents a model-predictive control (MPC) solution for optimal thermal load scheduling in support of buildings’ participation in the wholesale energy and frequency regulation markets. The solution combines 1) a lower-level regulation capacity reset strategy that identifies the available regulation capacity for each hour, and 2) an upper-level zone temperature scheduling algorithm to find the optimal load trajectory with a minimum net electricity cost. In the supervisory scheduling strategy, piece-wise linear surrogate models, derived from offline optimization analysis of the lower-level capacity reset mechanism, are used to predict the cooling power and regulation capacity; and a mixed-integer convex program is formulated and solved to determine the optimal control actions in a receding horizon scheme. The proposed strategy was compared to a baseline energy-priority control strategy in a simulation test case and achieved clear performance improvements including a 126% regulation credit increase and a net cost reduction of 16.3%.

Keywords: Building and facility automation
Abstract: This paper describes a model predictive control (MPC) strategy to optimize the operation of a building HVAC system with phase change material-based storage integrated in supply air ducts. The control problem is nonlinear due to the piece-wise linearity of the PCM dynamics and the variable airflow control. To eliminate the nonlinearity, a set of discrete airflow rates are used and the airflow mode switches are optimally scheduled through a MPC implementation. A mixed-integer linear program (MILP) is formulated for the MPC problem by using the classic big M method and is solved with mature MILP solvers. The developed MPC method was tested and compared to a baseline control strategy via simulation tests. The results showed that the developed strategy could lower the demand and energy charges by 30% and 8.1%, respectively.

Keywords: Energy systems, Power systems, Large-scale systems
Abstract: In this paper we are concerned with reliable operation of the electric power grid in presence of malicious cyber-attacks on measurement signals. We use the continuously changing operating conditions of the power systems to introduce an active defense method based on dynamic clustering. Our detection strategy uses a moving-target approach where information about the system’s varying operating point is first used to form dynamic clusters of measurements based on their dynamic response to disturbances. Then, similarity checks can be performed within each cluster to detect stealthy cyber-attacks. The proposed method is effective even when the attacker has extensive knowledge of the system parameters, model and detection policy at some point in time.

Keywords: Energy systems, Robust control, Control applications
Abstract: In the design of ocean wave energy converters, proper control design is essential to the maximization of the power generation performance for the device. However, in realistic applications, this control design must be undertaken in the presence of model uncertainty. This paper considers the use of robust control theory to optimize the nominal performance for a wave energy converter in stochastic waves, subject to the constraint that the controller be stability-robust to unstructured uncertainties. We formulate the problem as a multi-objective optimal control problem, in which the primary objective is the maximization of power generation for the nominal system, and the competing objective is the H_infty norm of the uncertainty input/output channel. This optimal control problem is nonconvex, and we therefore propose an iterative algorithm can be used to arrive at a local optimal solution. This iterative approach is employs the concept of Iterative Convex Overbounding, in the context of the classical Method of Centers. The methodology is demonstrated on a model of a single, buoy-type wave energy converter.

Keywords: Biological systems, Optimization, Biomolecular systems
Abstract: This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are common (along with limit cycles), and the aim is to program cells to perform both digital and analog computation, though developing genetic digital computation has been the main focus. We frame the analog computing challenge of generating a steady state input-output function inside living cells. To program the steady state, a data-driven approach is taken wherein an approximation of the Koopman operator, identified via deep dynamic mode decomposition, is used to describe the dynamics of the system linearly. The new representation of the dynamics are then used to solve an optimization problem for the input which maximizes a direction in state space. Some added structure on the Koopman operator learning process for controlled systems is given for dynamics that are separable in the state and input. Finally, the methods are demonstrated on simulation examples of an incoherent feedforward loop and a combinatorial promoter system, two common network architectures seen in the field of synthetic biology.

Keywords: Biological systems, Uncertain systems
Abstract: In this paper, we investigate a mathematical model describing interactions between cancer and the immune system. In this model, we take into account the detrimental effects of chemotherapy on both populations (cancer and immune cells) and incorporate the beneficial effects of the immune system in controlling the tumor growth. The problem of cancer treatment scheduling is considered as a robust optimal control problem (ROCP) in the sense that we derive statistically optimal combined strategies of chemo- and immunotherapy treatments, assuming the knowledge of the probability distribution of the chemotherapy killing parameter (effects on the immune population). Furthermore, we add in the ROCP a health constraint on the minimal allowed immune cells density. We use the moments optimization framework, which allows to consider uncertainties on model parameters implicitly.

Keywords: Biomedical, Fluid flow systems, Modeling
Abstract: The coupling issue between ratio (gas mix) and pressure controllers is addressed for blower based critical care ventilators. Complications can arise by how oxygen gas, supplied by a proportional flow valve, is introduced relative to the blower. A simple blower model explains why coupling effects are more sensitive when oxygen is introduced downstream of the air blower. A progressive design synthesis is described that eventually led to the solution of complementary flow actuation between blower and valve flow feedback loops. Complementary dynamic flow coupling filters connect with the pressure stage output of the feedback control cascade. The complementary coupling filters frequency response changes according to the set gas ratio helping to equalize differences in the dynamic response between blower and valve at different gas ratio settings. This design solution achieves a more uniform total flow and pressure response across all ratio settings throughout the range of expected patient load.

