Keywords: Autonomous systems
Abstract: Reachability analysis, which considers computing or approximating the set of future states attainable by a dynamical system over a time horizon, is receiving increased attention motivated by new challenges in, e.g., learning-enabled systems, assured and safe autonomy, and formal methods in control systems. Such challenges require new approaches that scale well with system size, accommodate uncertainties, and can be computed efficiently for in-the-loop or frequent computation. In this talk, we present and demonstrate a suite of tools for efficiently over-approximating reachable sets of nonlinear systems based on the theory of mixed monotone dynamical systems. A system is mixed monotone if its vector field or update map is decomposable into an increasing component and a decreasing component. This decomposition allows for constructing an embedding system with twice the states such that a single trajectory of the embedding system provides hyperrectangular over-approximations of reachable sets for the original dynamics. This efficiency can be harnessed, for example, to compute finite abstractions for tractable formal control verification and synthesis or to embed reachable set computations in the control loop for runtime safety assurance. We demonstrate these ideas on several examples, including an application to safe quadrotor flight that combines runtime reachable set computations with control barrier functions implemented on embedded hardware.

Keywords: Stochastic optimal control, Statistical learning
Abstract: Discrete-time stochastic optimal control remains a challenging problem for general, nonlinear systems under significant uncertainty, with practical solvers typically relying on the certainty equivalence assumption, replanning and/or extensive regularization. Control-as-inference is an approach that frames stochastic control as an equivalent inference problem, and has demonstrated desirable qualities over existing methods, namely in exploration and regularization. We look specifically at the input inference for control (i2c) algorithm, and derive three key characteristics that enable advanced trajectory optimization: An `expert' linear Gaussian controller that combines the benefits of open-loop optima and closed-loop variance reduction when optimizing for nonlinear systems, adaptive risk sensitivity for regularized exploration, and performing covariance control through specifying the terminal state distribution.

Keywords: Stochastic optimal control, Stochastic systems, Optimal control
Abstract: This study focuses on minimizing the expectation of a polynomial cost function for linear systems with time-invariant stochastic parameters. These polynomial and time-invariant properties cause difficulties in solving this optimal control problem. Conventional approaches such as the principle of optimality are not applied to the problem due to the time-invariant stochastic parameters. Whereas various performance metrics can be expressed by the polynomial cost, it makes the problem more complicated than well-known quadratic cost functions. To overcome these difficulties, this study derives an explicit relation between the polynomial cost function and a linear feedback gain of the controller. Using this relation, a gradient method yields sub-optimal feedback gains to the problem even for the polynomial cost.

Keywords: Stochastic systems, Optimization algorithms, Constrained control
Abstract: Projection and penalty function simultaneous perturbation stochastic approximation (SPSA) algorithms are two commonly used methods in stochastic optimization problems under inequality constraints where no direct gradient of the loss function is available. However, both methods have potential shortcomings. We propose an algorithm that uses sequential quadratic programming (SQP) to estimate the projection operator under complex explicit inequality constraints. This algorithm has some advantages over the penalty function method in practice. We prove the convergence of the proposed SQP-based projection SPSA algorithm and make a comprehensive comparison with the penalty function method in two numerical examples to show its superiority.

Keywords: Stochastic optimal control, Decentralized control
Abstract: The Witsenhausen's counterexmaple formulated in 1968 is a decentralized stochastic control problem that highlights the importance of information structure in a seemingly simple two player team problem. Despite immense attention towards the problem, the non-classical information structure therein had remained the key challenge to obtain the optimal solution until recently (2014), when the Person-by-Person nonlinear optimal laws that satisfy integral equations were derived using Girsanov's transformation. In this paper, we compute and implement the nonlinear optimal laws using the Gauss Hermite Quadrature to approximate the integrals and then solving a system of non-linear equations to compute the signaling levels. We then analyse and compare our results with costs previously reported in the literature.

Keywords: Stochastic optimal control, Constrained control
Abstract: This letter covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and chance constraints on their state and control input. We propose a simplified control parameterization under the framework of affine disturbance feedback, and we show that our method is equivalent to parameterization over the family of state feedback policies. Using our method, associated finitehorizon optimization can be computed efficiently, with a slight increase in conservativeness compared with conventional affine disturbance feedback parameterization.

Keywords: Stochastic optimal control, Decentralized control, Cooperative control
Abstract: A distributed stochastic optimal control solution is presented for cooperative multi-agent systems. The network of agents is partitioned into multiple factorial subsystems, each of which consists of a central agent and neighboring agents. Local control actions that rely only on agents' local observations are designed to optimize the joint cost functions of subsystems. When solving for the local control actions, the joint optimality equation for each subsystem is cast as a linear partial differential equation and solved using the Feynman-Kac formula. The solution and the optimal control action are then formulated as path integrals and approximated by a Monte-Carlo method. Numerical verification is provided through a simulation example consisting of a team of cooperative UAVs.

Keywords: Stochastic optimal control, Formal verification/synthesis, Markov processes
Abstract: We present a method to find an optimal policy with respect to a reward function for a discounted Markov decision process under general linear temporal logic (LTL) specifications. Previous work has either focused on maximizing a cumulative reward objective under finite-duration tasks or maximizing an average reward for persistent (e.g., surveillance) tasks. This paper extends and generalizes these results by introducing a pair of occupancy measures to express the LTL satisfaction objective and the expected discounted reward objective, respectively. These occupancy measures are then connected to a single policy via a novel reduction resulting in a mixed integer linear program whose solution provides an optimal policy. Our formulation can also be extended to include additional constraints with respect to secondary reward functions. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.

Keywords: Machine learning, Stochastic optimal control, Observers for nonlinear systems
Abstract: We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable learning-based control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct a contraction metric and its differential Lyapunov function, sampled via simplified convex optimization in the stochastic setting. Spectral normalization constrains the state-derivatives of the metric to be Lipschitz continuous, thereby ensuring exponential boundedness of the mean squared distance of system trajectories under stochastic disturbances. The trained NSCM model allows autonomous systems to approximate optimal stable control and estimation policies in real-time, and outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the deterministic NCM, as shown in simulation results.

Keywords: Stochastic optimal control, Information theory and control, Stochastic systems
Abstract: In this paper, we utilize information theory to study the fundamental performance limitations of generic feedback systems, where both the controller and the plant may be any causal functions/mappings while the disturbance can be with any distributions. More specifically, we obtain fundamental Lp bounds on the control error, which are shown to be completely characterized by the conditional entropy of the disturbance, based upon the entropic laws that are inherent in any feedback systems. We also discuss the generality and implications (in, e.g., fundamental limits of learning-based control) of the obtained bounds.

Keywords: Stochastic optimal control, Machine learning, Autonomous systems
Abstract: We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution embeddings to model the stochastic kernel using a data-driven approach. By embedding the dynamics and uncertainty within a reproducing kernel Hilbert space, it becomes possible to compute the safety probabilities for stochastic reachability problems as simple matrix operations and inner products. We employ a convergent approximation technique, random Fourier features, in order to alleviate the increased computational requirements for high-dimensional systems. This technique avoids the curse of dimensionality, and enables the computation of safety probabilities for high-dimensional systems without prior knowledge of the structure of the dynamics or uncertainty. We validate this approach on a double integrator system, and demonstrate its capabilities on a million-dimensional, nonlinear, non-Gaussian, repeated planar quadrotor system.

Keywords: Stochastic optimal control, Constrained control, Neural networks
Abstract: In this paper, we propose a new methodology for state constrained stochastic optimal control (SOC) problems. The solution is based on past work in solving SOC problems using forward-backward stochastic differential equations (FBSDE). Our approach in solving the FBSDE utilizes a deep neural network (DNN), specifically Long Short-Term Memory (LSTM) networks. LSTMs are chosen to solve the FBSDE to address the curse of dimensionality, non-linearities, and long time horizons. In addition, the state constraints are incorporated using a hard penalty function, resulting in a controller that respects the constraint boundaries. Numerical instability that would be introduced by the penalty function is dealt with through an adaptive update scheme. The control design methodology is applicable to a large class of control problems. The performance and scalability of our proposed algorithm are demonstrated by numerical simulations.

Keywords: Stochastic optimal control, Optimal control, Linear systems
Abstract: In order to optimally steer the state of a stochastic system to a desired value over a finite time horizon, a novel approach based on the Stochastic Minimum Principle is presented, which enforces a constraint on the expectation of the terminal state at all instances of time. In order to solve the associated optimal control problem, we invoke a version of the Stochastic Minimum Principle which we call the Terminally Constrained Stochastic Minimum Principle (TC-SMP). For linear stochastic systems with quadratic costs, analytical solutions to the adjoint equation of the TC-SMP are derived and are explicitly represented in terms of controllability Gramians and solutions of Riccati equations. Numerical examples are provided to illustrate the results, and the performance of the TC-SMP approach is compared to both penalty-based and covariance-steering alternative approaches.

Keywords: Stochastic optimal control, Optimization, Nonlinear systems identification
Abstract: The paper is about the optimal control of a stochastic dynamical system. We provide a convex formulation to the optimal control problem involving a stochastic dynamical system. The convex formulation is made possible by writing the stochastic optimal control problem in the dual space of densities involving the Fokker-Planck or Perron-Frobenius generator for a stochastic system. The convex formulation leads to an infinite-dimensional convex optimization problem for optimal control. We exploit Koopman and Perron-Frobenius generators' duality for the stochastic system to construct the finite-dimensional approximation of the infinite-dimensional convex problem. We present simulation results to demonstrate the application of the developed framework.

Keywords: Stochastic optimal control, Stochastic systems, Uncertain systems
Abstract: We consider a class of stochastic optimal control problems for discrete-time linear systems whose objective is the characterization of control policies that will steer the probability distribution of the terminal state of the system close to a desired Gaussian distribution. In our problem formulation, the closeness between the terminal state distribution and the desired (goal) distribution is measured in terms of the squared Wasserstein distance which is associated with a corresponding terminal cost term. We recast the stochastic optimal control problem as a finite-dimensional nonlinear program whose performance index can be expressed as the difference of two convex functions. This representation of the performance index allows us to find local minimizers of the original nonlinear program via the so-called convex-concave procedure [1]. Finally, we present nontrivial numerical simulations to demonstrate the efficacy of the proposed technique by comparing it with sequential quadratic programming methods in terms of computation time.

Keywords: Stochastic systems, Lyapunov methods
Abstract: This paper examines the safety verification of the sample path of Ito’s stochastic differential equations (SDE) using a notion of stochastic zeroing barrier function (SZBF). It is shown that an extension of the recently developed zeroing barrier function concept in deterministic systems can be derived to formulate an SZBF based safety verification method for Ito’s SDE sample paths. The main tools in the proposed method include Ito’s calculus and stochastic invariance concept.

Keywords: Stochastic systems, Modeling, Optimization
Abstract: The spread of fake news on online social networks (OSNs) has become a matter of concern. These platforms are also used for propagating important authentic information. Thus, there is a need for mitigating fake news without significantly influencing the spread of real news. We leverage users' inherent capabilities of identifying fake news and propose a warning-based control mechanism to curb this spread. Warnings are based on previous users' responses that indicate the authenticity of the news. We use population-size dependent continuous-time multi-type branching processes to describe the spreading under the warning mechanism. We also have new results towards these branching processes. The (time) asymptotic proportions of the individual populations are derived using stochastic approximation tools. Using these, relevant type 1, type 2 performances are derived and an appropriate optimization problem is solved. The proposed mechanism effectively controls fake news, with negligible influence on the propagation of authentic news. We validate performance measures using Monte Carlo simulations on network connections provided by Twitter data.

Keywords: Estimation, Stochastic systems, Markov processes
Abstract: The influence model (IM) is a discrete-time stochastic automaton that captures spatiotemporal network dynamics. It constitutes a reduced-order representation of networked Markov chains and has found broad stochastic network applications. Parameter estimation from observation data is critical for utilizing IM in real applications. The master Markov chain approach used in the literature incurs significant computational cost. In this paper, we develop an efficient estimation algorithm for a special class of IM, named the uniform completely connected homogeneous influence model (UCC-HIM), through exploiting its special network topology. Specially, we introduce a reduced-order Markov chain representation for the UCC-HIM, analyze its relationship with the master Markov chain, based on which an efficient estimation algorithm is developed. Two simulation studies verify the accuracy and computation reduction of the proposed estimation approach.

Keywords: Stochastic optimal control, Decentralized control, Agents-based systems
Abstract: In this paper, we discuss the methodology of generalizing the optimal control law from learned component tasks to unlearned composite tasks on Multi-Agent Systems (MASs), by using the linearity composition principle of linearly solvable optimal control (LSOC) problems. The proposed approach achieves both the compositionality and optimality of control actions simultaneously within the cooperative MAS framework in both discrete and continuous-time in a sample-efficient manner, which reduces the burden of re-computation of the optimal control solutions for the new task on the MASs. We investigate the application of the proposed approach on the MAS with coordination between agents. The experiments show feasible results in investigated scenarios, including both discrete and continuous dynamical systems for task generalization without resampling.

Keywords: Lyapunov methods, Markov processes, Stochastic systems
Abstract: In the paper, we study the so-called mathbf{p}-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.

Keywords: Markov processes, Stochastic systems, Agents-based systems
Abstract: This paper proposes and analyzes a stochastic Susceptible-Exposed-Infected-Removed (SEIR) spreading model on networks. Imagine a nursing home housing 28 seniors and 7 staff workers, in which one of the staff has tested positive for COVID-19. Unfortunately, the results of this test are 3 days late and the infected person had not been quarantining while waiting for their test results. What is now the individual risk to the different people living in this nursing home? If the home has access to two rapid COVID-19 viral tests, who should they be given to and why? In order to answer questions like this, we need to study stochastic models rather than deterministic ones. Unlike the vast majority of works that analyze various deterministic models, stochastic models are required when analyzing the risk of COVID-19 to individual people rather than tracking aggregate numbers in a given region. More specifically, this paper compares the results provided by analyzing stochastic and deterministic models and investigating when it is suitable to use the different models. In particular, we show why it is not suitable to use deterministic models when analyzing the spread in small communities and how these questions can be better addressed using stochastic ones. Finally, we show the added complications that arise due to the relatively long incubation period of COVID-19, and how it can be addressed. A simulated case study of the spread of COVID-19 in a 35-person nursing home is used to help illustrate our results.

Keywords: Control applications, Adaptive systems, Optimal control
Abstract: While many theoretical works concerning Adaptive Dynamic Programming (ADP) have been proposed, application results are scarce. Therefore, we design an ADP-based optimal trajectory tracking controller and apply it to a large-scale ball-on-plate system. Our proposed method incorporates an approximated reference trajectory instead of using setpoint tracking and allows to automatically compensate for constant offset terms. Due to the off-policy characteristics of the algorithm, the method requires only a small amount of measured data to train the controller. Our experimental results show that this tracking mechanism significantly reduces the control cost compared to setpoint controllers. Furthermore, a comparison with a model-based optimal controller highlights the benefits of our model-free data-based ADP tracking controller, where no system model and manual tuning are required but the controller is tuned automatically using measured data.

Keywords: Control applications, Energy systems
Abstract: With increase in the frequency of natural disasters such as hurricanes that disrupt the supply from the grid, there is a greater need for resiliency in electric supply. Rooftop solar photovoltaic (PV) panels along with batteries can provide resiliency to a house in a blackout due to a natural disaster. Our previous work showed that intelligence can reduce the size of a PV+battery system for the same level of post-blackout service compared to a conventional system that does not employ intelligent control. The intelligent controller proposed is based on model predictive control (MPC), which has two main challenges. One, it requires simple yet accurate models as it involves real-time optimization. Two, the discrete actuation for residential loads (on/off) makes the underlying optimization problem a mixed-integer program (MIP) which is challenging to solve. An attractive alternative to MPC is reinforcement learning (RL) as the real-time control computation is both model-free and simple. These points of interest accompany certain trade-offs; RL requires computationally expensive off-line learning, and its performance is sensitive to various design choices.

In this work, we propose an RL-based controller. We compare its performance with the MPC controller proposed in our prior work and a non-intelligent baseline controller. The RL controller is found to provide a resiliency performance---by commanding critical loads and batteries---similar to MPC with a significant reduction in computational effort.

Keywords: Control applications, Manufacturing systems, Emerging control applications
Abstract: In the context of additive manufacturing (AM) and 3D Printing, vat photopolymerization is an established technique in which photopolymer is selectively solidified to form a near-net-shape part. Photopolymerization-based AM is increasingly being adopted by the high-tech industry, but the technology still faces several challenges in terms of consistency in product quality, understanding of the UV curing process, in-situ process monitoring, and real-time closed-loop control. This paper aims to demonstrate the potential of model-based control of the UV curing process. The curing process is modelled and anticipatively controlled with an optimal control law for nonlinear systems, derived via a sequential linearization strategy. The potential of this approach is proven by means of both simulations that illustrate a one-dimensional spatial optimal tracking problem and experiments that validate a zero-dimensional controlled system.

Keywords: Control applications, Process Control, Observers for nonlinear systems
Abstract: Algorithms for regulation of the vertical rate of penetration and the drilling power in rotary drilling systems are presented. The algorithms are designed under the assumption that the parameters of the rock-bit interaction are unknown. In contrast with the previous results, the algorithms do not require real-time measurement and communication of the downhole variables, such as rotational velocity, torque-on-bit, etc. This is achieved through the use of high-order sliding mode observers which estimate the required downhole variables based on measurements performed at the ground level. Simulation results are presented which confirm efficiency of the proposed control methods.

Keywords: Control applications, Flight control, Optimal control
Abstract: There are too many control surfaces for over-actuated aircraft. The coordination and distribution of the efforts between these control surfaces is a problem, and this problem can be solved by Control Allocation (CA). With CA, the required moment, force, or rate can be allocated to actuators more easily. For one of the over-actuated aircraft, NASA GTM, a dynamic CA method is used in this work. For CA, Weighted Least Square (WLS) equation is used, and this equation is solved with an active set method that can be used with real-time implementation. As a baseline controller, State-Dependent Riccati Equation (SDRE) is used to generate a reference moment. As a Fault-Tolerant Flight Controller (FTFC), CA can be reconfigured depending on the control surface or actuator problem and level. In this work, reconfiguration is especially for the CA's control effectiveness matrix and steady-state distribution matrix. Besides, depending on the problem, especially compensating for an undesirable rolling moment, outer elevators behave like elevons after reconfiguration. Loss of effectiveness (degradation), lock in place (stuck), and control surface damages are studied for emergency cases. Simulations demonstrate that this reconfiguration feature is effective for reference tracking and vital for recovery.