Keywords: Biomolecular systems, Cellular dynamics, Biological systems
Abstract: One of the rapidly emerging research topics in synthetic biology focuses on how genetic modules are affected by their context, a fundamental challenge in the modular design of large-scale genetic systems. A major source of such context-dependence is due to the sharing of scarce common cellular resources, such as transcriptional and translational machinery. Since toggle switches are one of the fundamental building blocks of genetic systems, in this paper we reveal how competition for shared resources affects the robustness of bistable toggle switches to noise. To this end, we study the mean transition time between the two stable equilibria by leveraging the Eyring-Kramers law, and show that it decreases due to the scarcity of shared resources, thus the system becomes less robust to noise. In order to achieve this, we define a quasi-potential function that allows us to formulate the problem as the overdamped motion of a Brownian particle in a potential field. In addition to revealing how various parameters affect the mean transition time, thus the robustness of the toggle switch, we also develop explicit design guidelines for creating toggle switches that are minimally affected by their context.

Keywords: Biomolecular systems, Genetic regulatory systems, Biological systems
Abstract: We consider a mechanistic stochastic model of an autoregulatory genetic circuit with time delays. More specifically, a protein is expressed in random bursts from its corresponding gene. The synthesized protein is initially inactive and becomes active after a time delay. Rather than considering a deterministic delay, a key aspect of this work is to incorporate stochastic time delays, where delay is an independent and identically distributed random variable. The active protein inhibits its own production creating a negative feedback loop. Our analysis reveals that for an exponentially-distributed time delay, the noise in the protein levels decreases to the Poisson limit with increasing mean time delay. Interestingly, for a gamma-distributed time delay contrasting noise behaviors emerge based on the negative feedback strength. At low feedback strengths the protein noise levels monotonically decreases to the Poisson limit with increasing average delay. At intermediate feedback strengths, the noise levels first increase to reach a maximum, and then decrease back to the Poisson limit with increasing average delay. Finally, for strong feedbacks the protein noise levels monotonically increase with the average delay. For each of these scenarios we provide approximate analytical formulas for the protein mean and noises levels, and validate these results by performing exact Monte Carlo simulations. In conclusion, our results uncover a counter intuitive feature where inclusion of stochastic delays in a negative feedback circuit can play a beneficial role in buffering deleterious fluctuations in the level of a protein.

Keywords: Biomolecular systems, Genetic regulatory systems, Systems biology
Abstract: Synthetic biology applications have the potential to have lasting impact; however, there is considerable difficulty in scaling up engineered genetic circuits. One of the current hurdles is resource sharing, where different circuit components become implicitly coupled through the host cell's pool of resources, which may destroy circuit function. One potential solution around this problem is to distribute genetic circuit components across multiple cell strains and control the cell population size using a population controller. In these situations, perturbations in the availability of cellular resources, such as due to resource sharing, will affect the performance of the population controller. In this work, we model a genetic population controller implemented by a genetic circuit while considering perturbations in the availability of cellular resources. We analyze how these intracellular perturbations and extracellular disturbances to cell growth affect cell population size. We find that it is not possible to tune the population controller's gain such that the population density is robust to both extracellular disturbances and perturbations to the pool of available resources.

Keywords: Control laboratories, Control education, Mechatronics
Abstract: Low-cost DC motor system kits are used by undergraduate students to investigate the basics of automatic controls and enhance their ability to apply classroom theory to real-world applications utilizing Hardware-In-the-Loop (HIL) simulation. The kits provide students with a range of learning experiences, from controller design to reduced order model verification. Additionally, the low-cost kits allow the students the ability to work on an open-ended controller design problem outside of the laboratory. This manuscript presents (1) the DC motor system bill of materials, (2) a pedagogical approach to introducing automatic controls to undergraduate students utilizing HIL simulations, (3) experimentally determined motor parameters for motors used in the kit, (4) a reduced order model for a motor used in the kit, and (5) results contrasting real-world performance of the DC motor used in the kits with that from simulated models based on experimental motor parameters.

Keywords: Control laboratories, Mechatronics, Modeling
Abstract: This paper explores the modeling of a brushless DC motor (BLDC) system with an eye toward developing inexpensive microcontroller-based apparatus for classroom use or applications where robustness requirements allow an optical encoder. Field-oriented control (FOC) requires sensors to measure current for torque control purposes and rotor position through Hall Effect sensors for commutation purposes, all of which drive up costs. This paper proposes a BLDC voltage control approach requiring only an optical encoder. Typical classroom BLDC setups contain an external encoder for position sensing. The encoder can become the only sensor in an otherwise sensorless BLDC configuration, allowing the motor to operate in voltage control mode without an expensive external amplifier. This paper models an existing laboratory test article utilizing FOC in Simulink. The presentation compares experimental and simulated results to verify model accuracy. The simulation model is then modified for voltage control. The resulting simulations demonstrate the performance, in both speed and position control applications, and uncover potential pitfalls which are then explored. The paper discusses a design for the realization of the voltage control approach and avenues to investigate the extension of the performance range.

Keywords: Feedback linearization, Mechatronics, Biomedical
Abstract: Magnetic fields render a unique ability to control magnetic objects without a direct mechanical contact. To exploit this potential for a broad range of medical, microrobotics, and microfluidics applications, noncontact magnetic manipulators have been designed using both electromagnets and permanent magnets. By feedback control of these manipulators, magnetic objects can be precisely driven in the directions required by an application of interest. The feedback design process for these manipulators is normally complicated by their highly nonlinear nature, particulary for those utilizing permanent magnets. Yet, feedback linearization techniques can be applied to compensate for the nonlinear nature of most magnetic manipulators. This goal can be achieved by solving an underdetermined system of nonlinear algebraic equations. This paper adopts a homotopy continuation approach to solve this system of equations. It is shown by simulations that the proposed feedback linearization scheme drastically improves the control performance compared to the alternative control design methods used in prior work.

Keywords: Mechatronics, Predictive control for nonlinear systems, Output regulation
Abstract: With the advantages of high modeling accuracy and large bandwidth, recurrent neural network (RNN) based inversion model control has been proposed for output tracking. However, some issues still need to be addressed when using the RNN-based inversion model. First, with limited number of parameters in RNN, it cannot model the low-frequency dynamics accurately, thus an extra linear model has been used, which can become an interference for tracking control at high frequencies. Moreover, the control speed and the RNN modeling accuracy cannot be improved simultaneously as the control sampling speed is restricted by the length of the RNN training set. Therefore, this article focuses on addressing these limitations of RNN-based inversion model control. Specifically, a novel modeling method is proposed to incorporate the linear model in a way that it does not affect the existing high- frequency control performance achieved by RNN. dditionally, an interpolation method is proposed to double the sampling frequency (compared to the RNN training sampling requency). Analysis on the stability issues which may arise when the proposed new model is used for predictive control is presented along with the instructions on determining the parameters for ensuring the closed-loop stability. Finally, the proposed approach is demonstrated on a commercial piezo actuator, and the experiment results show that the tracking performances can be significantly improved.

Keywords: Mechatronics, Switched systems, Control applications
Abstract: In this paper, the use of multiple hybrid integrator-gain elements in a PID-based control design is discussed. From a describing function perspective, each individual element possesses similar magnitude characteristics as a linear-equivalent filter, but with significantly reduced phase lag. These preferable phase properties potentially facilitate a closed-loop controller design with increased bandwidths. However, as a drawback, the use of multiple nonlinearities in the controller may increase the discrepancy between a performance prediction on the basis of describing functions, and true time-domain system behaviour. For the proposed nonlinear controller, conditions are formulated by which a describing function analysis may still yield meaningful time-domain performance predictions. The usefulness of these conditions, and effectiveness of the nonlinear control design are experimentally demonstrated on a motor-load motion system.

Keywords: Variable-structure/sliding-mode control, Mechatronics
Abstract: In this article, we find an “on the average” equivalence between observer-based Sliding Mode control and classical output feedback compensation networks. The average output feedback control actions are found to be naturally implemented via a one-dimensional Delta-Sigma modulator circuit absorbing the underlying sliding regime defined in the state space. We focus on perturbed pure-integration switched systems, representing a paradigm of the input-output representation of an on-off controlled flat system. The simplified model is assumed to undergo endogenous (state-dependent) and exogenous disturbances in the form of a, lumped, total disturbance input. Experimental results are presented for the output trajectory tracking task on a single link manipulator-DC motor combination.

Keywords: Optimal control, Variational methods, Nonholonomic systems
Abstract: We consider a continuous-time optimal control problem for a swarm of single thruster, single reaction wheel spacecraft aiming to reach a target formation. The dynamic model of each spacecraft is obtained by augmenting the Hill-Clohessy-Wiltshire equations with the coupled dynamics of the reaction wheel and thruster. For the optimal control problem, we penalize the deviation from the target formation, the overall fuel usage, and the fuel imbalance between agents. The optimal control law is then obtained by using the minimum principle to formulate a split-boundary-value ODE, which is then solved numerically. Numerical simulations for a simple swarm of three satellites show that the proposed approach successfully reduces the fuel consumption of the most fuel-intensive spacecraft, thus extending the overall lifetime of the formation system.

Keywords: Fluid flow systems, Distributed parameter systems, Control applications
Abstract: We utilize the frequency response analysis of the linearized Navier-Stokes equations to quantify amplification of exogenous disturbances in a hypersonic flow over a compression ramp. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks. Our analysis of the laminar shock/boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favorably with observations from two different hypersonic compression ramp experiments. Furthermore, we utilize the dominant response to analyze the physical effects in the linearized dynamical system responsible for amplification of disturbances. We show that flow compressibility that arises from base flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Both these effects contribute to the appearance of temperature streaks observed in experiments and are critically important for the development of control-oriented models for transition to turbulence in hypersonic flows.

Keywords: Quantum information and control, Simulation, Model Validation
Abstract: CsPbBr3 perovskite nanocrystals (NCs) have recently garnered a lot of attention owing to its applications in solar cells, next-generation displays, and other optoelectronic devices that can surpass the performance of currently existing semiconductors. By synthesizing NCs of sizes smaller than the Bohr-exciton diameter, one can control the photoluminescence peaks. However, at this quantum confinement level, there is a dearth of simulation studies to elaborate recent experimental studies on the thermodynamic equilibrium as the major mechanism for the size control of NCs. Here, we present the first instance of a Kinetic Monte Carlo (KMC) investigation to qualitatively explain the process. We demonstrate that the size of NCs is inversely proportional to the solution phase Br concentration. We could explain this observation by incorporating physisorption, chemisorption, migration and desorption events in a traditional solid-on-solid KMC model. The results are in good agreement with experimental observations. The proposed modeling framework can be utilized broadly to explain the crystallization kinetics of the family of ABX3 perovskite NCs.

Keywords: Optimization, Modeling, Simulation
Abstract: Autonomous rendezvous and docking/berthing in the presence of two main attracting bodies is considered one of the key operations for future space explorations. Dynamic modeling,and relative guidance and control algorithms must be designed so as not to compromise the safety of the mission and to provide a collision-free environment. The two main approaches to guarantee collision avoidance are a closed loop active control design, and an open loop passive strategy. The paper presents the development of a passive safety procedure based on manifold theory, which provides collision-free trajectory in the presence of specific actuator failures. The proposed procedure is applied to the scenario defined by the European Space Agency Heracles study, for rendezvous in cislunar orbits.

Keywords: Pulp and Paper Control, Modeling, Model Validation
Abstract: During the Kraft pulping process, the fiber morphology such as fiber length and cell wall thickness changes due to degradation reactions. In this work, a multiscale model that integrates a widely employed mathematical model (i.e., extended Purdue model) and a microscopic model (i.e., kinetic Monte Carlo algorithm) is proposed to capture the dynamic evolution of the fiber morphology while cooking, as well as conventionally measured pulp quality index (i.e., Kappa number). To deal with the computational requirement of this multiscale model, a reduced-order model is identified and implemented to a model-based controller to regulate the fiber length and Kappa number to desired values.