Keywords: Control applications, Optimal control, Optimization
Abstract: This paper presents a multidisciplinary and multi-objective optimal design of an aircraft wing with two, three, and four control surfaces. The study aims to compare the performance of the wing in terms of aerodynamic loads rejection, stability robustness, and energy consumption. An LQR (Linear Quadratic Regulator) is designed for each control surface. The geometrical parameters of the control surfaces such as the span-wise and chord lengths, and the diagonal elements of the LQR weighting matrices are optimally adjusted by an NSGA-II (Non-dominated Sorting Genetic Algorithm). The algorithm returns a set of solutions called a emph{Pareto set} and its function evaluation forms another set known as a emph{Pareto front}. The solution set holds optimal geometrical and control decision variables that produce various degrees of optimal trade-offs among the design goals. To facilitate the comparison between the three optimization problems, a post-processing algorithm that operates on the Pareto front is utilized. Then, the knee points and portions of the Pareto fronts are compared. The optimal solutions show that there are conflicting relationships between the design objectives. The disturbance rejection of the wing with the two ailerons is the least effective however control energy consumption is the smallest as compared to the other configurations. The wing with the three ailerons at 18 different design options has the best relative stability. At the knee point, a wing having four control surfaces can offer the best disturbance rejection but at the expense of the control energy. With these considerations, a wing with three surfaces can be the best compromise among the other configurations.

Keywords: Control applications, Predictive control for nonlinear systems, Optimal control
Abstract: During functional electrical stimulation (FES), muscle force saturation and a user's tolerance levels of stimulation intensity limit a controller's ability to deliver the desired amount of stimulation, which, if unaddressed, degrade the performance of high-gain feedback control strategies. Additionally, these strategies may overstimulate the muscles, which further contribute to the rapid onset of muscle fatigue. Cooperative control of FES with an electric motor assist may allow stimulation levels within the imposed limits, reduce overall stimulation duty cycle, and compensate for the muscle fatigue. Model predictive controller (MPC) is one such optimal control strategy to achieve these control objectives of the combined hybrid system. However, the traditional MPC method for the hybrid system requires exact model knowledge of the dynamic system, i.e., cannot handle modeling uncertainties, and the recursive feasibility has been shown only for limb regulation problems. So far, extending the current results to a limb tracking problem has been challenging. In this paper, a novel tube-based MPC method for tracking control of a human limb angle by cooperatively using FES and electric motor inputs is derived. A feedback controller for the electrical motor assist is designed such that it reduces the error between the nominal MPC and the output of the actual hybrid system. Further, a terminal controller and terminal constraint region are derived to show the recursive feasibility of the robust MPC scheme. Simulation results were performed on a single degree of freedom knee extension model. The results show robust performance despite modeling uncertainties.

Keywords: Control applications
Abstract: In this paper, a modeling-free inversion-based iterative feedforward control scheme is designed for single-input single-output piezoelectric actuators with rate-dependent hysteresis nonlinearities. The adopted scheme only utilizes input-output data of the controlled system to start a non-causal learning process, and to achieve the desired performance. The experimental results show that both the root-mean-square and relative error of the output tracking are significantly reduced after 3 iterations. The relative tracking error of a sine wave signal is less than 0.3% and the relative tracking error of a triangle wave signal is less than 0.91%, both of which can meet the actual engineering needs.

Keywords: Estimation, Control applications
Abstract: Modulating functions method is a non-asymptotic estimation method, which provides accurate and robust estimations of states, parameters, and inputs for different classes of systems, which include unknown linear ordinary differential systems, fractional systems and linear partial differential equations. In the case of time or space varying unknown, the method requires the decomposition of the unknown into predefined basis functions. However, the estimation performance will depend on the nature of the basis functions which in some cases are not easy to determine. This paper proposes a new iterative learning-based modulating functions method, which combines the standard modulating functions with a dictionary learning procedure. The dictionary learning step allows the determination of an appropriate set of functions to decompose the unknown, while the modulating function step allows the non-asymptotic and robust estimation of the projection coefficients. The performance of the proposed method is illustrated in a distributed solar collector application, modeled by partial differential equations and where the unknown solar irradiance is estimated.

Keywords: Iterative learning control, Control applications
Abstract: Iterative learning control (ILC) is an effective control technique to enhance system performance. ILC requires the system to execute identical operations repetitively such that the system performance can be improved by learning from previous iterations. To remove the requirement of repetitive operation, this paper leverages recent advances in deep learning and proposes a new ILC scheme, named Deep ILC, with detailed formulation, analysis, and validation. The proposed Deep ILC consists of two main components, the long short-term memory (LSTM) neural network based prediction and the optimization based learning filter design. In particular, we formulate the learning filter design problem into an optimization problem by purposely constructing an augmented dynamic feedback system, of which the to-be-designed learning filter is in the feedback loop. The proposed Deep ILC is applied to the trajectory tracking of quadrotor unmanned aerial vehicles (UAVs) and its effectiveness is validated through experimental studies.

Keywords: Machine learning, Emerging control applications, Markov processes
Abstract: Supplemental lighting in greenhouses has contributed to an improvement in crop growth. However, lighting costs account for a large portion of greenhouse expenses; as a result, it is important to find optimal lighting strategies to minimize supplemental lighting costs. Although light-emitting diodes (LEDs) with precise and quick dimmability are becoming a popular choice for greenhouse supplemental lighting, other common types of horticultural lights, such as high-intensity discharge (HID) lamps, are still used in greenhouses. In this work, we formulate the supplemental lighting control problem in greenhouses equipped with HID lamps as a discrete constrained optimization problem. We aim to minimize electricity costs of supplemental lighting considering sunlight prediction, plant light needs, and variable electricity pricing in our model. By combining Q-learning and method of multipliers, we determine the optimal solution of this discrete optimization problem and then evaluate its performance through exhaustive simulation studies using a whole year of data for a site located at West Virginia. Compared to a heuristic method, which supplies a fixed minimum photosynthetic photon flux density (PPFD) to plants at each time step during the day, the proposed strategy shows about 44% (on average) electricity cost reduction throughout the year.

Keywords: Autonomous systems, Control applications, Robotics
Abstract: Autonomous underwater vehicles (AUVs) find many applications in oceanography, environmental research, and inspection and maintenance of subsea energy assets. Subsea Resident AUVs remain in subsea for extended periods of time which could last for several months. Maintaining depth using traditional hard actuators (HAs) is very energy expensive. Mimicking aquatic creatures, it is shown in this paper that HAs and proposed soft actuators (SAs) can collaborate in a novel way. This collaboration can stabilize AUVs at any desired depth with minimum energy consumption at steady state. This is demonstrated using a laboratory AUV for which a nonlinear dynamic model was developed that uses experimentally validated system parameters. The AUV uses HAs to quickly reach any desired depth, while SAs generate volume change to adjust the system’s buoyancy to maintain neutral buoyancy at the desired depth. In the neutral buoyancy state, the HAs shut off while the SAs stabilize and maintain the depth with virtually zero energy consumption. A control algorithm architecture is developed to manage the HA and SA collaboration. The HAs use a proportional controller with a dead-band, while the SAs use a proportional-derivative-acceleration (PDA) feedback controller. The ability of both types of actuators to mitigate disturbance forces are explored and analyzed. Simulation results show that SAs alone can reject small disturbances while using both SAs and HAs in collaboration can reject large disturbances. Simulation results demonstrate that combining traditional HAs with SAs leads to dynamic performance and very low energy consumption capabilities that cannot be achieved by either one alone.

Keywords: Control applications, Simulation, Computer-aided control design
Abstract: A usage and benchmarks for a new proposed MATLAB tool for efficient evaluation of fractional-order backward differences, sums, differintegrals, and fractional-order differential equations (FODE) are presented in this paper. The tool also supports solving the generalized differential equations formulated with the time-varying fractional orders (VFODE), commonly employed, e.g., in the algorithm of a variable fractional-order PID controller. Optimized C language implementation overpasses other existing popular solutions written mostly in MATLAB scripting language in terms of the computation time. Comparative performance with the FOTF toolbox has been conducted in this paper analyzing the Grunwald-Letnikov-related numerical methods for three example tasks, essential in the modeling and simulation of fractional-order control systems. These are: obtaining values of binomial coefficients (oblivion function); calculating a fractional-order derivative (FOD); solving a fractional-order differential equation (closed-form). A significant increase in performance starting from 70% up to 90% was obtained. Software and binaries described in the paper are available at the referred repository.

Keywords: Maritime control, Control applications, Hybrid systems
Abstract: In this paper, we propose a hybrid adaptive feedback control law for global asymptotic tracking control for marine surface vehicles in the presence of parametric uncertainties. The hybrid feedback is derived from a family of potential functions and employs a hysteretic switching mechanism that is independent of the vehicle velocities. The tracking references are constructed from a given parametrized loop and a speed assignment specifying the motion along the loop. Finally, we provide simulation results for a ship subject to parametric modeling uncertainties and unknown ocean currents.

Keywords: Control applications, Model/Controller reduction, Stability of linear systems
Abstract: Controlling infinite dimensional models remains a challenging task for many practitioners since they are not suitable for traditional control design techniques or will result in a high-order controller too complex for implementation. Therefore, the model or the controller need to be reduced to an acceptable dimension, which is time-consuming, requires some expertise and may introduce numerical error. This paper tackles the control of such a system, namely a continuous crystallizer, and compares two different data-driven strategies: the first one is a structured robust technique while the other one, called L-DDC, is based on the Loewner interpolatory framework.

Keywords: Optimal control, Maritime control, Control applications
Abstract: Pontryagin’s Minimum Principle is a way of solving hybrid powertrain optimal energy management. This paper presents an improvement of a classical implementation. The core of this improvement consists in relaxing the tolerance on some intermediate steps of the algorithm in order to reduce the number of iterations and thereby reducing the number of operations required to compute an optimal solution. The paper describes both a classical implementation of Pontryagin’s Minimum Principle as well as the improved version. Numerical simulations are conducted on an academic example to demonstrate the benefits of the proposed approach.

Keywords: Emerging control applications, Estimation, Adaptive systems
Abstract: Feedback control methodologies have provided scalable solutions to many optimization problems encountered in online programmatic advertising systems. This paper is concerned with the identification of seasonality in Internet user traffic of an advertising campaign, critical for optimal budget delivery and performance management. The seasonality typically manifests itself as a time-of-day (TOD) periodic pattern, which in this paper is modeled by a truncated Fourier series. An adaptive estimation scheme is proposed for the identification of the parameters, running alongside a feedback controller for the advertising campaign. Effectiveness and robustness of the proposed scheme are demonstrated with both simulation and experiment results from real advertising campaigns with the Demand Side Platform (DSP) at Verizon Media.

Keywords: Machine learning, Smart structures, Emerging control applications
Abstract: Automatic optimization of individual thermal comfort in indoor spaces shared by multiple occupants is difficult, because it requires understanding of the individual thermal comfort preferences, modeling of the room thermodynamics, and fast online optimization to account for movements of the occupants. We explore an approach to optimizing individual thermal comfort subject to the seating arrangement of a group of individuals through temperature set-point optimization of Heating, Ventilation, and Air Conditioning (HVAC) equipment. In this paper, we learn both the individual thermal comfort preferences using a weakly supervised approach and the room thermodynamics via static approximations. Finally, we use optimization to determine the HVAC set points that maximize individual thermal comfort subject to the current seating arrangement. The proposed method is tested on a real data set obtained from workers in an open office. The results show that, on average, the temperature in the room at each user's location can be regulated on average to within 0.85C of the user's desired temperature, with a standard deviation of 0.12C.

Keywords: Control applications, Biomedical
Abstract: The goal of the present paper is to apply a pressure field generated by the collapsing bubble in blood under ultrasound to removing blood clots. The Rayleigh–Plesset (RP) equation has been used to obtain a realistic estimate of the bubble’s radius and calculate the collapse pressure within the bubble. Ultrasound frequency has been properly selected to reach the desired pressure to cause a bubble fracture. Moreover, a coupling simulation of the flow and clot structure is performed using the full Navier-Stokes equations, which governs the blood domain, and linearized discrete equations for the clot medium to calculate the desired bubble collapsing pressure necessary to deform the clots, which has immense importance in medical applications. In numerical simulations of this paper, the clot is considered as a solid deformed by flow impulse pressure due to bubble collapse. Simulation results are presented to show the effectiveness of the proposed method.

Keywords: Control applications, Autonomous robots, Mechanical systems/robotics
Abstract: Mobile robots are remarkable cases of highly developed technology and systems. The robot community has developed a complex analysis to meet the increased demands of the control challenges pertaining to the movement of robot. An approach using Explicit Model Predictive Control (MPC) in combination with Sliding Mode Control (SMC) in the context of a decoupling controller is proposed. The MPC works in the outer loop of the control and is used to generate the unique optimal reference trajectory. The generated reference resulting from the convex optimisation problem is to be tracked by the SMC. The SMC works in the inner loop of the proposed control strategy to compensate the nonlinearities. MPC is used over the more common PID strategy as it is able to handle saturation with better tracking and error. Implementation of three possible different SMC strategies such as classical SMC, Finite Time Sliding Mode Control (FTSMC), and Fast Finite Time Sliding Mode Control (FFTSMC) using Matlab/Simulink shows promising results even in the presence of external disturbances. In particular, in the case of FFTSMC, the paper exhibits a Proposition and a Theorem. In particular, the Theorem gives sufficient condition to avoid saturating inputs, while in the meantime preserving asymptotic stability. We were able to validate the approach using simulations to compare outcomes and tune to optimal results.

Keywords: Distributed parameter systems, Traffic control, Multivehicle systems
Abstract: This paper considers a class of cyber-attacks wherein an attacker has the ability to hack into a subset of vehicles driving on a highway, and inject subtle velocity changes in them. By performing such velocity changes, these vehicles (referred to as malicious vehicles) are able to manipulate the velocity/density profile of the non-malicious (normal) vehicles. The malicious and normal vehicles are modeled using a system of Partial Differential Equations (PDEs). A control system is demonstrated, using which, the malicious vehicles are able to modulate the velocity/density profile of the normal vehicles, so as to track a reference profile, chosen by the malicious vehicles. The effects of imperfection in information available to the attacker is considered, and it is seen that if the level of imperfection exceeds a threshold, then the attacker's intent can be foiled. Simulations results are presented.

Keywords: Hybrid systems, Optimal control, Traffic control
Abstract: Multilane traffic is hard to model because of its hybrid nature: continuous dynamics on each lane and discrete event for lane-change. We design a hybrid system, where the lane-changing mechanism has three components: safety, incentive and cool-down time. We model traffic flow using two populations: human-driven vehicles and autonomous vehicles. Recently, a lot of attention was given to control of traffic with autonomous vehicles. We consider the mean-field as one population (human-driven) pass to the limit. Gamma-convergence is proven for optimal control problems at the microscopic scale to the mean-field ones, consisting of coupled controlled hybrid ODEs and Vlasov-type PDE with source terms representing lane-change.

Keywords: Distributed parameter systems
Abstract: Employing mobile actuators and sensors for control and estimation of spatially distributed processes offers a significant advantage over immobile actuators and sensors. In addition to the control performance improvement, one also comes across the economic advantages since fewer devices, if allowed to be repositioned within a spatial domain, must be employed. While simulation studies of mobile actuators report superb controller performance, they are far from reality as the mechanical constraints of the mobile platforms carrying actuators and sensors have to satisfy motional constraints. Terrain platforms cannot behave as point masses without inertia; instead they must satisfy constraints which are adequately represented as path-dependent reachability sets. When the control algorithm commands a mobile platform to reposition itself in a different spatial location within the spatial domain, this does not occur instantaneously and for the most part the motion is not omnidirectional. This constraint is combined with a computationally feasible and suboptimal control policy with mobile actuators to arrive at a numerically viable control and guidance scheme. The feasible control decision comes from a continuous-discrete control policy whereby the mobile platform carrying the actuator is repositioned at discrete times and dwells in a specific position for a certain time interval. Moving to a subsequent spatial location and computing its associated path over a physics-imposed time interval, a set of candidate positions and paths is derived using a path-dependent reachability set. Embedded into the path-dependent reachability sets that dictate the mobile actuator repositioning, a scheme is proposed to integrate collocated sensing measurements in order to minimize costly state estimation schemes. The proposed scheme is demonstrated with a 2D PDE having two sets of collocated actuator-sensor pairs onboard mobile platforms.

Keywords: Distributed parameter systems, Optimal control, Agents-based systems
Abstract: This paper proposes an optimization framework for steering a team of mobile actuators to control a diffusion process with unknown initial conditions. The optimization problem seeks a guidance strategy that minimizes the quadratic cost of controlling the diffusion process subject to the worst possible initial condition and the quadratic cost of steering the mobile actuators. We turn the problem into an unconstrained optimization and use a gradient-descent method to solve it. The solution of the proposed problem is suboptimal for the same problem with a known initial condition---even for the worst-case initial condition. This suboptimality property suggests the guidance strategy can be implemented when the initial condition of the diffusion process is unknown. A numerical example compares solutions with known and unknown initial conditions.

Keywords: Optimal control, Machine learning, Distributed parameter systems
Abstract: In this letter we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations arising in optimal feedback control. Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. We train the augmented models on data generated without discretizing the state space, enabling application to high-dimensional problems. We use the proposed method to design a candidate optimal regulator for an unstable Burgers' equation, and through this example, demonstrate improved robustness and accuracy compared to existing neural network formulations.

Keywords: Distributed parameter systems, Control applications, Modeling
Abstract: This paper presents an enthalpy based full-state feedback control law with respect to a reference solution for a one-phase Stefan problem under unknown boundary input hysteresis. The one-phase Stefan problem describes the evolution of the temperature and the liquid-solid interface location in a solidifying material. In this paper, this setting is used to model an industrial continuous casting process, which produces nearly all steel currently used worldwide. Regulation of both the steel temperature and the liquid-solid interface location history is the key to the steel quality. Experiments have revealed the existence of hysteresis due to boiling of the cooling water at the surface of the outer (solid) boundary of the solidifying steal shell. This work addresses this difficulty by considering control of the Stefan problem with unknown boundary hysteresis. To reduce the problem complexity, the hysteresis effect uncertainty is represented through the changing parameters. Then, the hysteresis inverse is designed and the recalibration method for the hysteresis inverse is proposed. Simulation results are provided, showing that under this setting, both the temperature and the interface location converge to the reference states.

Keywords: Estimation, Stability of nonlinear systems, Distributed parameter systems
Abstract: In this paper we propose a method for adaptive sampling using Unmanned Aerial Vehicles (UAVs) in oil spill management. The goal is to measure and estimate oil spill concentrations at the sea surface, while at the same time identify the leak rates of sources at known positions. First we construct a cost which approximates the benefit of sampling locations at specific times. This cost is based on measures of observability and persistency of excitation for the oil spill model. A receding horizon Mixed-Integer Linear Programming (MILP) problem is solved in order to find UAV trajectories which are optimal with respect to the cost. For UAV trajectory tracking we use a Lyapunov based controller. The oil spill concentration measurements taken by the UAVs by following these tracks are used in an adaptive observer, which provides state (concentration) and parameter (leak rate) estimates. Under the assumption that the sampling strategy described above lead to uniform complete observability and persistency of excitation, we prove Uniform Global Asymptotic Stability (UGAS) of the state estimation, parameter identification and UAV trajectory tracking errors. Finally, we provide a simulation of the proposed strategy, and compare it with two other strategies.