Keywords: Human-in-the-loop control, Machine learning, Autonomous robots
Abstract: Human motion prediction is non-trivial in modern industrial settings. Accurate prediction of human motion can not only improve efficiency in human-robot collaboration, but also enhance human safety in close proximity to robots. Although many prediction models have been proposed with various parameterization and identification approaches, some fundamental questions remain unclear: what is the necessary parameterization of a prediction model? Is online adaptation of models necessary? Can a prediction model help improve safety and efficiency during human-robot collaboration? These un-addressed questions result from the difficulty of quantitatively evaluating different prediction models in a closed-loop fashion in real human-robot interaction. This paper develops a method to evaluate the closed-loop performance of different prediction models. In particular, we compare models with different parameterizations and models with or without online parameter adaptation. Extensive experiments were conducted on a human-robot collaboration platform. The experimental results demonstrate that human motion prediction significantly enhance the collaboration efficiency and human safety. Adaptable prediction models that are parameterized by neural networks achieve better performance.

Keywords: Autonomous robots, Modeling, Intelligent systems
Abstract: It is expected that human-driven vehicles and autonomous vehicles (AVs) will coexist in a mixed traffic for a long time. To enable AVs to safely and efficiently maneuver in this mixed traffic, it is critical that the AVs can understand how humans cope with risks and make driving-related decisions. In this work, we incorporate a human decision-making model in reinforcement learning to control AVs for safe and efficient operations. Specifically, we adapt regret theory to describe a human driver's lane-changing behavior and fit the personalized models to individual drivers for predicting their lane-changing decisions. The predicted decisions are incorporated in the safety regulations for reinforcement learning in training and in implementation. We then use an extended version of double deep Q-network (DDQN) to train our AV controller within the safety set. By doing so, the number of collisions in training and testing is reduced to zero, while the training accuracy is not impinged.

Keywords: Human-in-the-loop control, Autonomous robots, Optimal control
Abstract: For automated vehicles (AVs) to reliably navigate through crosswalks, they need to understand pedestrians’ crossing behaviors. Simple and reliable pedestrian behavior models aid in real-time AV control by allowing the AVs to predict future pedestrian behaviors. In this paper, we present a Behavior-aware Model Predictive Controller (B-MPC) for AVs that incorporates long-term predictions of pedestrian crossing behavior using a previously developed pedestrian crossing model. The model incorporates pedestrians’ gap acceptance behavior and utilizes minimal pedestrian information, namely their position and speed, to predict pedestrians’ crossing behaviors. The BMPC controller is validated through simulations and compared to a rule-based controller. By incorporating predictions of pedestrian behavior, the B-MPC controller is able to efficiently plan for longer horizons and handle a wider range of pedestrian interaction scenarios than the rule-based controller. Results demonstrate the applicability of the controller for safe and efficient navigation at crossing scenarios.

Keywords: Automotive control, Human-in-the-loop control, Adaptive systems
Abstract: Haptic shared control of an autonomy-enabled vehicle is used to manage the control authority allocation between a human and autonomy smoothly. Existing haptic shared control schemes, however, do not take the workload condition of human into account. To fill this research gap, this study develops a novel haptic shared control scheme that adapts to a human operator's workload in a semi-autonomous driving scenario. Human-in-the-loop experiments with 8 participants are reported to evaluate the new scheme. In the experiment, a human operator and an autonomous navigation module shared the steering control of a simulated teleoperated vehicle in a path tracking task while the speed of the vehicle is controlled by autonomy. High and low screen refresh rates were used to create moderate and high workload cases, respectively. Results indicate that adaptive haptic control leads to less driver control effort without sacrificing the path tracking performance when compared with the non-adaptive case.

Keywords: Human-in-the-loop control, Statistical learning, Machine learning
Abstract: Intelligent blending of human and automatic control inputs to collaboratively achieve shared control robotic tasks has received considerable attention in recent years. The benefits of such blending are many, including achieving better performance while maintaining robust situation awareness. Effective modeling of a given task using data obtained from human operator's demonstration is an important building block for shared control because the model is used as a reference for predicting operator's intent and generating automatic control input to facilitate task execution. Subgoal-based modeling, in which a complicated task is encoded as a finite number of subgoals, has yielded good results for practical tasks in shared control applications. In this paper, we present a new method for learning subgoals of a task based on human operator's demonstration. The modeling process involves: (1) extracting distributions of potential subgoals by effectively quantifying human operator's commands via a unified metric and (2) learning subgoals and their execution sequence from the extracted distributions via a Bayesian non-parametric clustering method with temporal ordering. We apply the proposed method and present the learned subgoals based on two demonstrations: a construction earth-moving task with a hydraulic excavator and an acrobatic flight task with a quadrotor.

Keywords: Human-in-the-loop control, Estimation, Optimization
Abstract: In this paper, we address the online threshold tracking problem in Cyber-Physical-Human systems (CPHS) based on binary feedback signals from users. We model the CPHS system as a linear discrete time-varying system, and consider both estimation error minimization and user experience in our cost function. Based on dynamic programming (DP), this paper proposes an optimal control which greatly reduces the rate of dissatisfaction while maintaining comparable performance in our simulation of braille display users. Besides, stability analysis is provided to guarantee that the cost is bounded in long-run problems.

Keywords: Networked control systems, Network analysis and control, Cooperative control
Abstract: In this paper, we study the resilient vector consensus problem in multi-agent networks and improve resilience guarantees of existing algorithms. In resilient vector consensus, agents update their states, which are vectors in mathbb{R}^d, by locally interacting with other agents some of which might be adversarial. The main objective is to ensure that normal (non-adversarial) agents converge at a common state that lies in the convex hull of their initial states. Currently, resilient vector consensus algorithms, such as approximate distributed robust convergence (ADRC) are based on the idea that to update states in each time step, every normal node needs to compute a point that lies in the convex hull of its normal neighbors' states. {To compute such a point, the idea of Tverberg partition is typically used, which is computationally hard. Approximation algorithms for Tverberg partition negatively impact the resilience guarantees of consensus algorithm.} To deal with this issue, we propose to use the idea of centerpoint, which is an extension of median in higher dimensions, instead of Tverberg partition. We show that the resilience of such algorithms to adversarial nodes is improved if we use the notion of centerpoint. Furthermore, using centerpoint provides a better characterization of the necessary and sufficient conditions guaranteeing resilient vector consensus. We analyze these conditions in two, three, and higher dimensions separately. We also numerically evaluate the performance of our approach.

Keywords: Networked control systems, Observers for Linear systems, Uncertain systems
Abstract: A novel observer architecture is proposed for networked control systems corrupted by unknown sparse errors between the controller and the sensors and between the actuators and the controller. The source of the unknown sparse errors could be malicious packet drops or disturbances. The sparse error between the controller and the sensors is recovered using a novel output sensor error estimator architecture. The sparse error between the actuators and the controller can be estimated using two proposed unknown input estimators. A combined approximator and the unknown input observer (UIO) architecture forms the observer to estimate the state of the plant corrupted by unknown sparse errors simultaneously at the plant's inputs and outputs. The observer design is formulated in terms of linear matrix inequalities (LMIs). The proposed observer can be used to construct a combined controller-observer compensator for a given networked system. It can also be used to detect an isolate sensor and actuator faults.

Keywords: Networked control systems, Optimization algorithms, Fault tolerant systems
Abstract: The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or ``Byzantine'') agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multi-dimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to F Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer.

Keywords: Networked control systems, Sampled-data control
Abstract: In this paper, we address the problem of synchronization among heterogeneous agents in a sampled-data setting. The key observation is that the sample-and-hold process introduces additional node-wise weights on the Laplacian matrix in the discrete-time domain. We then show that in the sampled-data setting, all of the agents’states approach the state of the so-called weighted averaged dynamics, an auxiliary dynamics that represents the collective behavior of heterogeneous agents when they are synchronized. In addition, admissible ranges of the sampling period and the diffusive coupling gain are computed, with which the consensus among the agents is achieved in a practical sense.

Keywords: Networked control systems, Stability of linear systems, Linear systems
Abstract: In this paper, a new event-triggering approach for guidance data scheduling between an operator (such as a ground station) and a controlled dynamical system (such as a vehicle equipped with feedback algorithm) over a network is proposed. Specifically, we explore three event-triggering rules based on an error signal constructed from the state of a reference model that is accessible to the operator and the guidance commands. The first rule is a standard one in the literature in which data exchanged over the network is the sampled points of the guidance command. Unlike existing results in the literature, in the second and third rule, data exchanged over the network is the approximated curve-fitted guidance command functions and the exact guidance command functions, respectively. Finally, our contribution is validated through an illustrative numerical example.

Keywords: Networked control systems
Abstract: We consider time-varying distributed averaging dynamics. We show a necessary and a sufficient condition for ergodicity of such dynamics. First, we extend a well-known result in ergodicity of time-homogeneous (time-invariant) averaging dynamics and we show that ergodicity of a dynamics necessitates that its (directed) infinite flow graph has a spanning rooted tree. Then, we show that if groups of agents are connected using a rooted tree and the averaging dynamics restricted to each group is P* and ergodic, then the dynamics over the whole networks is ergodic. In particular, this provides a general condition for convergence of consensus dynamics where groups of agents capable of reaching consensus follow each other on a time-varying network.

Keywords: Emerging control applications, Filtering
Abstract: Differential privacy has emerged as a formal framework for protecting sensitive information in control systems. One key feature is that it is immune to post-processing, which means that arbitrary post-hoc computations can be performed on privatized data without weakening differential privacy. It is therefore common to filter private data streams. To characterize this setup, in this paper we present error and entropy bounds for Kalman filtering differentially private state trajectories. We consider systems in which an output trajectory is privatized in order to protect the state trajectory that produced it. We provide bounds on a priori and a posteriori error and differential entropy of a Kalman filter which is processing the privatized output trajectories. Using the error bounds we develop, we then provide guidelines to calibrate privacy levels in order to keep filter error within pre-specified bounds. Simulation results are presented to demonstrate these developments.

Keywords: Filtering, Aerospace, Algebraic/geometric methods
Abstract: In this paper, we propose a new probability density function, referred to as the matrix Fisher-Gaussian (MFG) distribution, on the product of the special orthogonal group and the Euclidean space. MFG is constructed by conditioning a multivariate Gaussian distribution from the ambient Euclidean space, where the correlation between attitudes and linear components is formulated at the tangent space of the mean attitude. The desirable feature is that it can globally represent large uncertainties in the attitude of a rigid body correlated with any variable in the Euclidean space, thereby eliminating singularities and complexities inherent to local coordinates. Several stochastic properties and an approximate maximum likelihood estimation (MLE) are derived for MFG, and it is further utilized for unscented attitude estimation with a gyro bias. It is illustrated that the proposed attitude estimation scheme with MFG exhibits more accurate estimates than the multiplicative extended Kalman filter for a challenging case of large initial estimation errors.