Keywords: Robust control, Predictive control for linear systems, Distributed parameter systems
Abstract: The design of a Robust Model Predictive Control for an unstable coupled ODE-PDEs system is considered in this work. The proposed design takes into account the uncertainty in the model's parameters and state feedback to stabilize the system while satisfying input and output constraints. The discrete-time representation of the system is obtained by application of the Cayley-Tustin discretization. For the stabilization, the stability constraint is considered such that the unstable eigenmodes are canceled. Finally, the simulations show the performance of the designed controller for proper stabilization and constraint satisfaction, while taking into account model uncertainty.

Keywords: Identification for control, Automotive systems, Automotive control
Abstract: Many control vehicle systems are based on the knowledge of the current load. This trend has recently emerged also in heavy-duty and agricultural vehicles. Knowing the mass has in fact benefits both on safety and driving comfort. This paper proposes a mass estimation algorithm, based on already available sensors for an agricultural tractor equipped with a Continuously Variable Transmission. To this aim, the transmission model is derived, as the key ingredient of the mass estimate is the preliminary knowledge of the wheel torque. The latter, however, may be useful also for other control purposes, concerning, for example, longitudinal dynamics control. In the paper, the estimators proposed are applied on real world data.

Keywords: Estimation, Autonomous systems, Sensor networks
Abstract: We consider path-planning for a mobile agent in an unknown environment to be mapped by a sensor network, where the location and field of view of each sensor can be configured. To solve this problem we propose a coupled sensor configuration and path-planning (CSCP) iterative method, which finds an optimal sensor configuration (location and FoV) at each iteration, applies Gaussian process regression to construct a threat field estimate, and then finds a candidate optimal path with minimum expected threat exposure. We define a so-called task-driven information gain (TDIG) metric, the maximization of which provides sensor configurations. The TDIG quantifies the notion of acquiring sensor data of "most relevance" to path-planning. The CSCP iterations terminate when the path cost variance reduces below a prespecified threshold. Through numerical simulations we demonstrate that the CSCP algorithm finds near-optimal paths with significantly fewer sensor measurements compared to traditional methods.

Keywords: Estimation, Filtering, Sensor fusion
Abstract: Terrain Aided Navigation (TAN) provides a drift-free navigation approach for Unmanned Underwater Vehicles. This paper focuses on an improved version of the Weighted Ensemble Kalman Filter (WEnKF) to solve the TAN problem. We analyze some theoretical limitations of the WEnKF and derive an improved version which ensures that the asymptotic variance of weights remains bounded. This improvement results in an enhanced robustness to nonlinearities in practice. Numerical results are presented and the robustness is demonstrated with respect to conventional WEnKF, yielding twice as less non-convergence cases.

Keywords: Optimization algorithms, Estimation, Machine learning
Abstract: We develop an online convex optimization method for predicting time series based on streaming observations. We first approximate the evolution of time-varying autoregressive integrated moving average (ARIMA) processes and then propose a discounted online Newton method for estimating time-varying ARIMA time series. Under practical assumptions, we establish dynamic regret bounds that quantify the tracking performance of our algorithm. To verify the effectiveness and robustness of our method, we conduct experiments on prediction problems based on both artificial data and real-world COVID-19 data. To the best of our knowledge, we are the first to report a COVID-19 prediction that utilizes online learning.

Keywords: Estimation, Optimization, Machine learning
Abstract: To handle optimization with only historical data, we present a novel learning framework combining parametric estimation and pricing optimization in the multi-product pricing problem. Motivated by the existence of errors, we first introduce the task-based learning with decision bias for handling estimation errors, which can lead to better decision making under demand parameter uncertainty. Then, we follow the idea of model-free learning, which can design better revenue estimators without knowing the parameter structure to handle model misspecification. Furthermore, to design a more robust estimator, we incorporate the boosting idea to combine a number of estimators for more robust pricing. We validate the superior performance of this framework with numerical studies.

Keywords: Distributed control, Estimation, Stochastic systems
Abstract: This paper considers the multi-agent persistent monitoring problem defined on a network (graph) of nodes (targets) with independent uncertain states. The agent team's goal is to persistently observe the target states so that an overall measure of estimation error covariance evaluated over a finite period is minimized. Each agent's trajectory is fully defined by the sequence of targets it visits and the corresponding dwell times spent at each visited target. To find the optimal set of agent trajectories for this estimation task over the network, we develop a distributed on-line agent controller that requires each agent to solve a sequence of receding horizon control problems (RHCPs) in an event-driven manner. We use a novel objective function form for these RHCPs to optimize the effectiveness of this distributed estimation process and establish its unimodality under certain conditions. Finally, extensive numerical results are provided, indicating significant improvements compared to other agent control methods.

Keywords: Estimation, Filtering, Modeling
Abstract: A major challenge in moving average (MA) estimation is the selection of an appropriate averaging window length or timescale over which measurements remain relevant to the estimation task. Prior works typically perform timescale selection by examining multiple window lengths (or models) before selecting the ‘optimal’ one using heuristics, domain knowledge expertise, goodness-of-fit, or information criterion (e.g. AIC, BIC etc.). In the presented work, we propose an alternative mechanism based on Allan Variance (AVAR) that obviates the need for assessing multiple models and systematically reduces reliance on heuristics or rules-of-thumb. The Allan Variance approach is used to identify the timescale that minimizes bias, thus determining the timescale over which past information remains most relevant. We also introduce an alternative method to obtain AVAR for unevenly-spaced timeseries. The results from moving average estimation using an Allan Variance-determined window length are compared to the optimal moving average estimator that minimizes mean square error (MSE) for a variety of signals corrupted with Gaussian white noise. While the relevant timescales determined through AVAR tend to be longer than those associated with minimum MSE (i.e. AVAR-based MA estimation requires more measurements spread over a longer period of time), the AVAR-based moving average approach provides a valuable, systematic technique for near-optimal simple moving average estimation.

Keywords: Estimation, Kalman filtering, Agents-based systems
Abstract: In this paper the tracking problem of multi-agent systems, in a particular scenario where a segment of agents entering a sensing-denied environment or behaving as non-cooperative targets, is considered. The focus is on determining the optimal sensor precisions while simultaneously promoting sparseness in the sensor measurements to guarantee a specified estimation performance. The problem is formulated in the discrete-time centralized Kalman filtering framework. A semi-definite program subject to linear matrix inequalities is solved to minimize the trace of precision matrix which is defined to be the inverse of sensor noise covariance matrix. Simulation results expose a trade-off between sensor precisions and sensing frequency.

Keywords: Sensor fusion, Estimation, Filtering
Abstract: In this paper we develop the Multiple Model Particle Filter (MMPF) for nonlinear systems. The particle filter is used to estimate the conditional probability for the modes while the Conjugate Unscented Transform (CUT) based Kalman filter is used to estimate the dynamical state of the system. The resultant particle filter is a bank of nonlinear filters with the sequence of modes given by the samples. A tracking example is used to illustrate the working and efficacy of the MMPF with respect to the Interactive Multiple Model (IMM) filter. Comparison results are shown using the Extended Kalman filter and Conjugate Unscented Kalman filter for both the MMPF and IMM filters.

Keywords: Cellular dynamics, Estimation, Observers for nonlinear systems
Abstract: Dorsal closure is an essential step during Drosophila development through which a hole is sealed in the dorsal epidermis and serves as a model for cell sheet morphogenesis and wound healing. It involves the dynamic regulation of cell machinery to bring about shape changes, mechanical forces, and emergent properties. In this paper a modeling framework is developed to provide insights into the regulation of dorsal closure. Towards this end, a moving horizon estimator is used to estimate the cell’s dynamics written under the form of quasi-linear parameter-varying system with bounded unknown parameter. We perform estimation through the minimization of the least-squares moving horizon cost w.r.t both state variables and variable parameter simultaneously. Simulation results are reported to verify the derived results.

Keywords: Estimation, Automotive control, Automotive systems
Abstract: In semi-active suspensions, the damping force is not regulated by acting directly on the damping ratio itself, but rather on a related variable, usually a current. Unfortunately, the same current may produce different damping ratios, depending on the status of the shock absorber. Many unpredictable factors modify the damper behavior, such as aging, temperature, or damages. In this paper, we propose an on-line, computationally efficient, damping estimation algorithm for electronic suspensions. The approach is based only on inertial measurements signals already available on-board. Experiments performed on a real vehicle proved the effectiveness of our approach.

Keywords: Mechatronics, Robotics
Abstract: is paper investigates actuator fault detection in linear systems with a large number of actuators. We consider some of the most common actuator faults such as actuator loss of effectiveness and fatigue crack in the connection hinges. We use transmissibility operators, which are mathematical models that characterize the relationship between sensors in an underlying system, for fault detection of actuators. Transmissibilities identified under healthy conditions can be used along with measurements of healthy sensors to predict other sensors measurements without knowledge of the dynamics of the system or the excitation that acts on the system. We apply the proposed approach to an analytical model with twelve actuators, and an experimental setup consisting of twelve electromechanical actuators and two accelerometers.

Keywords: Fault diagnosis, Pattern recognition and classification, Neural networks
Abstract: Fault diagnosis is an important way to ensure the operation security in complex industrial processes. Considering the inherent multiscale characteristics and time dependency about industrial process monitoring data, a novel fault diagnosis method based on multiscale temporal convolutional network (MS-TCN) was proposed in this paper. Firstly, different from the widely used time-domain features with one single scale, the multiscale time-frequency information extracted with the discrete wavelet transform was also introduced to represent the raw data. And a temporal convolutional network was then combined to capture longer-term temporal feature from the sequential processing data. The experimental results on the Tennessee Eastman process indicated that, our proposed method outperformed these state-of-the-art fault diagnosis methods, especially for the 3 incipient faults hard to classify.

Keywords: Large-scale systems, Sensor networks, Optimal control
Abstract: Recent years have seen an increased interest in using mean-field density based modelling and control strategy for deploying robotic swarms. In this paper, we study how to dynamically deploy the robots subject to their physical constraints to efficiently measure and reconstruct certain unknown spatial field (e.g. the air pollution index over a city). Specifically, the evolution of the robots' density is modelled by mean-field partial differential equations (PDEs) which are uniquely determined by the robots' individual dynamics. Bayesian regression models are used to obtain predictions and return a variance function that represents the confidence of the prediction. We formulate a PDE constrained optimization problem based on this variance function to dynamically generate a reference density signal which guides the robots to uncertain areas to collect new data, and design mean-field feedback-based control laws such that the robots' density converges to this reference signal. We also show that the proposed feedback law is robust to density estimation errors in the sense of input-to-state stability. Simulations are included to verify the effectiveness of the algorithms.

Keywords: Sensor fusion, Sensor networks, Estimation
Abstract: When performing decentralized data fusion, one of the major challenges is the well-known "track-to-track" correlation problem. One approach to handling this correlation is to use correlation-agnostic fusion techniques that generate conservative estimates of the fused probability distribution, irrespective of the amount of common information present. When working with Gaussian distributions, past approaches have only considered the covariance of the input distributions to compute the covariance of the fused distribution. In this paper, we introduce another constraint that considers the means of the input distributions. While this constraint cannot 100% guarantee the output is conservative, it can "probabilistically" -- to a user-specified certainty -- ensure the output is conservative. This introduction of a probabilistic bound enables fused probability distributions with less excess covariance. Specifically, we modify the ellipsoidal intersection technique to include the probabilistically conservative constraint. We present results that show using the probabilistic bound generates a fused distribution that is still conservative but with less excess covariance than Ellipsoidal Intersection without the probabilistic constraint.

Keywords: Statistical learning, Large-scale systems, Sensor networks
Abstract: We consider the model of cooperative learning via distributed non-Bayesian learning, where a network of agents tries to jointly agree on a hypothesis that best described a sequence of locally available observations. Building upon recently proposed weak communication network models, we propose a robust cooperative learning rule that allows asynchronous communications, message delays, unpredictable message losses, and directed communication among nodes. We show that our proposed learning dynamics guarantee that all agents in the network will have an asymptotic exponential decay of their beliefs on the wrong hypothesis, indicating that the beliefs of all agents will concentrate on the optimal hypotheses. Numerical experiments provide evidence on a number of network setups.

Keywords: Automotive control, Delay systems, Automotive systems
Abstract: In this paper, we design an energy-optimal longitudinal controller for connected automated trucks driving in mixed traffic with lean penetration of connected vehicles. The controller utilizes information received via vehicle-to-vehicle connectivity from vehicles traveling ahead of the truck, and additional delays are introduced into the control law to improve energy efficiency. We evaluate the robustness of the energy-optimal control parameters and calculate the amount of energy benefits. Simulation results show 18% improvement of energy efficiency compared to a non-connected design, and 3% improvement compared to the connected design without additional delay.

Keywords: Optimal control, Hybrid systems, Numerical algorithms
Abstract: This paper discusses the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This paper introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.

Keywords: Autonomous systems, Control applications, Automotive systems
Abstract: In this paper we consider the problem of navigation and motion control in an area densely populated with other agents. We propose an algorithm that, without explicit communication and based on the information it has, computes the best control action for all the agents and implements its own. Notably, the host agent (the agent executing the algorithm) computes the differences between the other agents' computed and observed control actions and treats them as known disturbances that are fed back into a robust control barrier function (RCBF) based quadratic program. A feedback loop is created because the computed control action for another agent depends on the previously used disturbance estimate. In the case of two interacting agents, stability of the feedback loop is proven and a performance guarantee in terms of constraint adherence is established. This holds whether the other agent executes the same algorithm or not.

Keywords: Automotive control, Optimal control, Predictive control for nonlinear systems
Abstract: A priori information about the future traffic conditions along the planned route can be essential for optimal hybrid powertrain energy management. However, due to the limited sensor range of a single vehicle, it cannot be acquired locally. In recent time, V2X (decentralized wireless vehicle to everything) has been receiving much attention as a way to obtain and share information from different distributed sources. V2X data can provide updated information on traffic at different locations. Still, this information will be obsolete when the corresponding positions are reached due to changing traffic, and an optimal strategy based on outdated information may not bring the full benefit. Against this background, we propose a method based on a velocity prediction approach which utilizes V2X data currently available in the market in combination with historical data, to obtain a prediction of the expected traffic conditions at in the close future. Actual measurements on a city highway in Linz, Austria, are used to estimate the potential of the approach. Even for rather mild changes in traffic conditions, a reduction of up to 4% in terms fuel consumption over this track was found, confirming the potential benefit of this method.

Keywords: Simulation, Traffic control, Automotive control
Abstract: The ability of connected and autonomous vehicles (CAVs) to share information such as road friction and geometry has the potential to improve the safety, capacity, and efficiency of roadway systems, and the study of these systems often necessitates synergistic investigation of the vehicle, traffic behavior, and road conditions. This paper presents a micro-simulation framework for studying CAVs behavior and control utilizing a traffic simulator, chassis simulation, and a shared roadway friction database. The simulation utilizes three levels of data representations: 1) a traffic representation that explains how vehicles interact with each other and follow location-specific rules of the road, 2) a vehicle dynamic representation of the Newtonian response of the vehicle to driver inputs interacting with the vehicle which in turn interacts with the pavement, and finally 3) a road surface representation that represents how friction of roadway changes with space and time. The interactions between these representations are mediated by a spatiotemporal database. The framework is demonstrated through a CAVs application example showing how the mapping of road friction enables advanced vehicle control by allowing the database-mediated preview of road friction. This framework extends readily to real-time implementation on actual CAVs systems, providing great potential for improving CAVs control performance and stability via database-mediated feedback systems, not only in simulation, but also in practice.

Keywords: Automotive systems, Automotive control, Modeling
Abstract: Oncoming vehicle high-beams pose a potential risk to the object detection performance of cameras in autonomous driving. In this scenario, modeling stochastic human driving behavior becomes a challenging task. This paper provides an integrated framework that generates appropriate driving operations to handle the oncoming high-beams scenario based on human driver data. By decomposing human drivers’ pedal and steering signals, a parallel autoregressive input-output hidden Markov model (p-AIOHMM) is developed to capture the temporal dependencies of the decomposed driving actions. Besides, parallel generative adversarial networks (p-GAN) are proposed to reconstruct the pedal positions and the steering angles from the p-AIOHMM-based actions. All the parameters can be learned from the naturalistic driver data. Experimental results have verified that the developed parallel AIOHMMGAN solution can perform a better task of driving behavior generation when suffering from oncoming high beams.

Keywords: Modeling, Automotive control
Abstract: Hazardous and inevitable tire blowout accidents significantly threaten vehicle stability and road safety, and need to be safely controlled. An authentic model to describe tire blowout impacts on vehicle dynamics is crucial for model-based control design. However, existing vehicle models typically simplify the forces and/or moments caused by tire blowout as continuous and smooth (differentiable) disturbances, and thus consist of normal linear or nonlinear ordinary differential equations (ODEs). To accurately describe tire blowout impacts that correspond to an intensive and quick physical process, this paper proposes a new control-oriented vehicle model through an impulsive differential system (IDS) approach. In the IDS-based vehicle model, the lateral force and moment caused by tire blowout, are described by impulsive inputs that are not differentiable. Consequently, vehicle states are modeled by impulsive differential equations instead of ODEs. Through both simulation and experimental results, the proposed IDS-based control-oriented model is more accurate than existing models in describing tire blowout impacts on vehicle dynamics. The developed model will benefit the control design of tire blowout to ensure vehicle stability and safety on road.

Keywords: Autonomous systems, Autonomous vehicles, Robotics
Abstract: This paper presents a control method for vehicles with first-order nonholonomic constraints that guarantees asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in front of the vehicle can be controlled to track a desired trajectory, albeit with a steady-state error. To eliminate steady state error, a sufficiently smooth trajectory is reformulated for the new reference point such that, when tracking the new trajectory, the vehicle asymptotically converges to the original trajectory. The results of the control method are evaluated to view the effects of errors due to estimation and initial conditions.

Keywords: Aerospace, Computational methods, Lyapunov methods
Abstract: This paper concerns the robustness of attitude controllers for dynamics configured on the SO(3) manifold and poses a set of bilinear matrix inequalities to find an optimal controller tuning with respect to (i) the ultimate bound of the error-state trajectories when perturbed by naturally arising disturbances, and (ii) the worst-case decay rate of the tracking errors. The presented optimization problem can be solved both to generate a robust tuning for experimental applications, and also to facilitate qualitative comparisons of different attitude controllers present in the literature. To solve the tuning problem, we propose an algorithm based on alternating semidefinite programming, with local linearizations of an upper bound of the associated cost function. The soundness of this approach is illustrated by comparison to an interior-point method. The algorithm is subsequently used to provide insights for the tuning of the considered controllers and finally demonstrated by a closed-loop simulation example.

Keywords: Air traffic management, Autonomous systems, Transportation networks
Abstract: Urban air mobility, in which air transportation is used for relatively short trips within a city or region, is emerging as a possible component in future transportation networks. In this paper, we study the problem of how to schedule urban air mobility trips when travel times are uncertain. Unlike in ground transportation, urban air mobility scheduling has to take into account that there is limited landing capacity at each destination, and for safety reasons, it must be guaranteed that an air vehicle will be able to land before it can be allowed to take off. We first present a network model for an on-demand urban air mobility service with uncertain travel times and limited landing capacity at nodes. For the practically relevant special case of one final destination and many origins, we give necessary and sufficient conditions for a feasible schedule to exist for a given demand of flights. Next, we present a mixed integer program for obtaining an optimal schedule in this case. The paper concludes with a numerical study for a previously proposed urban air network in the city of Atlanta, Georgia.