Keywords: Filtering, Estimation, Kalman filtering
Abstract: Accurate carrier-phase integer ambiguity resolution is fundamental for high precision global navigation satellite systems (GNSSs). In this paper we extend a recently proposed mixture Kalman filter solution to integer ambiguity resolution. We utilize the Fisher information matrix to project the acquired measurements in into a lower-dimensional subspace, formulating an optimization program to find the projected measurement that minimally degrades filter performance with respect to the mean squared error (MSE) of the estimate. Using the projected measurements, our method achieves a significant computational speedup while retaining the performance of the original filter. Theoretical results are presented regarding the optimal projection computation, and the claims are subsequently illustrated in by simulation examples in a Monte Carlo study.

Keywords: Kalman filtering, Statistical learning, Estimation
Abstract: This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a stochastic process of the state vector. This is achieved by estimating the state according to the extended Kalman filtering applied to the marginal distribution of the state, and by estimating the disturbance from a backward smoothing technique. The corresponding pair of the estimated states and disturbances are fetched to a Gaussian process, which is constantly updated to resemble the disturbance process. The unique feature is that all of uncertainties in the estimated state and disturbance are accounted throughout the learning process. The efficacy of the proposed approach is illustrated by a numerical example.

Keywords: Pattern recognition and classification, Kalman filtering, Neural networks
Abstract: Terrain relative navigation can improve the precision of a spacecraft’s position estimate by detecting global features that act as supplementary measurements to correct for drift in the inertial navigation system. This paper presents a system that uses a convolutional neural network (CNN) and image processing methods to track the location of a simulated spacecraft with an extended Kalman filter (EKF). The CNN, called LunaNet, visually detects craters in the simulated camera frame and those detections are matched to known lunar craters in the region of the current estimated spacecraft position. These matched craters are treated as features that are tracked using the EKF. LunaNet enables more reliable position tracking over a simulated trajectory due to its greater robustness to changes in image brightness and more repeatable crater detections from frame to frame throughout a trajectory. LunaNet combined with an EKF produces a decrease of 60% in the average final position estimation error and a decrease of 25% in average final velocity estimation error compared to an EKF using an image processing based crater detection method when tested on trajectories using images of standard brightness.

Keywords: Robotics, Spacecraft control, Kalman filtering
Abstract: This paper addresses control allocation for redundant systems with the Extended Kalman Filter formalism. This method is compatible with the low computational power available in space environment, and presents a flexible framework to include constraints such as singularity avoidance. The convergence domain of the allocator is derived from the contraction theory framework, depending on specific parameters of the system. A general formulation is proposed to maximize the convergence domain with regard to these parameters. The method is applied to design a steering law of Control Moment Gyroscopes. Experimental tests show that the control allocation allows the actuators to work efficiently along nominal trajectories while avoiding singularities when necessary.

Keywords: Model/Controller reduction, Stochastic systems, Machine learning
Abstract: The practical applicability of analytical model reduction methods is limited. In this paper, we show an optimality of Proper Orthogonal Decomposition (POD) based nonlinear model reduction. POD is a simulation-based model reduction method that has been widely applied to nonlinear large-scale systems, but there is no theoretical background in general. An observability-based analytical nonlinear model reduction is not well proposed. In this paper, after deriving a stochastic observability using a duality between optimal control and optimal estimation, we show that the observability-based and simulation-based methodologies with weights are equivalent when the input is only stochastic signal. We also show an example of nonlinear model reduction method using the deep autoencoder.

Keywords: Uncertain systems, Linear systems, Modeling
Abstract: We study the convex geometry of the forward reach sets for integrator dynamics in finite dimensions with bounded control. We derive closed-form expressions for the volume and the diameter (i.e., maximal width) of these sets in terms of the state space dimension, control bound, and time. These results are novel, and use convex analysis to give an analytical handle on the ``size" of the integrator reach set. Several concrete examples are provided to illustrate our results. We envision that the ideas presented here will motivate further theoretical and algorithmic development in reach set computation.

Keywords: Uncertain systems, Robust control, LMIs
Abstract: In this paper, a polynomial chaos based framework for designing controllers for discrete time linear systems with probabilistic parameters is presented. Conditions for exponential-mean-square stability for such systems are derived and algorithms for synthesizing optimal quadratically stabilizing controllers are proposed in a convex optimization formulation. The solution presented is demonstrated on the derived discrete-time models of a nonlinear F-16 aircraft model trimmed at a set of chosen points.

Keywords: Uncertain systems, Robust control, Simulation
Abstract: Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Keywords: Uncertain systems, Statistical learning, Agents-based systems
Abstract: This work extends non-Bayesian social learning theory for real-valued measurements from uncertain likelihood models. The theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through likelihood updates from their observations. Typically, the likelihood models are assumed known precisely. However, in many situations the models are generated from sparse training exemplars due to lack of data availability because of the high cost of collection/calibration, limits within the communications network, and/or the high dynamics of the operational environment. Recently, we extended social learning theory for uncertain likelihoods due to categorical observations. In this paper, we introduce the theory of uncertain models for Gaussian distributed observations and study the properties of the resulting beliefs. We show that the Gaussian uncertain models exhibit similar properties as the multinomial uncertain models, which enables convergence proofs for the achievable beliefs due to distributed inference over real valued measurements with uncertain likelihood models.

Keywords: Uncertain systems, Statistical learning, Observers for Linear systems
Abstract: This paper studies the characterization of Wasserstein ambiguity sets for dynamic random variables when noisy partial observations are progressively collected from their evolving distribution. The ambiguity sets are accompanied by quantitative guarantees about the true distribution of the data, which renders them appropriate for the formulation of robust stochastic optimization problems. To describe the evolution of the variable, we consider a linear discrete-time dynamic model with random initial conditions, stochastic uncertainty in the dynamics, and partial noisy measurements. The probability distribution of all the involved random elements is supposed to be unknown. To make inferences about the distribution of the state vector, we collect several output samples from multiple realizations of the process. We use a classical Luenberger observer to obtain full-state estimators for the independent realizations and exploit these further to build the centers of the ambiguity sets.

Keywords: Traffic control, Fluid flow systems, Distributed control
Abstract: We consider a freeway traffic network described by the linearized Aw-Rascle-Zhang (ARZ) model, which can be monitored at the boundaries by a set of sensors. Inspired by the consensus-based distributed filtering for the initedimensional systems, an extension to the infinite dimensional case by using Lyapunov techniques is studied. When consensus weights are known, we provide sufficient conditions under which the network model is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors are exponentially stable for every agent. Some numerical studies provide a further insight on the effects of consensus-based boundary filtering.

Keywords: Distributed parameter systems, Estimation, Observers for Linear systems
Abstract: In this work, we propose a novel framework for the state estimation of first-order hyperbolic partial integral differential equation (PIDE) systems in the presence of multiplicative sensor uncertain parameter and uncertain exogenous disturbance. We consider the sensor uncertainty to be a sensor fault. In this context, a classical Luenberger observer no longer applies since no prior information is available to compensate the influence of uncertain parameters. Moreover, the estimation problem becomes a nonlinear problem due to the coupling between the uncertainty and the plant state. We develop a new adaptive law for the estimation of sensor uncertain parameter and embed the proposed laws into the state observer design. By selecting an appropriate Lyapunov function, we prove that the state estimation and parameter estimation error exponentially converge to an arbitrarily small neighborhood of the origin despite unknown disturbance. The effectiveness of the proposed method is studied via numerical simulation.

Keywords: Adaptive control, Delay systems, Distributed parameter systems
Abstract: We consider a system of a reaction-advection-diffusion partial differential equation (PDE) with a distributed input subject to an arbitrarily large and unknown time-delay. Using Lyapunov technique, we derive an adaptive controller and design a suitable update law to ensure the global stability of the closed-loop system in the L^2 sense.

Keywords: Distributed parameter systems, Traffic control, Fluid flow systems
Abstract: In this paper, we propose a control design methodology for a linearized continuum traffic model in the congested regime. The continuum traffic flow on a highway is modeled using a linearized version of the quasilinear system of hyperbolic partial differential equations known %in the literature as the Aw-Rascle-Zhang (ARZ) model. The linear traffic model is augmented with a novel non-local boundary condition representing car influx due to the use of routing apps such as Google Maps and Waze. The routing apps act as real-time previews for highway traffic, introducing potentially destabilizing feedback in the app-based navigation decision process, necessitating the development of a feedback controller. We first study small-time H^1 solutions of the linearized model with the addition of the app-routing for sufficiently small initial data. We introduce an extended, multi-tiered boundary control design based upon the method of infinite-dimensional backstepping. Using an intermediate decoupling transformation, we account for the non-local boundary condition arising from routing app feedback. It is shown that for sufficiently small H^1 data, the equilibrium congestion solution is exponentially stable and guarantees the existence of closed-loop solutions on the infinite time interval. The existence of the extended backstepping method is studied by characterizing the existence of the companion kernels.

Keywords: Distributed parameter systems, Chemical process control, Optimal control
Abstract: This manuscript addresses the design of a model predictive controller for a system of coupled ODE-PDE equations. The ODE describes a simple CSTR dynamics and the output of this system is coupled to the entrance of convection-diffusion reactor. The proposed controller is able to optimize the system performance while being able to handle input constraint and stabilize the system. As a discrete representation of the system is necessary, this is achieved by the application of structure preserving Cayley-Tustin time discretization to the coupled ODE-PDE system, without the use of spatial approximations or order reduction. Finally, the simulation results show the controller performance with and without constraints by comparing the results with the open-loop response.

Keywords: Reduced order modeling, Aerospace, Fluid flow systems
Abstract: The temporal features of a cylinder-generated shock-wave/transitional boundary-layer interaction (XSWBLI) in response to supersonic flow (Mach 2) are investigated using various model reduction techniques. Experimental data are obtained using schlieren imaging at 100 kHz and image analysis is performed using proper orthogonal decomposition (POD). The POD framework is used as a starting point to define a reduced set of data-driven isostable coordinates that characterize the transient behavior of an underlying dynamical system. Observed unsteady behaviors in the shock-wave/boundary-layer interactions are well-represented as an externally forced dynamical system with a pair of complex-conjugate isostable coordinates. Results are validated against well-established reduction methodologies including POD and spectral POD. These results indicate that the isostable reduced coordinate framework can be used to provide an accurate, low-dimensional representation of the dynamical features of supersonic fluid flow, even when the relationships between underlying dynamical model and observed output are not explicitly considered.

Keywords: Nonlinear systems identification, Energy systems, Identification for control
Abstract: The moving boundary nature of hydraulic fracturing process makes it extremely difficult to approximate using local models (i.e., approximate models whose validity is limited by the training data). In this work, we implement and evaluate the Koopman operator methodology for system identification and control of fracture propagation during a hydraulic fracturing process. The Koopman theory models nonlinear dynamical systems as linear systems by lifting the states to an infinite-dimensional space of functions called observables. It is particularly attractive because of its ability to provide (nearly) global linearization valid in a larger domain (in some cases the entire basin of attraction) compared to local models. Additionally, due to its linear structure, it allows convex predictive control formulations that avoid any issues associated with nonlinear optimization. An approximate linear model of the hydraulic fracturing process is constructed using this method and used to design a controller to regulate the fracture propagation phenomena. The results show that the Koopman linear model shows excellent agreement with the real system and successfully achieves the desired fracture geometry.