Keywords: Flight control, Feedback linearization, Optimization
Abstract: Current control methods for winged eVTOL UAVs consider the vehicle primarily as a fixed-wing aircraft with the addition of vertical thrust used only during takeoff and landing. These methods provide good long-range flight handling but fail to consider the full dynamics of the vehicle for tracking complex trajectories. We present a trajectory tracking controller for the full dynamics of a winged eVTOL UAV in hover, fixed-wing, and partially transitioned flight scenarios. We show that in low- to moderate-speed flight, trajectory tracking can be achieved using a variety of pitch angles. In these conditions, the pitch of the vehicle is a free variable which we use to minimize the necessary thrust, and therefore energy consumption, of the vehicle. We use a geometric attitude controller and an airspeed-dependent control allocation scheme to operate the vehicle at a wide range of airspeeds, flight path angles, and angles of attack. We provide simulation results and theoretical guarantees for the stability of the proposed control scheme assuming a standard aerodynamic model.

Keywords: Lyapunov methods, Aerospace, Stability of nonlinear systems
Abstract: This paper concerns trajectory tracking control of attitude dynamics configured on SU(2). Inspired by a popular geometric tracking controller on SO(3), differential geometric tools are used to derive both continuous and discontinuous attitude controllers on the SU(2) manifold, relating these to preexisting controllers operating with imaginary quaternion errors. Additionally, a robustness result is given for the controllers on SU(2), which is illustrated by simulation examples.

Keywords: Aerospace
Abstract: The availability of a swift, reliable and efficient algorithm to design the path of UAVs is very critical in overall mission planning of any task. This study utilizes the concepts of fluid analogy to design an algorithm for path planning of UAVs to move around the static and dynamic obstacles in a 3D environment. The algorithm has been structured around the improved and modified version of Interfered Fluid Dynamical System (IFDS). Firstly the concept has been established and validated for static obstacles, and subsequently multiple obstacles in motion have been introduced. Simulation results demonstrate the effectiveness of the model.

Keywords: Discrete event systems, Optimal control, Aerospace
Abstract: This paper proposes an overarching trajectory-power-propulsion co-optimization framework by incorporating actual discrete operation modes of electric thrusters within the optimal control formulation of spacecraft trajectory design. An interplanetary trajectory from Earth to comet 67P/Churyumov–Gerasimenko is formulated and solved using a spacecraft that is equipped with a thruster with 21 operation modes. It is the first time a systematic methodology is devised to select the most optimal operation modes in accordance with Pontryagin’s minimum principle (PMP) to solve a textit{payload-maximization} trajectory design problem. It is also shown that there is a possibility to obtain near-optimal solutions with a reduced number of modes and negligible loss of optimality. The maximum payload useful mass solution is shown to have a significant advantage over the traditional textit{final-mass-maximization} formulation.

Keywords: Optimization, Aerospace, Fault diagnosis
Abstract: It is essential to detect hypervelocity impact damage of spacecraft. We propose an enhanced algorithm for representative thermal response point selection of infrared thermal response sequences to derive features in this paper. The discrepancies between the selected representative points and the coherence of the representative points within their category are taken into account simultaneously in this algorithm. For better fitting the complex detection needs of spacecraft to select regionally representative thermal response points, Boundary Intersection Approach with penalty term is adopted to do the decomposition part of the multi-objective functions. Associated experiments and comparative analysis are described to substantiate the effectiveness of our algorithm for defect detection.

Keywords: Optimization algorithms, Aerospace, Pattern recognition and classification
Abstract: Advances in the aerospace industry have made reusable spacecraft increasingly important. However, hypervelocity impact damage will seriously affect the performance of aerospace materials. Detecting the impact damage of space debris is an urgent problem to be solved. In addition, there is also the problem of a large area of aerospace materials, and the testing equipment can only handle a partial area. Therefore, this paper proposes an automatic recognition and reconstruction model of local damage regions based on infrared sequence, and proposes an optimized mosaic algorithm for mosaic damage reconstructed images based on matching optimization.

Keywords: Mechanical systems/robotics, Feedback linearization
Abstract: The problem of energy-based orbital stabilization of underactuated mechanical systems with one passive degree-of-freedom is addressed. The orbit is a manifold where the active generalized coordinates are fixed and the total mechanical energy is equal to some desired value. A hybrid control strategy comprised of continuous and intermittent impulsive inputs is presented. The continuous controller is designed using partial feedback inearization to converge the active generalized coordinates to their desired values. The choice of desired energy characterizes a unique orbit which is stable but not asymptotically stable. To stabilize the desired orbit, a Poincar'e section is constructed at a fixed point and the Poincar'e map is linearized about the fixed point. This results in a discrete LTI system. To stabilize the desired orbit, impulsive inputs are applied when the system trajectory crosses the Poincar'e section. The applicability of the control design is demonstrated by stabilization of the homoclinic orbit of the cart-pendulum system.

Keywords: Mechanical systems/robotics, Quantitative feedback theory, Mechatronics
Abstract: A linear controller for the unstable flywheel inverted pendulum (also known as a reaction wheel inverted pendulum or inertia wheel pendulum) is designed using Quantitative Feedback Theory (QFT) to provide response that stays withing upper and lower bounds in the face of significant variations of the plant parameters. A mathematical model of the plant, including both the mechanics of the pendulum and the electromechanics of the motor, is derived. Simulation is used to compare performance of the QFT controller to that of simple PID compensation. It is shown that while the QFT controller consistently satisfies the robust performance bounds for all plant uncertainty in both frequency and time domains, the PID controller fails to provide robust tracking performance.

Keywords: Mechanical systems/robotics, Robotics, Optimization algorithms
Abstract: This paper presents a new path planning procedure for transportation tasks of three degrees of freedom tower cranes assuming a known, regularly updated and quadratic obstacle map derived by imaging sensors. Key objectives are the identification of either short, energy-efficient or low exciting load sway paths and the capability to be combined with an anti-sway controller and its trajectory generation module. An exact cell decomposition is carried out for the workspace of the tower crane introducing cells in the shape of circle parts. The height of each cell is determined considering the payload dimensions to ensure collision free paths. Moreover, a graph is derived by assigning a node to each cell and connecting the neighbors with circle arcs in tangential direction and lines in radial direction. The path finding is carried out utilizing an extended version of the novel graph searching algorithm L^*. The extension follows from the fact that the height costs depend on the investigated path and thus need to be considered during the search. A simulation example of a realistic scenario is provided in order to discuss the generated paths.

Keywords: Mechanical systems/robotics, Variable-structure/sliding-mode control, Robotics
Abstract: The precise motion control of a multi-degree of freedom~(DOF) robot manipulator is always challenging due to its nonlinear dynamics, disturbances, and uncertainties. Because most manipulators are controlled by digital signals, a novel higher-order sliding mode controller in the discrete-time form with time delay estimation is proposed in this paper. The dynamic model of the manipulator used in the design allows proper handling of nonlinearities, uncertainties and disturbances involved in the problem. Specifically, parametric uncertainties and disturbances are handled by the time delay estimation and the nonlinearity of the manipulator is addressed by the feedback structure of the controller. The combination of terminal sliding mode surface and higher-order control scheme in the controller guarantees a fast response with a small chattering amplitude. Moreover, the controller is designed with a modified sliding mode surface and variable-gain structure, so that the performance of the controller is further enhanced. We also analyse the condition to guarantee the stability of the closed-loop system in this paper. Finally, the simulation and experimental results prove that the proposed control scheme has a precise performance in a robot manipulator system.

Keywords: Mechatronics, Energy systems, Smart structures
Abstract: A self-powered system is a control actuation technology that derives all energy to power its operations, from the dynamic response of the plant in which it is embedded. In order to maintain persistent operation, it must not exhaust its rechargeable energy storage subsystem. If the technology were perfectly efficient, this constraint would require that feasible feedback laws be passive. In the non-ideal case the constraint is more restrictive than mere passivity, because it must account for dissipations in the transduction network. One of the most significant factors limiting overall efficiency is the dissipation incurred when power is transmitted to or from storage. In the presence of these losses, the domain of feasible control laws includes a sub-domain of static colocated feedback laws, for which a certain static constraint holds for the feedback gain matrix. To obtain superior performance, this static feedback gain can be adapted in real-time, based on feedback measurements. This paper presents a nonlinear control design technique that accomplishes this adaptation while also guaranteeing feasibility. Although sub-optimal, the technique is guaranteed to improve upon the performance of the optimized static gain. The methodology is demonstrated in a simulation example pertaining to the self-powered control of a five-story civil structure subjected to seismic excitation.

Keywords: Mechatronics, Fault detection, Closed-loop identification
Abstract: Fault detection is essential in precision mechatronics to facilitate maintenance and minimize operational downtime. The aim of this paper is to develop a systematic procedure from identification to accurate nullspace-based fault diagnosis, accounting for the influence of noise and interaction in multivariable closed-loop control configurations. The influence of noise and interaction on the model estimate and fault diagnosis system are investigated through the use of closed-loop operators and by means of an illustrative case study.

Keywords: Mechatronics, Hybrid systems, Constrained control
Abstract: Despite many accomplishments by legged robot designers, state-of-the-art bipedal robots are prone to falling over, cannot negotiate extremely rough terrains and cannot directly regulate unilateral contact forces. Our objective is to integrate merits of legged and aerial robots in a single platform. We will show that the thrusters in a bipedal legged robot called Harpy can be leveraged to stabilize the robot's frontal dynamics and permit jumping over large obstacles which is an unusual capability not reported before. In addition, we will capitalize on the thrusters action in Harpy and will show that one can avoid using costly optimization-based schemes by directly regulating contact forces using an Reference Governor (RGs). We will resolve gait parameters and re-plan them during gait cycles by only assuming well-tuned supervisory controllers. Then, we will focus on RG-based fine-tuning of the joints desired trajectories to satisfy unilateral contact force constraints.

Keywords: Optimal control, Mechanical systems/robotics, Stability of linear systems
Abstract: Walking on slippery surfaces presents a challenge for bipedal walkers. A moving contact point between a biped foot and the ground introduces nonlinearities, which are usually not explicitly captured in the existing biped dynamics models. This work uses a two-mass linear inverted pendulum (LIP) model to describe the dynamics of walking gait in both the presence and absence of a foot slip. A single optimization-based controller is presented for control of both the normal walking and slip gait. The appropriate control strategy is determined by recoverability analysis. Based on the current state of the walker that lies within the recoverable or the fall-prone set, the proposed algorithm determines single and multiple step targets that lead the walker to recover to either the stationary configuration or to the periodic gait, respectively. An optimal control is designed within every swing phase to track the target states. When the within-step control is not sufficient, the algorithm searches for the optimal foot placement location and commands a recovery step to regain stability. The performance of the proposed control algorithm is validated by simulation, and results demonstrate successful recovery for within step and multi-step recovery of a walker.

Keywords: Reduced order modeling, Predictive control for linear systems, Simulation
Abstract: Wind farms are high order systems whose dynamics are governed by non linear partial differential equations with no known analytic solution, making the design and implementation of numerical optimal controllers in high fidelity fluid dynamics solvers computationally expensive and unsuitable for real time usage. Reduced order state models provide a possible route to the design and implementation of practical cooperative wind farm controllers. This work makes use of an innovative algorithm in the context of wind farm modelling - Input Output Dynamic Mode Decomposition - to find suitable reduced order models to be used for model predictive control. The contribution of the work in this article resides in deriving a reduced order model from high fidelity simulation data where wake redirection control by yaw misalignment is evaluated. A model based predictive controller is designed and tested. In the present case study it is shown that a reduced order linear state space model with 37 states can accurately reproduce the downstream turbine generator power dynamics with a fit of 88%, reconstruct the upstream turbine wake with an average normalised root mean squared error of 4% and that optimal controllers can be designed for a collective power reference tracking problem.

Keywords: Energy systems, Simulation, Stochastic systems
Abstract: Wake steering is a wind farm control strategy in which upstream turbines operate with a yaw misalignment to deflect their wakes away from downstream turbines, yielding a net power gain for the wind plant. But the inability of wake-steering controllers to perfectly track the wind direction leads to suboptimal performance. In this paper, we propose the use of preview wind direction measurements upstream of the turbine to improve controller performance by anticipating wind direction changes. Further, data from an operational wind plant are used to determine realistic preview measurement accuracy. Using the FLOw Redirection and Induction in Steady State (FLORIS) engineering wind farm control tool, we compare the performance of standard and preview-enabled baseline and wake-steering control for a two-turbine array during below-rated operation. Assuming perfect preview information, preview-based wake steering increases energy production by the equivalent of 8.9% of the baseline wake losses, compared to a wake loss recovery of 5.8% with standard wake steering. However, when realistic measurement accuracy is included, the preview-based controller provides no advantage over standard control, motivating the need for more sophisticated control and wind direction forecasting strategies.

Keywords: Energy systems, Robust control, Hierarchical control
Abstract: A hierarchical Wind Farm Control (WFC) approach was previously developed that uses Power Adjusting Controllers (PACs) on each wind turbine in a wind farm. The PACs can be retrofitted to existing assets with no knowledge of, or change to, the wind turbine full envelope controller (FEC). However, knowledge of the wind turbine aerodynamics is required and is not usually directly available from the Original Equipment Manufacturer (OEM), necessitating estimation.

In this work, estimated aerodynamic properties are obtained via a scanning LIDAR that directly measures the shape of a 2.5MW commercial wind turbine’s blades. The impact of the resulting aerodynamic uncertainty on the PAC tuning and the accuracy of the change in power output from the PAC at a turbine level and at a wind farm level is assessed. It is shown that it is possible to tune a stable PAC using aerodynamic information estimated via blade scanning.

Although the requested turbine change in power suffers from some inaccuracy, the slow integral action at a WFC level causes the impact on the accuracy of the change in wind farm power output to be negligible. As such, the application of a WFC methodology utilising PACs without prior knowledge of the turbine aerodynamics is shown to be possible by using blade scanning to estimate the aerodynamic coefficients. Hence it is practical to retrofit the methodology to wind farms when aerodynamic information from the OEM is not available.

Keywords: Energy systems, Learning, Fluid flow systems
Abstract: This paper provides a model-free framework for real-time control of wind farms to accurately track a power reference signal. This problem requires tractable dynamical models for capturing the aerodynamic interaction between wind turbines and controllers that can make decisions in real-time given varying atmospheric conditions. In this paper, we propose a deep reinforcement learning framework to provide real-time yaw control of a wind farm. Modifications have been made to FLOw Redirection and Induction in Steady State (FLORIS), a modeling tool that incorporates transient wake behavior. The control problem is formulated to track a synthetic power reference signal based on historical atmospheric (wind speed and direction) information, price signals, and regulation deployment data from U.S. regional transmission operators. Results indicate that a wind farm, with this control paradigm, can achieve good tracking performance when tested with real atmospheric data.

Keywords: Energy systems, Estimation, Network analysis and control
Abstract: This paper describes an estimation algorithm for velocity and power output signals in a wind farm under changing wind direction. A graph-theoretic definition describes the wind farm as a collection of nodes (turbines) and time-varying weighted edges (inter-turbine wake propagation) that change as a function of incoming wind direction. The velocity at each turbine is determined through a discrete input-output model. Changes in wind direction serve as the input and the output is defined in terms of a time-varying weighted adjacency matrix that depends on the time-delay of information propagation between turbines. These delays, which are defined in terms of the advection speed of the wind and the distance between the turbines, capture the delayed effect of wind direction changes on the inter-connectivity of the graph as the wind conditions at the farm inlet propagate through the turbine array. An event-based update framework is employed to capture time-dependent topology changes due to shifts in wind direction. Simulation results for dynamically changing wind inlet directions to a circular wind farm are compared to predictions from both the static and dynamic versions of the FLOw Redirection and Induction in Steady State (FLORIS) model. The approach is shown to enable real-time tracking of dynamic changes to wind farm power output within a framework that can be easily integrated into real-time, horizon-based, control strategies that typically do not account for wind direction changes.

Keywords: Optimization, Modeling, Power systems
Abstract: This paper proposes a holistic framework of data-driven distributionally robust joint chance constrained economic dispatch (ED) optimization, which seamlessly incorporates deep learning-based optimization for effective utilization of renewable energy in power systems. By leveraging a deep generative adversarial network (GAN), an f-divergence-based ambiguity set of wind power distributions is constructed as a ball centered around the probability distribution induced by a generator neural network. In particular, the GAN is well suited for capturing complicated temporal and spatial correlations among renewable energy sources. Based upon this ambiguity set, a distributionally robust joint chance constrained ED model is developed to hedge against distributional uncertainty present in multiple constraints, without assuming a perfectly known probability distribution. The proposed deep learning based ED optimization framework greatly mitigates the conservatism inflicting on distributionally robust individual chance constrained optimization. Theoretical a priori bound on the required number of synthetic wind power data generated by GAN is explicitly derived for the multi-period ED problem to guarantee a predefined risk level. The effectiveness of the proposed approach is demonstrated in the six-bus system by comparing with the state-of-the-art method.

Keywords: Power systems, Smart grid, Power electronics
Abstract: Stability of power grids with synchronous generators (SGs) and renewable generation interfaced with grid-forming converters (GFCs) under dc-side current limitation is studied. To that end, we first consider a simple 2-bus test system and reduced-order models to highlight the fundamental difference between two classes of GFC controls – (A) droop, dispatchable virtual oscillator control (dVOC) and virtual synchronous machine (VSM), and (B) matching control. Next, we study Lyapunov stability and input-output stability of the dc voltage dynamics of class-A GFCs for the simple system and extend it to a generic system. Next, we provide a sufficiency condition for input-to-state stability of the 2-bus system with a class-B GFC and extend it for a generic system. Finally, time-domain simulations from a reduced-order averaged model of the simple test system and a detailed switched model of the GFC validate the proposed conditions.

Keywords: Model/Controller reduction, Linear parameter-varying systems, Power systems
Abstract: We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric reduced model in which we concatenate the local bases obtained via mathcal{H}_2-based interpolatory model reduction. The residue of the underlying dynamics corresponding to the simple pole at zero varies with the parameters. Therefore, to have bounded mathcal{H}_2 and mathcal{H}_infty errors, the reduced model residue for the pole at zero should match the original one over the entire parameter domain. Our framework achieves this goal by enriching the global basis based on a residue analysis. The effectiveness of the proposed method is illustrated through two numerical examples.