Keywords: Nonlinear systems identification, Adaptive systems, Estimation
Abstract: This paper introduces two new notions of persistence of excitation (PE) in reproducing kernel Hilbert spaces (RKHS) that can be used to establish convergence of function estimates generated by the RKHS embedding method. The two PE conditions are proven to be equivalent provided a type of uniform equicontinuity holds for the composition operator gmapsto gcirc x, where tmapsto x(t) is the unknown state trajectory. The paper then establishes sufficient conditions for the uniform asymptotic stability (UAS) of the error equations of RKHS embedding in term of these PE conditions. The proof is self-contained and treats the general case. Numerical examples are presented that illustrate qualitatively the convergence of the RKHS embedding method where function estimates converge over the positive limit set, a smooth, regularly embedded submanifold of the state space.

Keywords: Nonlinear systems identification, Agents-based systems, Computational methods
Abstract: This paper presents a parallel data-driven method to identify finite-dimensional subspaces that are invariant under the Koopman operator describing a dynamical system. Our approach builds on Symmetric Subspace Decomposition (SSD), which is a centralized scheme to find Koopman-invariant subspaces and Koopman eigenfunctions. Given a dictionary of functions, a collection of processors communicating through a strongly connected time-invariant directed graph, and a set of data snapshots gathered from the dynamical system, our approach distributes the data snapshots among the processors and initializes each processor with the original dictionary. Then, at each iteration, processors prune their dictionary by using the information received from their neighbors and applying the SSD method on the pruned dictionary with their local data. We prove that the algorithm terminates in a finite number of iterations and that the processors, upon termination, reach consensus on the maximal Koopman-invariant subspace in the span of the dictionary (and is therefore equivalent to SSD). A simulation example shows significant gains in time complexity by the proposed method over SSD.

Keywords: Computational methods, Nonlinear systems identification, Learning
Abstract: In this work, we developed new Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, the bistable toggle switch is considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments cannot be performed at the same time starting from several initial conditions.

Keywords: Nonlinear systems identification, Optimization, Observers for nonlinear systems
Abstract: Nonlinear dynamic systems can be classified into various classes depending on the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian, one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes essentially yield bounding constants characterizing the nonlinearity. This is then used to design observers and controllers through Riccati equations or matrix inequalities. While analytical expressions for bounding constants of Lipschitz and bounded Jacobian nonlinearity are studied in the literature, OSL and QIB classes are not thoroughly analyzed---computationally or analytically. In short, this paper develops analytical expressions of OSL and QIB bounding constants. These expressions are posed as constrained maximization problems, which can be solved via various optimization algorithms. This paper also presents a novel insight particularly on QIB function set: any function that is QIB turns out to be also Lipschitz continuous.

Keywords: Distributed control, Large-scale systems, Control of networks
Abstract: This work presents a novel distributed supervision architecture for reference signals management of dynamically coupled constrained linear systems where the dynamic interconnection among them can vary on-line to accomplish different operative scenarios. The strategy is based on non-iterative distributed command governor ideas that are here specialized to properly schedule modification on the couplings involving more than one subsystem. The main feature of the approach concerns the capability to avoid constraints violation regardless of any configuration change occurring on-line in the global plant/constraint structure. To this end, formal conditions to guarantee safe system configuration switchings are investigated by involving also graph colorability concepts. Simulation results on a water network are presented to illustrate the effectiveness of the proposed strategy.

Keywords: Distributed control, Large-scale systems, Stability of linear systems
Abstract: This paper considers the design of distributed H∞ finite-time controllers for large-scale systems under gossip communication protocol. In such protocol, each sub-controller receives the state information from one randomly chosen neighbor at each time instant. Based on Lyapunov stability theory, sufficient conditions are established such that the considered system is mean-square finite-time bounded and that the prescribed H∞ performance is satisfied. Distributed controller gains can be obtained by solving a set of linear matrix inequalities efficiently. Finally, a numerical example is presented to illustrate the proposed results in this paper.

Keywords: Distributed control, Observers for Linear systems, Algebraic/geometric methods
Abstract: A solution is given to the basic distributed feedback control problem for a multi-channel linear system assuming only that the system is jointly controllable, jointly observable and has an associated neighbor graph which is strongly connected. The solution is an observer-based control system which is implemented in a distributed manner. Using these ideas, a solution is also given to the distributed set-point control problem for a multi-channel linear system in which each and every agent with access to the system is able to independently adjust its controlled output to any desired set-point value. An example is given to briefly illustrate how network transmission delays might be dealt with.

Keywords: Distributed control, Optimal control, Linear systems
Abstract: Distributed optimal control has emerged as an exciting possibility; however, existing algorithms tend to require excessive computational time and thus may not be able to stabilize systems with fast dynamics. We develop instant distributed model predictive control (iDMPC) with a realization of the primal-dual algorithm embedded in the controller dynamics. Under assumptions on fast communication, we show that the input and state trajectories of iDMPC are equivalent to a centralized suboptimal MPC scheme. We utilize a dissipativity analysis to show that the closed-loop system trajectories asymptotically converge to a desired reference.

Keywords: Distributed control, Optimal control, Optimization
Abstract: We study the distributed Linear Quadratic Gaussian (LQG) control problem in discrete-time and finite-horizon, where the controller depends linearly on the history of the outputs and it is required to lie in a given subspace, e.g. to possess a certain sparsity pattern. It is well-known that this problem can be solved with convex programming within the Youla domain if and only if a condition known as Quadratic Invariance (QI) holds. In this paper, we first show that given QI sparsity constraints, one can directly descend the gradient of the cost function within the domain of output-feedback controllers and converge to a global optimum. Note that convergence is guaranteed despite non-convexity of the cost function. Second, we characterize a class of Uniquely Stationary (US) problems, for which first-order methods are guaranteed to converge to a global optimum. We show that the class of US problems is strictly larger than that of strongly QI problems and that it is not included in that of QI problems. We refer to Figure 1 for details. Finally, we propose a tractable test for the US property.