Keywords: Automotive control, Stochastic optimal control, Modeling
Abstract: Dilute combustion using exhaust gas recirculation (EGR) is a cost-effective method for increasing engine efficiency. At high EGR levels, however, its efficiency benefits diminish as cycle-to-cycle variability (CCV) intensifies. In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be adjusted by a single parameter embedded in the cost function. Simulation results indicated that combustion CCV can be reduced by as much as 65% by using at most 1% additional fuel. Although the control design presented here does not include fuel trim to maintain stoichiometric combustion for three-way catalyst compatibility, it is envisioned that this approach would be implemented alongside such an external controller, and the theoretical contribution presented here provides a first insight into the feasibility of CCV control using fuel injection.

Keywords: Automotive systems, Identification for control, Automotive control
Abstract: In vehicles without additional heat sources but the combustion engine, fast cabin heating tends to be in conflict with engine heating. This negatively effects consumption, as the engine efficiency is lower at low temperatures, so that a tradeoff is necessary between windscreen heating, cabin temperature and fuel consumption. This is even more the case for hybrid electric vehicles (HEVs), as they may have to use the thermal mode even if an electrical operation would be preferable, for instance in city traffic conditions. A fixed strategy may not be optimal, as the actual heating behavior will depend on several environmental factors, like wind, presence of snow on the roof or sun radiation, which might be difficult to determine precisely. In order to optimize the heating strategy in real time, computationally efficient – whilst still accurate – models of the different thermal systems are required. This paper presents a fast data based approach to model the heat flows based on data from real drives. The chosen model structure enables the possibility of online identification in case of parameter changes during a drive. A case study is performed to show the significance of the issue.

Keywords: Automotive control, Optimal control, Predictive control for nonlinear systems
Abstract: Waste heat recovery (WHR) is a promising technology that uses the thermal energy from the exhaust gases of an internal combustion engine (ICE) to aid propulsion in vehicles. This paper presents a model predictive control (MPC) framework to minimize the fuel consumption of an automotive ICE by integrating it with a WHR system. To this end, a control oriented model of a WHR system is developed and then integrated to a control oriented model of a turbocharged dual fuel diesel-natural gas ICE. The ICE model is derived based on experimental data collected from a 6.7 liter Cummins ISB engine modified for dual fuel operation. The designed MPC framework optimizes the ICE combustion, turbocharger, and organic Rankine cycle (ORC) system in the WHR to minimize fuel consumption of the ICE. The designed control framework also allows to meet time-varying exhaust gas temperature constraints for after treatment system light-off requirements and diesel particulate filter (DPF) regeneration. The results show that the optimal operation of the WHR and the ICE reduces the fuel consumption of the ICE by 5.9%.

Keywords: Optimal control, Automotive control, Numerical algorithms
Abstract: This paper presents new modifications to the previously developed economic model predictive control (EMPC) strategy [1] that co-optimizes the vehicle and powertrain dynamics of a plug-in hybrid electric vehicle (PHEV) in a car-following scenario. These modifications are made to improve the optimality of fuel efficiency and vehicle safety. Specifically, a time-weighted multi-level co-state update strategy is considered to address the optimality issue arising from a reduced number of single-shooting iterations. In addition, a scalable maximal-control invariant set is considered to modify the control action obtained from the EMPC as needed to resolve potential safety-critical constraint violations due to insufficient single-shooting iterations. To evaluate the performance of the proposed strategy in the presence of uncertainties of information about a target lead vehicle, we integrate the speed prediction algorithm in [2]. Simulation results on a 2-hour trip demonstrate an 8–13% fuel economy benefit with the proposed co-optimization strategy over an optimal charge-depleting, charge-sustaining (CDCS) strategy on a similar trip driven by a human.

Keywords: Linear parameter-varying systems, Automotive control, Control applications
Abstract: This paper presents linear parameter-varying (LPV) controller design for the urea-based selective catalytic reduction (SCR) system in diesel engines to reduce nitrogen oxides (NOx) and ammonia (NH3) emissions. Although such LPV SCR controller design has been previously developed, this paper extends it in various ways. The extension includes the usage of NH3 slip sensor for feedback LPV control, the adoption of NOx and NH3 measurements downstream of the catalyst as gain-scheduling parameters, the simultaneous design of feedforward and feedback LPV controllers, and a robustness analysis of the LPV controllers. Quasi-LPV SCR models derived from an existing control-oriented nonlinear parameter-varying model are utilized in the LPV controller design. The LPV controller performance is demonstrated based on an SCR simulation utilizing experimentally obtained engine-out NOx, and exhaust gas temperature and flow rate. It is shown that the LPV controller provides satisfactory emission performance, as well as robustness against sensor noise and model parameter uncertainty.

Keywords: Automotive control, Optimal control, Autonomous vehicles
Abstract: Connecting automated vehicles to traffic lights can lead to significant energy savings by enabling them to pass through intersections in an energy-efficient way without unnecessary stops. A cellular-based communication system connecting multiple traffic lights can help realize the full potential of energy-efficient driving at intersections. Thus, we propose a hierarchical speed planner that can leverage information from multiple connected traffic lights. The proposed speed planner consists of two modules: a green window selector and a reference trajectory generator. The green window selector, based on Dijkstra’s algorithm, finds a series of "green windows" for connected traffic lights that builds an energy-optimal path for vehicles to follow. The reference trajectory generator finds optimal entering times, based on the selected green window at each intersection, and then computes reference trajectories. Deriving and using analytical optimal entering speeds as a function of entering times allows us to guarantee the computational simplicity suitable for real-time implementation. We also demonstrate how to balance energy and traffic flow perspectives in the reference trajectory generator. Finally, a high-fidelity simulation framework is used to evaluate the proposed speed planner and quantify the extent to which it can save energy in various real-world urban route scenarios.

Keywords: Predictive control for linear systems, Autonomous systems, Simulation
Abstract: Knowledge of the fuel impacts of traffic control signals, particularly traffic lights, is important for assessing benefits of coordinated control of connected and/or autonomous Vehicles (CAVs) with traffic elements, and for determining sites best suited for smart infrastructure deployments based on environmental impacts. The objective of this work is to determine the region over which knowledge of traffic light information is useful in informing fuel-efficient decisions. This includes the region before a traffic light in where a preview-based controller benefits from planning for the upcoming traffic light, and the region after a light where the vehicle returns to free-flow behavior after coming to a complete stop. In this paper, we collectively refer to these regions as the traffic light's Region Of Influence (ROI). In particular, this work identifies the start and end position of the ROI for a signalized intersection based on simulations and in-vehicle experiments using a heavy-duty diesel truck. To evaluate the fuel consumption of the vehicle accurately, this work uses a gravimetric fuel measurement method to calibrate on-board fuel flow meters for both the inlet and outlet of the fuel tank; the results show agreement within 1% error. Next, this work analyzes the difference in fuel consumption for the heavy-duty vehicle within the ROI, comparing fuel usage of the vehicle traveling through green vs. red traffic lights using simulations of previously published MPC velocity controllers designed to improve fuel usage using traffic light SPaT information. The ROI for MPC-based control was found to be 200m before and 175m after the light. Finally, experimental results are given showing driver, rather than controller, responses that indicate: 1) the human-driven ROI starts approximately 140 m before an intersection and ends approximately 500 m after the intersection; and 2) the heavy-duty diesel vehicle consumes on average 88 grams (34%) less fuel within the ROI when encountering a green light, for each traffic light encounter, compared with encountering a red light.

Keywords: Automotive control, Discrete event systems, Sensor fusion
Abstract: This paper investigates how multiple in-cycle closed-loop combustion controllers can be integrated for a seamless operation under a wide-range of operating conditions. The stochastic cyclic variations of the combustion can be successfully compensated by the adjustment of the fuel injection pulses within the same cycle. The feedback information and controllability obtained relies on the different operating conditions, emissions regulations and fuels. Various in-cycle closed-loop combustion controllers are found in the literature to overcome the numerous challenges of the combustion control. In this paper, the modularization for the controller design and their integration is investigated, and how the transition between the available information, control actions and control strategy affects the final combustion behaviour. The approach consists in the design of a finite-state machine that supervises the transition between virtual sensors and measurements, regulators and the possibility of additional fuel injections. The proposed approach was tested in a Scania D13 engine for a wide-range of operating conditions. The results confirm the improved controllability and reduced steady-state RMSE of the controlled parameters, with a smoother transition between set-points, regardless of operating conditions and fuel.

Keywords: Genetic regulatory systems, Systems biology
Abstract: Competition for cellular resources often indirectly creates unintended connections between otherwise independent genetic modules, leading to loss of modularity and impairment of intended circuit function. Both global and local negative feedback control strategies have been widely-used as attempts to mitigate the undesired effects of resource competition. However, these controllers demonstrate limited tunability and scalability with increasing circuit complexity. Our previous work attempting to achieve two successive cell fate transitions via cascading bistable switches demonstrates how resource competition can lead to winner-take-all (WTA) dynamics that deviate from the intended behavior. Here, we attempt to remediate these issues by synthetically introducing a shared and tunable system of negatively competitive regulation (NCR), incorporating repressive CRISPR moieties to free up cellular resources from the winner module to a degree proportional to its activity. This system punishes transcriptional modules that take up more than their fair share of resources while having minimal effect on modules operating within normal activity ranges. We compare this novel mode of regulation to global and local negative feedback controllers and demonstrate the significantly increased efficacy of controlling WTA resource competition NCR can achieve. Thus, we provide an alternative strategy for controlling resource competition.

Keywords: Neural networks, Genetic regulatory systems, Pattern recognition and classification
Abstract: Cellular signaling pathways are responsible for decision making that sustains life. Most signaling pathways include post-translational modification cycles, that process multiple inputs and are tightly interconnected. Here we consider a model for phosphorylation/dephosphorylation cycles, and we show that under some assumptions they can operate as molecular neurons or perceptrons, that generate sigmoidal-like activation functions by processing sums of inputs with positive and negative weights. We carry out a steady-state and structural stability analysis for single molecular perceptrons as well as for feedforward interconnections, concluding that interconnected phosphorylation/dephosphorylation cycles may work as multi-layer biomolecular neural networks (BNNs) with the capacity to perform a variety of computations. As an application, we design signaling networks that behave as linear and non-linear classifiers.

Keywords: Systems biology, Predictive control for nonlinear systems, Biological systems
Abstract: Bacterial colony formations exhibit diverse morphologies and dynamics. A mechanistic understanding of this process has broad implications to ecology and medicine. However, many control factors and their impacts on colony formation remain underexplored. Here we propose a reaction-diffusion based dynamic model to quantitatively describe cell division and colony expansion, where control factors of colony spreading take the form of nonlinear density-dependent function and the intercellular impacts take the form of density-dependent hill function. We validate the model using experimental E. coli colony growth data and our results show that the model is capable of predicting the whole colony expansion process in both time and space under different conditions. Furthermore, the nonlinear control factors can predict colony morphology at both center and edge of the colony.

Keywords: Systems biology, Biological systems
Abstract: Synthetic biology constructs often rely upon the introduction of "circuit" genes into host cells, in order to express novel proteins and thus endow the host with a desired behavior. The expression of these new genes "consumes" existing resources in the cell, such as ATP, RNA polymerase, amino acids, and ribosomes. Ribosomal competition among strands of mRNA may be described by a system of nonlinear ODEs called the Ribosomal Flow Model (RFM). The competition for resources between host and circuit genes can be ameliorated by splitting the ribosome pool by use of orthogonal ribosomes, where the circuit genes are exclusively translated by mutated ribosomes. In this work, the RFM system is extended to include orthogonal ribosome competition. This Orthogonal Ribosomal Flow Model (ORFM) is proven to be stable through the use of Robust Lyapunov Functions. The optimization problem of maximizing the weighted protein translation rate by adjusting allocation of ribosomal species is formulated and implemented.

Keywords: Systems biology, Biological systems, Modeling
Abstract: For many intracellular signaling pathways, it can be quite difficult to construct accurate mechanistic models since their underlying mechanisms are only partially understood. As a result, any mechanistic models developed for such systems will not be reliable. To mitigate potential model-system mismatches, this work proposes a hybrid modeling approach by combining a first-principle model and an artificial neural network (ANN) to improve the prediction accuracy. First, the proposed scheme identifies a subset of model states whose dynamics have the highest correlations with outputs, and correction terms are added to these states' differential equations to compensate for the model-system mismatches. Second, the values of the correction terms are estimated from experimental measurements by solving an L2-regularized least-squares problem. Third, an ANN is developed with the states' dynamics and the correction terms as inputs and outputs, respectively, of the ANN, and the developed ANN is integrated with the original mechanistic model to finalize the hybrid model development process. Consequently, the final hybrid model will possess generalized prediction capabilities while retaining model interpretability. We have successfully validated the proposed methodology by developing a hybrid model of the simplified apoptosis signaling pathway, which is only partially known beforehand.

Keywords: Systems biology, Biomedical, Identification for control
Abstract: Sequences of different drugs have shown potential to improve treatment strategies for cancer. Typical switched system approaches model the population dynamics of each drug independently, not rigorously considering the effects of pre-treatment or drug-drug interactions. In this paper, a general model family incorporating pre-treatment effects and biological domain knowledge is proposed, and a model from this family is identified by using a novel experimental data set of two-drug sequences. Leveraging the data, a simulator for the cell population dynamics under sequences of up to nine drugs is developed and used to empirically evaluate the performance of a set of closed-loop drug scheduling controllers. We used the controllers to identifying promising drug schedules in silico and evaluated them in vitro. The experiments validated the effectiveness of the identified schedules in reducing the number of living cells to less than 10% of the initial. While only treating with certain toxic drugs achieves similar effectiveness, the schedules use toxic drugs for significantly shorter times which likely reduces toxicity to non-cancer cells.

Keywords: Genetic regulatory systems, Systems biology, Stochastic systems
Abstract: Living cells encode diverse biological clocks for circadian timekeeping and formation of rhythmic structures during embryonic development. A key open question is how these clocks synchronize across cells through intercellular coupling mechanisms. To address this question, we leverage the classical motif for genetic clocks the Goodwin oscillator where a gene product inhibits its own synthesis via time-delayed negative feedback. More specifically, we consider an interconnected system of two identical Goodwin oscillators (each operating in a single cell), where state information is conveyed between cells via a signaling pathway whose dynamics is modeled as a first-order system. In essence, the interaction between oscillators is characterized by an intercellular coupling strength and an intercellular time delay that represents the signaling response time. Systematic stability analysis characterizes the parameter regimes that lead to oscillatory dynamics, with high coupling strength found to destroy sustained oscillations. Within the oscillatory parameter regime we find both in-phase and anti-phase oscillations with the former more likely to occur for small intercellular time delays. Finally, we consider the stochastic formulation of the model with low-copy number fluctuations in biomolecular components. Interestingly, stochasticity leads to qualitatively different behaviors where in-phase oscillations are susceptible to inherent fluctuations but not the anti-phase oscillations. In the context of the segmentation clock, such synchronized in-phase oscillations between cells are critical for the proper generation of repetitive segments during embryo development that eventually leads to the formation of the vertebral column.

Keywords: Healthcare and medical systems, Emerging control applications, Human-in-the-loop control
Abstract: This paper presents a model-free insulin titration algorithm for patients with type 2 diabetes that automatically finds and maintains the optimal insulin dosage in order to maintain the blood glucose concentration within the desired target zone. The proposed method is based on recursive least square based extremum seeking control. Since the proposed method does not require a detailed model, it can be applied on a wide population of patients without the need to identify and adapt models to the patient data. We demonstrate the effectiveness of the proposed method using in silico simulations, which are benchmarked against the standard-of-care approach. We also show that the proposed method can handle intra-patient metabolic variations and non-adherence to the treatment regimen. Finally, using a population of 50 virtual patients, we show that the proposed method is able to handle inter-patient variations.

Keywords: Machine learning, Output regulation, Optimal control
Abstract: In this paper, for the two leading and following vehicles, a data-driven optimal control approach is proposed to achieve the combined longitudinal and lateral control of the following autonomous vehicle. Firstly, the dynamics of the following vehicle is derived. In order to overcome the cutting-edge limitation, a virtual preceding vehicle is defined which is perpendicular to the preceding vehicle. The tracking error is defined as the deviation between the look ahead point of the following vehicle and the virtual preceding vehicle. Then, the error system is derived. Secondly, based on the error system, in order to minimize the cost determined by the tracking error and the energy consumption, the Hamilton-Jacobi-Bellman (HJB) equation is established. A model-based policy iteration technique is proposed to solve the HJB equation. Thirdly, a two-phase data-driven policy iteration algorithm is proposed and implemented by using adaptive dynamic programming (ADP). The efficacy of the proposed data-driven optimal control approach is validated by computer simulations.

Keywords: Estimation, Statistical learning, Learning
Abstract: Gaussian graphical models have been well studied as a way to represent the relationships between various entities, and numerous algorithms have been proposed to learn the dependencies in such models. However, these algorithms process data in a batch, and may not be suitable for real-time estimation. In this paper, we propose an online sparse inverse covariance algorithm to infer the network structure (i.e., dependencies between nodes) in real-time from time-series data. Our approach is based on an alternating minimization algorithm and allows users to select the number of iterations per data point. We provide theoretical guarantees showing that the online estimates converge to that of the batch mode as the number of data increases and characterize its asymptotic rate of convergence. Finally, we evaluate our online algorithm on synthetic data sets.

Keywords: Nonlinear systems identification, Identification for control
Abstract: This paper presents an online memory-augmented finite-sample model learning approach for uncertain nonlinear systems with prescribed-performance guarantees. Experience replay is leveraged to form a memory of events that have a significant effect on the performance of the learning mechanism, and the events in the memory are reused in the learning rule to guarantee that the modeling error converges to zero within a predefined settling time while remaining in a preselected prescribed bound during learning. An easy-to-check and verifiable metric defined on finite samples collected along the system’s trajectories is provided to certify the prescribed-performance convergence. Finally, a simulation example verifies the efficiency of the proposed memory-augmented model learning approach.

Keywords: Statistical learning, Predictive control for linear systems
Abstract: In this paper, we present a methodology to implement the stochastic policy gradient method using actor-critic techniques, when the policy is approximated using an MPC scheme. The paper proposes a computationally inexpensive approach to build a stochastic policy generating samples that are guaranteed to be feasible for the MPC constraints. For a continuous input space, imposing hard constraints on the policy poses technical difficulties in the computation of the score function of the policy, required in the policy gradient computation. We propose an approach that solves this issue, and detail how the score function can be computed based on parametric Nonlinear Programming and the primal-dual interior point method. The approach is illustrated on a simple example.

Keywords: Iterative learning control, Markov processes, Optimization algorithms
Abstract: A wide range of applications require autonomous agents that are capable of learning an a priori unknown task. Additionally, an autonomous agent may be put in the same environment multiple times, each time having to learn a different task. Motivated by these applications, we study the problem of learning an a priori and evolving task in an online manner. In particular, we consider an agent whose behavior is modeled by an episodic Markov decision process. The agent's task, captured by a loss function, is unknown to the agent and, furthermore, may change in an adversarial manner from episode to episode. However, in each episode, the agent receives a bandit feedback corresponding to the loss function at that episode every time it takes an action. Given a limited budget of T episodes, the objective is to learn a policy with minimum regret with respect to the best policy in hindsight. We propose a policy search algorithm that employs online mirror descent using an optimistically biased estimator of the loss function. We prove that the proposed algorithm achieves both on expectation and with high probability a sublinear regret of tilde{mathcal{O}}(sqrt{LT|S||A|}), where L is the length of each episode, |S| is the number of states, and |A| is the number of actions.

Keywords: Observers for Linear systems, Identification, Optimal control
Abstract: In this paper, a novel approach to the output-feedback inverse reinforcement learning (IRL) problem is developed by casting the IRL problem, for linear systems with quadratic cost functions, as a state estimation problem. Two observer-based techniques for IRL are developed, including a novel observer method that re-uses previous state estimates via history stacks. Theoretical guarantees for convergence and robustness are established under appropriate excitation conditions. Simulations demonstrate the performance of the developed observers and filters under noisy and noise-free measurements.

Keywords: Optimization algorithms, Randomized algorithms, Machine learning
Abstract: The paper sets out to obtain precise convergence rates for quasi-stochastic approximation (QSA), with applications to optimization and reinforcement learning. The main contributions are obtained for general nonlinear algorithms, under the assumption that there is a well defined linearization near the optimal parameter theta^ocp, with Hurwitz linearization matrix A^ocp. Subject to stability of the algorithm (general conditions are surveyed in the paper):

(i) If the algorithm gain is chosen as a_t = g/(1+t)^rho with g>0 and rhoin(0,1), then a ``finite-t'' approximation is obtained [ a_t^{-1} { ODEstate_t - theta^ocp } = barY + XiI_t + o(1) ] where ODEstate_t is the parameter estimate, barYinRe^d is a vector identified in the paper, and { XiI_t } is bounded with zero mean. (ii) The approximation continues to hold with a_t = g/(1+t) under the stronger assumption that I + g A^ocp is Hurwitz. (iii) The Ruppert-Polyak averaging technique is extended to this setting, in which the estimates { ODEstate_t } are obtained using the gain in (i), and ODEstate^{text{RP}}_t is defined to be the running average. The convergence rate is 1/t if and only if barY = Zero.

(iv) The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.

Keywords: Adaptive control, Optimal control, Machine learning
Abstract: This paper provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for a set of agents with homogeneous dynamics and common tracking objectives. Model-based reinforcement learning is implemented by simultaneously evaluating the Bellman error (BE) at the state of each agent and on nearby off-trajectory points, as needed, throughout the state space. Each agent will calculate and share their respective on and off-trajectory BE information with a centralized estimator, which computes updates for the approximate solution to the infinite-horizon optimal tracking problem and shares the estimate with the agents. In doing so, the computational burden associated with BE extrapolation is shared between the agents and a centralized updating resource. Edge computing is leveraged to share the computational load between the agents and a centralized resource. Uniformly ultimately bounded tracking of each agent's state to the desired state and convergence of the control policy to the neighborhood of the optimal policy is proven via a Lyapunov-like stability analysis.

Keywords: Adaptive control, Identification for control, Optimal control
Abstract: Safety awareness is critical in reinforcement learning when task restarts are not available and/or when the system is safety-critical. Safety requirements are often expressed in terms of state and/or control constraints. In the past, model-based reinforcement learning approaches combined with barrier transformations have been used as an effective tool to learn the optimal control policy under state constraints for systems with fully known models. In this paper, a reinforcement learning technique is developed that utilizes a novel filtered concurrent learning method to realize simultaneous learning and control in the presence of model uncertainties for safety-critical systems.

Keywords: Autonomous vehicles, Predictive control for nonlinear systems, Optimization
Abstract: In this paper, we present the use of Reinforcement Learning (RL) based on Robust Model Predictive Control (RMPC) for the control of an Autonomous Surface Vehicle (ASV). The RL-MPC strategy is utilized for obstacle avoidance and target (set-point) tracking. A scenario-tree robust MPC is used to handle potential failures of the ship thrusters. Besides, the wind and ocean current are considered as unknown stochastic disturbances in the real system, which are handled via constraints tightening. The tightening and other cost parameters are adjusted by RL, using a Q-learning technique. An economic cost is considered, minimizing the time and energy required to achieve the ship missions. The method is illustrated in simulation on a nonlinear 3-DOF model of a scaled version of the Cybership 2.

Keywords: Optimal control
Abstract: The optimal pursuer response to a fixed evader strategies within a single-pursuer, dual-evader engagement is examined. The evaders inflict a cost on the pursuer during the engagement based on the relative geometry of the three-agent system, and the pursuer strives to minimize the total accumulated cost over the duration of the engagement. Three possible termination cases are presented, and unique optimality conditions are examined for each. Singularities are then discussed, which include a singularity in the case of simultaneous capture and an analytically proven dispersal surface. We conclude by presenting a pair of unique dispersal surfaces and highlight the effect the solutions emanating from these surfaces have on their resultant value functions.

Keywords: Autonomous systems, Predictive control for nonlinear systems, Numerical algorithms
Abstract: Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problem—generating a trajectory that satisfies a given specification—can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this paper, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

Keywords: Machine learning, Uncertain systems, Nonlinear systems identification
Abstract: We present a novel online learning algorithm for a class of unknown and uncertain dynamical environments that are fully observable. First, we obtain a novel probabilistic characterization of systems whose mean behavior is known but which are subject to additive, unknown subGaussian disturbances. This characterization relies on recent concentration of measure results and is given in terms of ambiguity sets. Second, we extend the results to environments whose mean behavior is also unknown but described by a parameterized class of possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by learning the parametric dependence online, and retaining similar probabilistic guarantees with respect to the additive, unknown disturbance. We illustrate the results on a differential-drive robot subject to environmental uncertainty.

Keywords: Stochastic optimal control, Stochastic systems, Uncertain systems
Abstract: This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control problem as a semi-definite program (SDP). We adopt the Iterative Risk Allocation (IRA) formalism from [1], which uses a two-stage approach to solve the optimal risk allocation problem for covariance steering. The upper-stage of IRA optimizes the risk, which is proved to be a convex problem, while the lower-stage optimizes the controller with the new constraints. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies.

Keywords: Estimation, Identification, Nonlinear systems identification
Abstract: The motion of an Autonomous Underwater Vehicle (AUV) is often affected by unknown disturbances arising from underwater flow fields. These disturbances may result in large prediction errors when comparing the AUV's expected surfacing location (for example from dead reckoning) and the AUV's measured surfacing location. This error, referred to as the Motion Integration Error, has been used by Motion Tomography algorithm (MT) to reconstruct an estimate of the underwater flow field. In this paper, we extend the MT algorithm to solve the MT problem by introducing Laplacian regularization that penalizes the non-smoothness of the predicted flow field. We propose an iterative algorithm to solve the Regularized MT (RMT) problem. The convergence of the RMT algorithm in the single vehicle case is theoretically justified. The effectiveness of the algorithm for multiple vehicle applications is validated through simulations with cyclonic flow field models. We show that the RMT algorithm outperforms the parametric MT in terms of estimation accuracy and convergence rate.

Keywords: Optimal control, Autonomous systems
Abstract: We examine a real-time target engagement scenario in which a mobile attacker engages a fortified, static target and then retreats to a safety region. The mobile attacker possesses limited weapon energy (or ammunition) and must determine when to employ its limited resources to achieve maximum effect. Simultaneously, the hardened target inflicts an integral cost on the attacker over the course of the engagement. This instantaneous damage dealt by both agents is a function of the relative state with regions of high damage and low damage. We solve for the optimal attacker engagement strategy, which divides the state space into regions of qualitatively different behaviors, with different combinations and sequencing of holding fire, opening fire, approaching the target, and retreating. These regions are separated by several unique singular surfaces and constrained arcs. Furthermore, the global solution produces ”kiting behaviors” which are often found in video games as well as traditional combat strategies.

Keywords: Energy systems, Decentralized control, Control of networks
Abstract: Distributed control agents have been advocated asan effective means for improving the resiliency of our physicalinfrastructures under unexpected events. Purely local controlhas been shown to be insufficient, centralized optimal resourceallocation approaches can be slow. In this context, we putforth a hybrid low-communication saturation-driven protocolfor the coordination of control agents that are distributed over aphysical system and are allowed to communicate with peers overa “hotline” communication network. According to this protocol,agents act on local readings unless their control resourceshave been depleted, in which case they send a beacon forassistance to peer agents. Our ripple-type scheme triggers com-munication locally only for the agents with saturated resourcesand it is proved to converge. Moreover, under a monotonicityassumption on the underlying physical law coupling controloutputs to inputs, the devised control is proved to convergeto a configuration satisfying safe operational constraints. Theassumption is shown to hold for voltage control in electric powersystems and pressure control in water distribution networks.Numerical tests corroborate the efficacy of the novel scheme.

Keywords: Decentralized control, Large-scale systems, Linear systems
Abstract: Passivity theory has recently contributed to developing decentralized control schemes for large-scale systems. Many decentralized passivity-based control schemes are designed in continuous-time. It is well-known, however, that the passivity properties of continuous-time systems may be lost under discretization. In this work, we present a novel stabilizing decentralized control scheme by ensuring passivity for discrete-time systems directly and thus avoiding the issue of passivity preservation. The controller is synthesized by locally solving a semidefinite program offline for each subsystem in a decentralized fashion. This program comprises local conditions ensuring that the corresponding subsystem is locally passive. Passivity is ensured with respect to a local virtual output which is different from the local actual output. The program also comprises local conditions ensuring that the local passivity of all subsystems implies the asymptotic stability of the whole system. The performance of the proposed controller is evaluated on a case study in DC microgrids.

Keywords: Decentralized control, LMIs, Stability of linear systems
Abstract: This paper is concerned with the decentralized H-infinity control problem of discrete-time interconnected systems. The studied interconnected system is transformed equivalently into a single linear time invariant system with matrix inversion terms in the system matrices. This paper derives novel necessary and sufficient conditions such that the considered interconnected system is asymptotically stable with the prescribed H-infinity performance. The new conditions are computationally attractive because of the elimination of matrix inversion terms. Then these conditions are transformed into linear matrix inequalities. The decentralized controllers can be obtained by solving linear matrix inequalities to guarantee the stability and the H-infinity performance of the closed-loop interconnected system. Finally, the effectiveness and the advantages of the proposed results are demonstrated by one numerical example.

Keywords: Decentralized control, Stability of hybrid systems, Robotics
Abstract: This paper presents a formal foundation, based on decomposition, hybrid zero dynamics (HZD), and a scalable optimization, to develop distributed control algorithms for hybrid models of collaborative human-robot locomotion. The proposed approach considers a centralized controller and then decomposes the dynamics and feedback laws with a parameterization to synthesize local controllers. The Jacobian matrix of the Poincare map with local controllers is studied and compared to that with centralized ones. An optimization problem is then set up to tune the parameters of the local controllers for asymptotic stability. The proposed approach can significantly reduce the number of controller parameters to be optimized for the synthesis of distributed controllers. The analytical results are numerically evaluated with simulations of a multi-domain hybrid model with 19 degrees of freedom for stable amputee locomotion with a powered knee-ankle prosthetic leg.

Keywords: Optimization, Optimal control, Traffic control
Abstract: In this paper, we present an optimization framework for cooperative merging of platoons of connected and automated vehicles at highway on-ramps. The framework includes (1) an optimal scheduling algorithm, through which, each platoon derives the sequence and time to enter the highway safely, and (2) an optimal control problem that allows each platoon to derive its optimal control input (acceleration/deceleration) in terms of fuel consumption. We evaluate the efficacy of the proposed optimization framework through VISSIM-MATLAB simulation environment. The proposed framework significantly reduces the crossing time and fuel consumption of platoons at the highway on-ramps compared to the baseline scenario where the vehicles on the minor road yield to the vehicles on the highway.

Keywords: PID control, Communication networks, Decentralized control
Abstract: Distributed camera surveillance systems typically consist of multiple cameras that need to store some fraction of their video streams at a central storage node. The disk space of this node as well as the network between the cameras and this central node constitute shared resources. In the paper the disk space allocation as well as the network bandwidth reservation are solved using techniques normally associated with process control. These include mid-range control and tracking-based control of global shared resources. The approach is evaluated by simulations.

Keywords: Control applications, Linear systems, Decentralized control
Abstract: In this paper, the use of the Smith-McMillan form in decoupling multiple-input multiple-output system dynamics is analyzed. In short, from a transfer matrix plant model one can obtain a decoupling compensator which leads to a decoupled plant that contains the same transmission poles and zeros of the original system's transfer matrix. As a result, full decoupling of the plant transfer matrix is obtained for all frequencies, which can be individually addressed by single-input single-output control. The aim of this paper is to present conditions for the decoupled system that guarantee internal stability and performance requirements for the overall control system. The performance specifications are defined in terms of magnitude limits for the maximum singular value of the closed-loop transfer matrices. The potential of the decoupling procedure is shown in a theoretical mechanical system example.

Keywords: Decentralized control, Cooperative control, Autonomous vehicles
Abstract: We discuss an online decentralized decision making problem where the agents are coupled with affine inequality constraints. Alternating Direction Method of Multipliers (ADMM) is used as the computation engine and we discuss the convergence of the algorithm in an online setting. To be specific, when decisions have to be made sequentially with a fixed time step, there might not be enough time for the ADMM to converge before the scenario changes and the decision needs to be updated. In this case, a suboptimal solution is employed and we analyze the optimality gap given the convergence condition. Moreover, in many cases, the decision making problem changes gradually over time. We propose a warm-start scheme to accelerate the convergence of ADMM and analyze the benefit of the warm-start. The proposed method is demonstrated in a decentralized multiagent control barrier function problem with simulation.

Keywords: Predictive control for nonlinear systems, Constrained control, Emerging control applications
Abstract: We consider a known system that operates in an unknown environment, which is discovered by sensing and affects the known system through constraints. However, sensing quality is typically dependent on system operation. Thus, the control decisions should account for both the impact of control on sensing and the impact of sensing on control. Since the information acquired from sensing is of statistical nature, we develop a perception-aware chance-constrained model predictive control (PAC-MPC) strategy that leverages uncertainty propagation models to relate control and sensing decisions to the environment knowledge. We propose conditions for recursive feasibility and provide an overview of the stability properties in such a statistical framework. The performance of the proposed PAC-MPC is demonstrated on a case study inspired by an automated driving application.

Keywords: Robust control, Predictive control for nonlinear systems, Large-scale systems
Abstract: In this paper, we present a computationally efficient multistage nonlinear model predictive controller (NMPC) with a prediction horizon update using nonlinear programming (NLP) sensitivities. Computational delay is minimized by updating the prediction horizon to a sufficient length at every time step. For a set-point tracking multistage NMPC, we first determine a terminal region around an optimal equilibrium point for each uncertainty realization in offline mode. Then using NLP-sensitivity we estimate a sufficient horizon length for the next time step such that all scenarios will be driven into their respective terminal regions. This adaptive horizon multistage NMPC (AH-msNMPC) is recursively feasible and input-to-state practically stable. In a simulation study, the AH-msNMPC was used to control a benchmark cooled CSTR process under parametric uncertainty. The AH-msNMPC computations take 1.4% and 29.5% of the sampling interval duration for robust horizon of 1 and 2, respectively. With a robust horizon length of 1 the controller is 15 times faster than ideal-multistage NMPC with a long enough prediction horizon. The computational delay is halved with robust horizon length of 2. The performance of the two controllers was found to be similar. The improved efficiency is vital in practice for improved control performance and closed-loop stability. It is desired for real-time optimal decision making, and also under limited computing resources such as in embedded systems.

Keywords: Predictive control for linear systems
Abstract: Many stochastic model predictive control approaches use a fixed, virtual linear feedback law in the prediction to counteract noise. The feedback allows to reduce the error between a nominal prediction of the future state and its real evolution. While often overlooked, the control gain used in the feedback law is an important tuning parameter. In the stochastic case, it shapes the covariance of the closed-loop system. It thus directly influences the required constraint back-off and the influence of the noise on the cost function. Consequently, the achievable closed-loop control performance and the attainable attraction domain depend on the gain, often resulting in a trade-off between both. We propose to utilize a blending of multiple different feedback gains, which is also optimized online, to reduce the conservatism and optimize control performance. We discuss properties of the resulting optimization problem, implementation details, and properties of the closed-loop. Simulations illustrate the proposed approach and demonstrate its benefits.

Keywords: Uncertain systems, Randomized algorithms, Statistical learning
Abstract: Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of blackbox optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This paper focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.

Keywords: Predictive control for linear systems, Linear systems, Constrained control
Abstract: We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-approximated with a net-additive component. The resulting MPC controller guarantees robust satisfaction of state and input constraints in closed-loop with the uncertain system. With appropriately designed terminal components and an adaptive horizon strategy, we prove the controller's recursive feasibility and stability of the origin. With numerical simulations, we demonstrate that our proposed approach gains up to 15x online computation speedup over a tube MPC strategy, while stabilizing about 98% of the latter's region of attraction.

Keywords: Chemical process control, Stochastic systems, Simulation
Abstract: We present a black-box optimization approach for the integration of design and control of constrained nonlinear systems under uncertainty. The problems of interest are difficult to solve since the dynamics and uncertainties occur on much shorter timescales than the process lifetime, the uncertainties are described by continuous random variables with high variance, and key operational decisions are modeled with a mixture of discrete and continuous variables. Instead of aggressively simplifying the number of operational periods and uncertainty scenarios to improve tractability of the problem, we are interested in developing a simulation-based optimization strategy by employing a high-quality decision rule that maps information measured online to the control inputs. Due to the inclusion of discrete scheduling decisions, we focus on a variant of model predictive control that can handle both continuous and discrete variables. We use a sample average approximation at every iteration to approximate the expected operating costs and constraints appearing in the main problem. Since the black-box optimizer handles noisy objective and constraint evaluations, it can mitigate errors introduced by considering only a finite number of samples. The advantages of the proposed method compared to alternative sequential design and control schemes are demonstrated on the design of a building cooling system under uncertain weather and demand conditions.

Keywords: Intelligent systems, Optimal control, Predictive control for nonlinear systems
Abstract: This paper proposes an observer-based framework for solving Partially Observable Markov Decision Processes (POMDPs) when an accurate model is not available. We first propose to use a Moving Horizon Estimation-Model Predictive Control (MHE-MPC) scheme in order to provide a policy for the POMDP problem, where the full state of the real process is not measured and necessarily known. We propose to parameterize both MPC and MHE formulations, where certain adjustable parameters are regarded for tuning the policy. In this paper, for the sake of tackling the unmodeled and partially observable dynamics, we leverage the Reinforcement Learning (RL) to tune the parameters of MPC and MHE schemes jointly, with the closed-loop performance of the policy as a goal rather than model fitting or the MHE performance. Illustrations show that the proposed approach can effectively increase the performance of close-loop control of systems formulated as POMDPs.

Keywords: Optimization algorithms, Optimal control, Predictive control for linear systems
Abstract: Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed emph{proportional-integral projected gradient method}, for MPC where the underlying finite horizon optimal control problem has both state and input constraints. Instead of minimizing the (augmented) Lagrangian, each iteration of our method only computes a single projection onto the state and input constraint set. Our method ensures that, along a sequence of averaged iterates, both the distance to optimum and the constraint violation converge to zero at a rate of (O(1/k)) if the objective function is convex, where (k) is the iteration number. If the objective function is strongly convex, this rate can be improved to (O(1/k^2)) for the distance to optimum and (O(1/k^3)) for the constraint violation. We compare our method against existing methods via a trajectory-planning example with convexified keep-out-zone constraints.

Keywords: Stability of nonlinear systems, Variable-structure/sliding-mode control, Robust control
Abstract: Position tracking control in three spatial dimensions in the presence of unknown or uncertain dynamics, is applicable to unmanned aerial, ground, (under)water and space vehicles. This work gives a new approach to model-free position tracking control by designing an extended state observer to estimate the states and the uncertain dynamics, with guaranteed accuracy of estimates. The estimated states and uncertainties can be used in a control scheme in real-time for position tracking control. The uncertainty (disturbance input) estimate is provided by an extended state observer (ESO) that is finite-time stable (FTS), to provide accuracy and robustness. The ideas of homogeneous vector fields and real-valued functions are utilized for the ESO design and to prove FTS. The estimated disturbance is then utilized for compensation of this uncertainty in real-time, and to enhance the stability and robustness of the feedback tracking control scheme.

Keywords: Autonomous systems, Control applications, Robust control
Abstract: This work proposes a new gain adaptation strategy for sliding mode controller (SMC) employed in high fidelity operations. This research work derives an important condition for the proposed law to achieve chattering reduction without compromising system robustness. In the process, it compares an existing adaptive gain strategy with the proposed law in terms of chattering, accuracy and robustness. Further, it discusses the rationale behind the selection of the SMC reaching law used in the paper that is different from the existing strategy. Also, the proposed strategy is implemented and tested for its performance in a commercial unmanned aerial vehicle (UAV), for brick wall construction that requires good level of accuracy and robustness. During implementation, it considers practical constraints of the physical system such as actuator bandwidth, sensitivity and saturation limits. From a pragmatic perspective, this work also provides a detailed discussion on the selection and tuning of controller parameters with respect to the physical system limits and desired performance criteria set by the user.

Keywords: Variable-structure/sliding-mode control, Adaptive control, Mechanical systems/robotics
Abstract: In this work, the design and analysis of a Neural Adaptive Super-Twisting Sliding Mode Controller is presented. Radial Basis Function Neural Network (RBFNN) is used to estimate the model uncertainties and an adaptive super-twisting sliding mode controller is designed to provide robustness against the external disturbances. The stability of the proposed controller is proven and the adaptive laws are derived from the Lyapunov stability condition. The performance of the proposed controller is compared with an existing work using a numerical example and as a case study the controller is applied to the problem of slung load carrying using an aerial vehicle and the corresponding simulation results are presented.

Keywords: Variable-structure/sliding-mode control, Autonomous systems
Abstract: In this paper, a Sub-Optimal Sliding Mode (SOSM) guidance scheme is proposed to induce boundary tracking behaviours in autonomous vehicles. The spread of an environmental feature in 2-dimensional space is modelled as a scalar field characterised by an unknown spatial gradient. It is assumed that a single autonomous vehicle is deployed and this provides a point measurement of the density value of the spatial phenomenon at its current position. Based on this instantaneous reading, a novel control scheme is proposed to simultaneously regulate the heading angle and the speed of the vehicle to track the desired contour line in finite time. In contrast to the previous scheme upon which the work in this paper builds, the novel guidance scheme is capable of automatically regulating the speed to help accurately maintain the vehicle alignment with the contour line. Numerical simulations demonstrates the effectiveness of the proposed control scheme also when compared with other solutions available in the existing literature.

Keywords: Variable-structure/sliding-mode control, Decentralized control, Lyapunov methods
Abstract: In this paper, a decentralised control scheme is proposed for a class of nonlinear interconnected systems using sliding mode techniques. Both matched uncertainty and mismatched unknown interconnections are considered. Using geometric transformation, the considered system is transferred to a system with special structure to facilitate design of sliding surface and decentralised controllers. The sliding surface is designed based on the tracking error, and a set of conditions are proposed to guarantee that when sliding motion occurs, the tracking errors are convergent to zero asymptotically while the system states are bounded. Decentralised controllers are then designed such that the states of the interconnected systems can be driven to the designed sliding surface. Finally, simulation on a coupled inverted pendulum system demonstrates that the developed results are effective.

Keywords: Variable-structure/sliding-mode control, Robust control, Lyapunov methods
Abstract: A novel switched state feedback is proposed to stabilize a planar controllable system in prescribed time regardless of whichever uniformly bounded external disturbance affects the system. The approach is based on a successive application of time-varying linear feedback synthesis and twisting controller design. The underlying strategy is to utilize globally stabilizing non-autonomous linear feedback so that the system trajectories enter an arbitrarily small domain of attraction as fast as desired regardless of initial conditions and then switch to the twisting controller that settles the trajectories from the pre-specified attraction domain at the origin in prescribed time. Tuning rules to achieve the desired settling time are explicitly derived and illustrated in an experimental study of a simple pendulum to track a reference trajectory with periodic velocity jumps.

Keywords: Variable-structure/sliding-mode control, Switched systems, Observers for Linear systems
Abstract: In this article, a collaborative observer is proposed for a class of Linear Switched Systems affected by unknown inputs. The class of switched systems under study accepts a dwell-time and has a completely known exogenous switching signal. Two main elements compose the proposed observer: a point observer designed using High-Order Sliding-Modes, which provides finite-time exact convergence in the presence of disturbances with a time-varying known upper bound, and a collaborative observer that gives an interval estimation of the state in the presence of the unknown inputs.

Keywords: Iterative learning control, Distributed control, Machine learning
Abstract: Distributed learning can enable scalable and effective decision making in numerous complex cyber-physical systems such as smart transportation, robotics swarm, power systems, etc. However, the stability of the system is usually not guaranteed in most existing learning paradigms; and this limitation can hinder the wide deployment of machine learning in the decision making of safety-critical systems. This paper presents a stability guaranteed distributed reinforcement learning (SGDRL) framework for interconnected linear subsystems, without knowing the subsystem models. While the learning process requires data from a peer-to-peer (p2p) communication architecture, the control implementation of each subsystem is only based on its local state. The stability of the interconnected subsystems will be ensured by a diagonally dominant eigenvalue condition, which will then be used in a model-free RL algorithm to learn the stabilizing control gains. The RL algorithm structure follows an off-policy iterative framework, with interleaved policy evaluation and policy update steps. We numerically validate our theoretical results by performing simulations on four interconnected sub-systems.

Keywords: Iterative learning control, Identification for control, Optimization algorithms
Abstract: Learning can substantially increase the performance of control systems that perform repeating tasks. The aim of this paper is to develop an efficient iterative learning control algorithm for MIMO systems with a large number of inputs and outputs that does not require model knowledge. The gradient of the control criterion is obtained through dedicated experiments on the system. Using a judiciously selected randomization technique, an unbiased estimate of the gradient is obtained from a single dedicated experiment, resulting in fast convergence of a Robbins-Monro type stochastic gradient descent algorithm. Analysis shows that the approach is superior to earlier deterministic approaches and to related SPSA-type algorithms. The approach is illustrated on a multivariable example.

Keywords: Iterative learning control, Learning, Optimal control
Abstract: We propose an adaptive state aggregation scheme to be used along with temporal-difference reinforcement learning and value function approximation algorithms. The resulting algorithm constitutes a two-timescale stochastic approximation algorithm with: (a) a fast component that executes a temporal-difference reinforcement learning algorithm, and (b) a slow component, based on online vector quantization, that adaptively partitions the state space of a Markov Decision Process according to an appropriately defined dissimilarity measure. We study the convergence of the proposed methodology using Bregman Divergences as dissimilarity measures that can increase the efficiency and reduce the computational complexity of vector quantization algorithms. Finally, we quantify its performance on the Cart-pole (inverted pendulum) optimal control problem using Q-learning with adaptive state aggregation based on the Self-Organizing Map (SOM) algorithm.

Keywords: Iterative learning control, Machine learning, Intelligent systems
Abstract: We present a learning method to learn the mapping from an input space to an action space, which is particularly suitable when the action is an optimal decision with respect to a certain unknown cost function. {We use an inverse optimization approach to retrieve the cost function by introducing a new loss function and a new hypothesis class of mappings.} A tractable convex reformulation of the learning problem is also presented. The method is effective for learning input-action mapping in continuous input-action space with input-output constraints, typically present in control systems. The learning approach can be effectively transformed to learn a {Model Predictive Control (MPC)} behaviour and a case study to mimic an MPC is presented, which is a rather computationally heavy control strategy. Simulation and experimental results show the effectiveness of the proposed approach.

Keywords: Iterative learning control, Manufacturing systems, Robotics
Abstract: Single Point Incremental Forming (SPIF) is a flexible sheet manufacturing technology. While not viable for large scale production applications, SPIF excels in the small batch size and rapid prototyping environments, since geometry-specific tooling is not required. However, due to the lack of in-process support, SPIF typically results in parts with poor geometric tolerances when compared to more traditional part forming techniques such as stamping and deep drawing. For this reason, SPIF has yet to be widely adopted in the industry. In this work, a method of constructing a data-driven model for use with norm-optimal Iterative Learning Controller (ILC) is developed to improve the accuracy of a SPIF process. Using in-process measurements of the sheet along with knowledge of the input, a data-driven model is constructed to optimize the input by predicting the resulting geometry from a change in tool depth. This Iterative Learning Controller was tested on a truncated pyramid geometry, and the results showed that the controller was able to effectively reduce the process error from an MAE of 4.053 mm to 0.912 mm after five iterations.

Keywords: Iterative learning control, Optimal control, Identification for control
Abstract: In this paper, an approximate optimal control framework is developed to obtain a tracking controller for a nonlinear system that can be implemented as an online model-based learning approach. Assuming a structured unknown nonlinear system augmented with the dynamics of a commander system, we obtain a control rule minimizing a given quadratic tracking objective function. This is achieved by manipulating the cost and introducing a quadratic value function in terms of some nonlinear bases to comply with the structured dynamics. This problem formulation facilitates the computation of an update rule for the parameterized value function. As a result, a matrix differential equation of the coefficients is extracted, which gives a computationally efficient way for updating the value function and consequently attaining the tracking controller in terms of the reference and state trajectories. The proposed optimal tracking framework can be seen as an online model-based reinforcement learning approach, where we use a system identification method to update the system model, and generate a corresponding control in an iterative way. The presented learning algorithm is validated by implementing tracking control on two nonlinear benchmark problems.

Keywords: Iterative learning control, Robust control, Stochastic systems
Abstract: Linear systems with multiplicative noise (LSMN) generalize the more common case of additive noise models. The multiplicative noise can model state-dependent noise and variations in the dynamics. We present an LSMN system identification algorithm which estimates both the first and second moments of the system parameters, and offers a probability bound on the estimations. We further develop an online scheme for identification and a robust control scheme based on the estimation bounds. Numerical examples are provided.

Keywords: Iterative learning control
Abstract: This paper targets at realizing deterministic tracking tasks for continuous-time iterative learning control (ILC) systems subject to nonrepetitive time intervals. A modified P-type ILC algorithm is proposed such that the deterministic tracking of continuous-time ILC can be ensured in the presence of the nonrepetitive time intervals. Furthermore, the convergence analysis of continuous-time ILC is implemented by resorting to an extended contraction mapping-based method. An example is also included to validate our derived deterministic tracking results of ILC.

Keywords: Optimization, Machine learning, Stochastic systems
Abstract: This paper considers stochastic convex optimization problems where the objective and constraint functions involve expectations with respect to the data indices or environmental variables, in addition to deterministic convex constraints on the domain of the variables. Although the setting is generic and arises in different machine learning applications, online and efficient approaches for solving such problems has not been widely studied. Since the underlying data distribution is unknown a priori, closed-form solution is generally not available, and classical deterministic optimization paradigms are not applicable. Existing approaches towards solving these problems make use of stochastic gradients of the objective and constraints that arrive sequentially over iterations. Stateof-the-art approaches, such as those using the saddle point framework, are able to ensure that the optimality gap as well as the constraint violation decay as O(T^(-1/2)) where T is the number of stochastic gradients. In this work, we propose a novel conservative stochastic optimization algorithm (CSOA) that achieves zero average constraint violation and O(T^(-1/2)) optimality gap. The efficacy of the proposed algorithm is tested on a relevant problem of fair classification.

Keywords: Optimization algorithms, Optimization
Abstract: Motivated by emerging applications in wireless sensor networks and large-scale data processing, we consider distributed optimization over directed networks where the agents communicate their information locally to their neighbors to cooperatively minimize a global cost function. We introduce a new unifying distributed constrained optimization model that is characterized as a bilevel optimization problem. This model captures a wide range of existing problems over directed networks including: (i) Distributed optimization with linear constraints. (ii) Distributed unconstrained nonstrongly convex optimization over directed networks. Employing a novel regularization-based relaxation approach and gradient-tracking schemes, we develop an iteratively regularized push-pull gradient algorithm. We establish the consensus and derive new convergence rate statements for suboptimality and infeasibility of the generated iterates for solving the bilevel model. The proposed algorithm and the complexity analysis obtained in this work appear to be new for addressing the bilevel model and also for the two sub-classes of problems. The numerical performance of the proposed algorithm is presented.

Keywords: Optimization algorithms, Hybrid systems, LMIs
Abstract: Momentum methods for convex optimization often rely on precise choices of algorithmic parameters, based on knowledge of problem parameters, in order to achieve fast convergence, as well as to prevent oscillations that could severely restrict applications of these algorithms to cyber-physical systems. To address these issues, we propose two dynamical systems, named the Hybrid Heavy-Ball System and Hybrid-inspired Heavy-Ball System, which employ a feedback mechanism for driving the momentum state toward zero whenever it points in undesired directions. We describe the relationship between the proposed systems and their discrete-time counterparts, deriving conditions based on linear matrix inequalities for ensuring exponential rates in both continuous time and discrete time. We provide numerical LMI results to illustrate the effects of our reset mechanisms on convergence rates in a setting that simulates uncertainty of problem parameters. Finally, we numerically demonstrate the efficiency and avoidance of oscillations of the proposed systems when solving both strongly convex and non-strongly convex problems.

Keywords: Optimization algorithms, Distributed control, Lyapunov methods
Abstract: This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. Unlike previous work on distributed mirror descent, we incorporate an integral feedback in the update, allowing the algorithm to converge with a constant step-size when discretized. We establish the asymptotic convergence of the algorithm using Lyapunov stability analysis. We further illustrate numerical experiments that verify the advantage of adopting integral feedback for improving the convergence rate of distributed mirror descent.

Keywords: Optimization algorithms, Large-scale systems
Abstract: This paper considers the problem of multi-agent distributed linear regression in the presence of system noises. In this problem, the system comprises multiple agents wherein each agent locally observes a set of data points, and the agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. We consider a server-based distributed architecture where the agents interact with a common server to solve the problem; however, the server cannot access the agents' data points. We consider a practical scenario wherein the system either has observation noise, i.e., the data points observed by the agents are corrupted, or has process noise, i.e., the computations performed by the server and the agents are corrupted. In noise-free systems, the recently proposed distributed linear regression algorithm, named the Iteratively Pre-conditioned Gradient-descent (IPG) method, has been claimed to converge faster than related methods. In this paper, we study the robustness of the IPG method, against both the observation noise and the process noise. We empirically show that the robustness of the IPG method compares favorably to the state-of-the-art algorithms.

Keywords: Optimization algorithms, Numerical algorithms, Stability of nonlinear systems
Abstract: This paper focuses on the computation of joint spectral radii (JSR), when the involved matrices are sparse. We provide a sparse variant of the procedure proposed by Parrilo and Jadbabaie, to compute upper bounds of the JSR by means of sum-of-squares (SOS) relaxations. Our resulting iterative algorithm, called SparseJSR, is based on the term sparsity SOS (TSSOS) framework, developed by Wang, Magron and Lasserre, yielding SOS decompositions of polynomials with arbitrary sparse support. SparseJSR exploits the sparsity of the input matrices to significantly reduce the computational burden associated with the JSR computation. Our algorithmic framework is then successfully applied to compute upper bounds for JSR, on randomly generated benchmarks as well as on problems arising from stability proofs of controllers, in relation with possible hardware and software faults.

Keywords: Optimization algorithms, Machine learning, Statistical learning
Abstract: We consider a class of convex distributed statistical learning problems with inequality constraints in an adversarial scenario. At each iteration, an alpha-fraction of m machines, which are supposed to compute stochastic gradients of the loss function and send them to a master machine, may act adversarially and send faulty gradients. To guard against defective information sharing, we develop a Byzantine primal-dual algorithm. For alphain[0,0.5), we prove that after T iterations the algorithm achieves tilde{O}(1/T+1/sqrt{mT}+alpha/sqrt{T}) statistical error bounds on both the optimality gap and the constraint violation. Our result holds for a class of normed vector spaces and, when specialized to the Euclidean space, it attains the optimal error bound for Byzantine stochastic gradient descent.

Keywords: Lyapunov methods, Adaptive control, Robotics
Abstract: In this paper, we present a backstepping adaptive hybrid force/position control based on Barrier Lyapunov Function for a robotic manipulator to prevent constraint violation of applied force and position simultaneously. First, the task space is partitioned according to the constrained and unconstrained directions, and a new representation of dynamics is introduced. Next, force/position control is applied using the strict-feedback backstepping technique, in which a time-varying Barrier Lyapunov Function is employed to ensure that the force and position do not violate their constraints. Finally, to deal with uncertainty, disturbance and non-linearity of the system, an adaptive radial basis function neural network (RBFNN) is also implemented in the control algorithm. Stability proof of the proposed control method is presented, and simulation studies on a 2-link manipulator show the effectiveness as well as the performance of the proposed controller in preventing constraint violation.

Keywords: Lyapunov methods, Constrained control, Stability of nonlinear systems
Abstract: In this paper, we study the effect of control input constraints on the domain of attraction of an FxTS equilibrium point. We first present a new result on FxTS, where we allow a positive term in the time derivative of the Lyapunov function. We provide analytical expressions for the domain of attraction and the settling time to the equilibrium in terms of the coefficients of the positive and negative terms that appear in the time derivative of the Lyapunov function. We show that this result serves as a robustness characterization of FxTS equilibria in the presence of an additive, vanishing disturbances. We use the new FxTS result in formulating a provably feasible quadratic program (QP) that computes control inputs that drive the trajectories of a class of nonlinear, control-affine systems to a goal set, in the presence of control input constraints.

Keywords: Lyapunov methods, Constrained control
Abstract: In this paper, we propose a self-triggered control strategy to guarantee forward pre-invariance of a closed set for a control system modeled by a constrained differential inclusion. Using a (not necessarily periodic) zero-order hold control scheme, this paper addresses two key issues: i) computing the time of the next sampling event, and ii) the assurance of a uniform lower bound on the inter-event times, both while guaranteeing forward invariance. Our results allow the sets to render forward pre-invariant to be unbounded. Very importantly, the results impose mild regularity on the right-hand side of the system and on the barrier certificates. Simulations showcase the proposed algorithms and provide comparisons with the literature.

Keywords: Lyapunov methods, Control applications, Computational methods
Abstract: The study of control synthesis for reach-avoid-stay objectives for nonlinear systems has received considerable interest in recent years. Such objectives can be naturally treated as a formal specification and effectively handled by formal methods. While formal methods rely on constructing a fitine-state approximation and developing algorithms to capture the winning set (a set of initial states from which a controller exists to realize the given task), Lyapunov methods can characterize stability and safety properties without having to discretize the state space. Inspired by the recent work on converse Lyapunov-barrier theorems, we propose control Lyapunov-barrier functions to provide sufficient conditions for control synthesis with reach-avoid-stay specifications. A comparison between the Lyapunov method and the existing fixed-point algorithm based formal method is illustrated by an application to enhancing performance of jet engine compressors, which is based on a reduced Moore-Greitzer nonlinear ODE model. We apply a quadratic programming (QP) framework to reactively synthesize controllers in the case study.

Keywords: Lyapunov methods, Robust control, Constrained control
Abstract: This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under multiple constraints. We enforce forward invariance of static and dynamic safe sets to ensure the safety of the system trajectories and enforce convergence to a given goal set within a user-defined time in the presence of input constraints. We use robust variants of control barrier functions (CBF) and control Lyapunov functions (CLF) to incorporate a class of additive disturbances in the system dynamics, and sensing errors in the system states. To solve the underlying constrained control problem, we formulate a quadratic program and use the proposed robust CBF-CLF conditions to compute the control input. Finally, we showcase the efficacy of the proposed method on a numerical case study involving multiple underactuated marine vehicles.

Keywords: Lyapunov methods, Stability of nonlinear systems
Abstract: In this paper, we present estimates for solutions and for the attraction domain of the trivial solution for systems with delayed and nonlinear weighted homogeneous right-hand side of positive degree. The results are achieved via a generalization of the Lyapunov-Krasovskii functional construction presented recently for homogeneous systems with standard dilation. Along with the classical approach for the calculation of the estimates within the Lyapunov-Krasovskii framework, we develop a novel approach which combines the use of Lyapunov-Krasovskii functionals with ideas of the Razumikhin framework. More precisely, a lower bound for the functional on a special set of functions inspired by the Razumikhin condition is constructed, and an additional condition imposed on the solution of the comparison equation ensures that this bound can be used to estimate all solutions in a certain neighbourhood of the trivial one. An example shows that this approach yields less conservative estimates in comparison with the classical one.

Keywords: Lyapunov methods, Stability of nonlinear systems
Abstract: For the state-constrained control problem with complex barrier regions, this study presents an effective construction method of the state transformation for the barrier avoidance control design. The diffeomorphic transformation in barrier avoidance control converts a constrained control problem into an unconstrained one, and enables the nonlinear control design in the new coordinates. However, a systematic way to construct such a transformation under a non-hyperrectangular barrier shape has never been explored in the literature. This paper provides a guideline to choose this diffeomorphic transformation in a cascade manner for a class of complex barrier regions. The proposed method is applied to a high-order double integrator system through sliding mode control in the case study, showing the efficacy of this work.

Keywords: Lyapunov methods, Switched systems, LMIs
Abstract: This paper investigates stability analysis for implicit, switched linear systems using homogeneous Lyapunov functions (HLF). HLFs of increasing degree are constructed through an outer-product, lifting transformation of the state vector to higher dimensions. This paper presents linear matrix inequalities sufficient conditions for asymptotic stability of these systems based on HLFs. A method is provided to search for Lyapunov functions by incrementally increasing the degree of the homogeneous Lyapunov functions. To address the dimensional growth of the problem space incurred by the lifting transform, a method for dimensional reduction is derived.

Keywords: Constrained control, Optimization, Robust control
Abstract: Path planning and control is a crucial task for the robot, especially when considering noise measurements. In this paper, we propose a novel approach to design linear feedback controllers for a robot navigating in polygonal environments with noisy measurements. The stability and safety guarantees of the controller come from the chance Control Barrier Function constraints and the chance Control Lyapunov Function constraints, respectively. The controller design problem is set up as a chance constraint-based robust optimization. We apply convex over-approximations to obtain upper bounds of constraints, which lead to a quadratic constraint quadratic program (QCQP). We provide simulation results for equilibrium control and path control. Numerical experiments demonstrate that the controller is robust with noise measurements.

Keywords: Constrained control, Predictive control for linear systems, Linear systems
Abstract: This paper presents a constraint management strategy based on Scalar Reference Governors (SRG) to enforce control, state, and output constraints while taking into account the preview information of the reference signals. The strategy, referred to as the Preview Reference Governor (PRG), can outperform SRG while maintaining the highly-attractive computational benefits of SRG. However, as it is shown, the performance of PRG may suffer if large preview horizons are used. An extension of PRG, referred to as Multi-horizon PRG, is proposed to remedy this issue. Quantitative comparisons between SRG, PRG, and Multi-horizon PRG on a vehicle rollover example are presented to illustrate their performance and computation time.

Keywords: Constrained control, Predictive control for linear systems
Abstract: This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking.

Keywords: Constrained control, Robotics, Autonomous robots
Abstract: We rely on Nagumo's invariance theorem to develop a new approach for navigation in unknown environments of arbitrary dimension. The idea consists in projecting the nominal velocities (that would drive the robot to the target in the absence of obstacles) onto Bouligand's tangent cones (referred to as the safety velocity cones) when the robot is close to the boundary of the free space. The proposed projection-based controller is explicitly constructed to guarantee safety and convergence to a set of Lebesgue measure zero that contains the target. For specific free spaces such as Euclidean sphere worlds, the convergence to the target is guaranteed from almost all initial conditions in the free space. We provide a version of the controller (generating a continuous and piecewise smooth closed-loop vector field) relying on the robot's current position and local range measurements (e.g., from LiDAR or stereo vision) without global prior knowledge about the environment.

Keywords: Control applications, Mechatronics
Abstract: In safety-critical control, a system must satisfies stability/tracking objectives and safety constraints. This can be assured applying a control framework that unifies stability/tracking objectives, represented by a nominal control law, and safety constraints, represented by control barrier functions (CBFs), through quadratic programming (QP). This work considers systems with model uncertainties and high relative-degree safety constraints; thus, the safety constraints are expressed as robust exponential control barrier functions (ECBFs). The proposed control framework is numerically validated considering two applications: a Furuta pendulum and a magnetic levitation (MAGLEV) system. The numerical results show that the proposed controller respects the stability/tracking objectives and the safety constraints even with model uncertainties.

Keywords: Constrained control, Supervisory control, Robust control
Abstract: Incorporating predictions of external inputs, which can otherwise be treated as disturbances, has been widely studied in control and computer science communities. These predictions are commonly referred to as preview in optimal control and lookahead in temporal logic synthesis. However, little work has been done for analyzing the value of preview information for safety control for systems with continuous state spaces. In this work, we start from showing general properties for discrete-time nonlinear systems with preview and strategies on how to determine a good preview time, and then we study a special class of linear systems, called systems in Brunovsky canonical form, and show special properties for this class of systems. In the end, we provide two numerical examples to further illustrate the value of preview in safety control.

Keywords: Hybrid systems, Hierarchical control, Identification for control
Abstract: This paper presents a hierarchical structure to directly design controllers for (possibly nonlinear) constrained systems. The proposed architecture combines the advantages of an inner data-driven switching controller designed to achieve a predefined closed-loop behavior and an outer model predictive controller, which is used as a reference governor. These design choices enable us to avoid the identification step typical of model-based approaches while exploiting the ability of model predictive controllers to handle constraints and optimize the closed-loop performance. As a proof of concept, a benchmark simulation example is used to demonstrate the effectiveness of the proposed strategy.

Keywords: Algebraic/geometric methods, Constrained control, Stability of nonlinear systems
Abstract: This paper presents a novel approach for pointing direction control of a rigid body with a body-fixed sensor, in the presence of control constraints and pointing direction constraints. This scheme relies on the use of artificial potentials where an attractive artificial potential is placed at the desired pointing direction and a repulsive artificial potential is used to avoid an undesirable pointing direction. The proposed control law ensures almost global asymptotic convergence of the rigid body to its desired pointing direction, while satisfying the control input constraints and avoiding the undesirable pointing direction. These theoretical results are followed by numerical simulation results that provide an illustration of the scheme for a realistic spacecraft pointing control scenario.

Keywords: Robust control, Optimization, Computational methods
Abstract: We study the problem of finding closed-form outer approximations of Minkowski sums and products of sets in the complex plane. Using polar coordinates, we pose this as an optimization problem in which we find a pair of contours that give lower and upper bounds on the radial distance at a given angle. Through a series of variable transformations we rewrite this as a sum-of-squares optimization problem. Numerical examples are given to demonstrate the performance.

Keywords: Robust control, Stability of linear systems, Uncertain systems
Abstract: In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines the range of the interpolant, when evaluated on the imaginary axis, to a frequency-dependent set. By considering a sufficient condition for when this interpolation problem has a solution, we derive an approximate solution algorithm that can also be used for controller synthesis. The conservativeness of the method is reduced by introducing a shift, which can be tuned by the user. Finally, the theory is illustrated on a numerical example with a plant with uncertain gain, phase, and output delay.

Keywords: Stability of nonlinear systems, LMIs, Lyapunov methods
Abstract: The global asymptotic stability analysis and state feedback control design for Lur'e systems are formulated in terms of linear and bilinear matrix inequalities (LMIs and BMIs), respectively, for static nonlinearities that are both sector-bounded and slope-restricted. The LMI problem is solvable in polynomial time using standard solvers, and suboptimal solutions to the BMI problem can be obtained by iteratively solving LMI problems. In three numerical examples from the literature, the LMI stability condition is observed to produce stability margins that are either the same or less conservative than published stability criteria. In another example, the iterative-LMI method is used to design a state feedback controller that is guaranteed to provide global asymptotic stability for the closed-loop system.

Keywords: Time-varying systems, Linear systems, Numerical algorithms
Abstract: We present an efficient algorithm to compute the induced norms of finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both induced mathcal{L}_2 and terminal Euclidean norm penalties on outputs. Existing computational approaches include the power iteration and the bisection of a Riccati Differential Equation (RDE). The power iteration has low computation time per iteration but overall convergence can be slow. In contrast, the RDE condition provides guaranteed bounds on the induced gain but single RDE integration can be slow. The complementary features of these two algorithms are combined to develop a new algorithm that is both fast and provides provable upper and lower bounds on the induced norm within the desired tolerance. The algorithm also provides a worst-case disturbance input that achieves the lower bound on the norm. We also present a new proof which shows that the power iteration for this problem converges monotonically. Finally, we show a controllability Gramian based simpler computational method for induced mathcal{L}_2-to-Euclidean norm. This can be used to compute the reachable set at any time on the horizon. Numerical examples are provided to demonstrate the proposed algorithm.

Keywords: Robust control, Uncertain systems, LMIs
Abstract: This paper deals with the problem of computing ellipsoidal state invariant sets for uncertain systems that consist of a nominal part and an uncertainty feedback operator. The set of allowable uncertainty operators is characterized using point-wise integral quadratic constraints (IQCs). The proposed solution methodology combines the S-procedure and the notion of point-wise IQCs in a novel way. The approach allows for a point-wise characterization of the disturbance inputs and involves solving a grid of convex optimization problems. The paper concludes with an illustrative example.

Keywords: LMIs, Optimization, Algebraic/geometric methods
Abstract: Peak Estimation aims to find the maximum value of a state function achieved by a dynamical system. This problem has been previously cast as a convex infinite-dimensional linear program on occupation measures, which can be approximately solved by a converging hierarchy of moment relaxations. In this paper, we present an algorithm to approximate optimal trajectories if the solutions to these relaxations satisfy rank constraints. We also extend peak estimation to maximin and safety analysis problems, providing a certificate that trajectories are bounded away from an unsafe set.

Keywords: Computational methods, Lyapunov methods, Switched systems
Abstract: This paper proposes computational algorithms for analyzing conewise affine dynamical systems, where every neighborhood of the origin contains an affine mode. These algorithms are based on conewise linear Lyapunov functions. To make such algorithms useful, we present an algorithm to automatically search over partitions defining these conewise Linear functions. This algorithm is sound, although we present a counter-example to its completeness. We show that his approach verifies stability of 2D and 3D examples of conewise affine dynamical systems, including combinations of the harmonic and nonsmooth oscillators.

Keywords: Behavioural systems, Stochastic optimal control, Statistical learning
Abstract: A recently developed robust control technique builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an optimal transport based method for compressing such large dataset to a smaller synthetic one of representative behaviours, aiming to alleviate the computational burden of controllers to be implemented online. Specifically, the synthetic data are determined by minimizing the Wasserstein distance between atomic distributions supported on both the original dataset and the compressed one. We show that a distributionally robust control law computed using the compressed data enjoys the same type of performance guarantees as the original dataset, albeit enlarging the ambiguity set by an easily computable quantity. Numerical studies confirm that the control performance with the synthetic data is comparable to the one obtained with the original data, but with significantly less computation required.

Keywords: Adaptive control, Direct adaptive control, Hybrid systems
Abstract: This paper presents a novel framework for safety-critical adaptive control of hybrid systems with unknown disturbances using Control Barrier Functions (CBFs). Our proposed approach utilizes a hybrid update law to maintain and reset an estimate of the unknown disturbances. In contrast to continuous time adaptation laws for safety-critical control, this enables relaxation of assumptions on the unknown disturbances and permits less conservative behavior away from the boundary of safe region. To overcome the challenge of discrete behavior inherent in hybrid dynamics, we introduce a discrete state variable that enforces a hysteresis-type behavior. Lastly we illustrate the implementation of this framework on an adaptive cruise control (ACC) system.

Keywords: Adaptive control, Decentralized control, Large-scale systems
Abstract: In this paper, an observer-based decentralized event-triggered neuro-adaptive controller (DETNAC) is presented for complex uncertain nonlinear systems. Novelty of the study lies in the construction of the scheme and observer-based control design which uses artificial neural network (ANN), machine learning (polynomial regression), and nominal system dynamics along with Event-triggering. Event-triggering is based on actual system’s performance parameter (tracking error) and although multiple uncertainties are considered but online estimation using advance techniques makes controller much robust and efficient. Proposed method not only provide estimation and tracking performance, but its two tunable gains provide filtering effect which help to avoid transient high frequency oscillations. Lyapunov analysis is used for stability analysis and to develop event-triggering condition. Efficacy of the controller is demonstrated using a nonlinear numerical example of a chaotic complex system.

Keywords: Adaptive control, Delay systems, Linear systems
Abstract: The paper deals with the problem of adaptive compensation of {it unmatched} disturbances in linear time-invariant multi-input multi-output unstable plants with input delay. The external disturbances affects both the input and the output of the plant simultaneously and can be represented as multi-harmonic signals with unknown frequencies, phases, and amplitudes. The control scheme is based on disturbance parametrization with prediction as well as on a special swapping scheme being applicable to a MIMO unstable error model with delay. Three adaptation algorithms are represented: gradient-based one, and the algorithms with improved parametric convergence based on dynamic regressor extension and memory regressor extension.

Keywords: Adaptive control, Direct adaptive control, Adaptive systems
Abstract: For retrospective cost adaptive control (RCAC), this paper shows that the retrospective performance variable can be decomposed into the sum of a performance term and a model-matching term. The model-matching term consists of the difference between the closed-loop transfer function from the virtual external control perturbation to the retrospective performance variable driven by the virtual external control perturbation.The key insight arises from the observation that, at each step, recursive-least-squares (RLS) minimizes the magnitude of the retrospective performance variable by forcing the performance term and the model-matching term to have opposite signs. As the controller converges, the virtual external control perturbation, and thus the model-matching term, converges to zero, which, in turn, drives the performance term to zero. This mechanism thus prevents RLS from converging to a controller that is destabilizing or has poor performance. The contribution of this paper is thus to derive the decomposition of the retrospective performance variable and use this decomposition to elucidate the mechanism described above.

Keywords: Adaptive control, Estimation, Kalman filtering
Abstract: In this paper, the interacting multiple model was used to design two adaptive controllers for a dynamic spacecraft system. Using knowledge of the system mode, the gains of a proportional-derivative and sliding mode controller corresponding to a nominal and a fault mode of the system were mixed to create a control input that more accurately represented the current system state. By implementing the interacting multiple model with an unscented Kalman filter, this technique was extended to a nonlinear dynamic system. The developed strategies are validated on a simulated spacecraft system and evaluated using Monte Carlo simulations by means of root mean squared errors. Results emphasize the preservation and increase in tracking performance permitted by the adaptive strategies in the presence of faults.

Keywords: Adaptive control, Linear systems, Sampled-data control
Abstract: The present paper focuses on adaptive feedback disturbance rejection for high-order, lightly damped systems using retrospective cost adaptive control (RCAC). RCAC requires a closed-loop target model, which captures key features of the plant dynamics. In the SISO case, this information includes knowledge of the sign of the leading numerator coefficient, relative degree, and non-minimum phase zeros. The present paper investigates the feasibility of using a deverberated transfer function (DTF) as the closed-loop target model. A dereverberated model of a lightly damped plant captures the magnitude and phase trend but ignores resonances and anti-resonances, thus providing a simplified, low-order model of a lightly damped system. The present paper investigates the performance and robustness of RCAC using a dereverberated target model based on the nominal plant model.

Keywords: Adaptive control, Lyapunov methods, Stability of nonlinear systems
Abstract: In this letter, an advanced adaptive controller is designed for N-cascaded H-bridge multilevel inverters, each fed by a DC voltage source. The studied system provides an added-value to Uninterruptable Power Supply applications, and is able to generate a precise sinusoidal voltage using a low dimensional LC filter. The main objectives of this letter are: i. generating a low THD sinusoidal voltage, ii. developing adaptive control laws able to regulate the system even with the presence of parameters' variations, and iii. proving the stability of the designed system using some tools from Lyapunov stability, Lasalle's invariance principle and persistency of excitation. This latter proves that the closed-loop control system is uniformly exponentially stable. To achieve these objectives, the adaptive backstepping approach is used. The performance of the system is checked with the use of MATLAB/SIMULINK/ SimPowerSystems environment, where the synthesized regulator meets its objectives.

Keywords: Adaptive control, Nonlinear output feedback, Lyapunov methods
Abstract: In the paper the problem of adaptive backstepping control of an uncertain nonlinear plant represented in the parametric output feedback canonical form is addressed. The state of the plant is not accessible for measurement and its parameters are not known. New modular backstepping state feedback design with high-order tuners recently proposed in [7], [8], [9] provides improvement of the transient performance of the closed-loop system by appropriate compensation of the deteriorating effect caused by the transients of the adjustable parameters. The main focus of the present paper is to extend the approach proposed in [7], [8], [9] to the case of output-feedback control. It is proved and demonstrated via simulation that the output-feedback adaptive controller designed accelerates the tuning of controller parameters.