Keywords: Estimation, Distributed control, Robust control
Abstract: In this work, we study the problem of distributed sampling for the recovery of a remote source under information mismatch at the estimator. In particular, a centralized estimator seeks to estimate a remote Gaussian random signal, where unlike in the ‘classical’ estimation setup, we assume that the estimator has a fixed, unknown mismatch vis-à-vis source statistics, in particular, the source covariance matrix. Such a mismatched estimator deploys multiple samplers in the field, where each sampler observes an independently noise corrupted version of the remote source and then forwards its sampled version to the estimator. The estimator has a fixed limit on the number of samples it can concurrently process; given such a total sampling budget, it seeks to distribute these samples optimally among samplers so as to obtain a reasonably high fidelity sampled noisy observation of the remote source via the samplers. Using this sampled data, the mismatched estimator then outputs a source estimate which minimizes distortion (i.e., the overall mean squared error). Our principal goal in this work is to understand the distortion-versus-sampling rate trade-off for the mismatched Gaussian source estimation problem under general distributed configurations. In the high-rate sampling regime, where the estimator has a ‘large’ sampling budget and essentially every sampler can operate at ‘high’ sampling rate, we show the interesting result that for a wide range of parameters, the optimal distributed sampling strategy is a uniform sampling strategy but one which, interestingly, does not depend on the mismatch at the estimator. We also characterize the optimal distortion, which we show does indeed depend on the degree of mismatch. Our results also bring to the fore an interesting phenomenon where the optimal distortion behaves asymmetrically w.r.t. the nature of mismatch, i.e., even for identical mismatch magnitude, the distortion is significantly different depending on the sign of the mismatch.

Keywords: Estimation, Kalman filtering, Filtering
Abstract: In this paper a filtering method for non-Gaussian linear systems is adopted to face the problem of the target tracking in the presence of the glint noise. In particular, we extend the quadratic filtering method with virtual measurements to the three-dimensional case of the target tracking problem. Moreover, we present extensive numerical simulation by comparing our method with several filtering algorithms used in the case of heavy tailed noises. The latter numerical results confirm the effectiveness of the proposed approach.

Keywords: Filtering, Optimal control, PID control
Abstract: Non-iterative data-driven controller design methods are very convenient for their ease of implementation and for only using a collected data set for the design. One of these methods is Optimal Controller Identification (OCI), which uses the Prediction Error Method to identify a model of the system parameterized by the controller's parameters and the desired response of the controlled system, the Reference Model. The Virtual Reference Feedback Tuning (VRFT), another data-driven method, has a widely used filter that benefits its performance in the case of designing underparameterized controllers, but the same has not been yet presented for OCI. In this paper, a specific filter for OCI is developed for the underparameterized controller case and tested in a series of situations, resulting in a gain of performance.

Keywords: Kalman filtering, Information theory and control, Uncertain systems
Abstract: Maximum correntropy criterion (MCC) has been widely used in Kalman filter to cope with heavy-tailed measurement noises. However, its performance on mitigating non-Gaussian process noises and unknown disturbance is rarely explored. In this paper, we extend the definition of correntropy from a single kernel to multiple kernels. Then, we derive a multi-kernel maximum correntropy Kalman filter (MKMCKF) to cope with multivariate non-Gaussian noises and disturbance. Three examples are provided to show the effectiveness of the proposed methods.

Keywords: Output regulation, Distributed parameter systems, Linear systems
Abstract: In this paper, we consider robust output tracking problem of an undamped Euler-Bernoulli beam with boundary control and boundary observation. In particular, we study a cantilever beam which has control and observation at the free end. As our main result, we construct a finite-dimensional,internal model based controller for the output tracking of the beam system. In addition, we consider a case where the controller achieves the robust output tracking for the cantilever beam with distributed control and observation. Numerical simulations demonstrating the effectiveness of the controller are presented.

Keywords: Biomedical, Differential-algebraic systems, Modeling
Abstract: The lack of methods to evaluate mechanical function of donated hearts in the context of transplantation imposes large precautionary margins, translating into a low utilization rate of donor organs. This has spawned research into cyber-physical models constituting artificial afterloads (arterial trees), that can serve to evaluate the contractile capacity of the donor heart.

The Windkessel model is an established linear time-invariant afterload model, that researchers committed to creating a cyber-physical afterload have used as a template. With aortic volumetric flow as input and aortic pressure as output, it is not directly obvious how a Windkessel model will respond to changes in heart contractility.

We transform the classic Windkessel model to relate power, rather than flow, to pressure. This alters the model into a differential-algebraic equation, albeit one that is straightforward to simulate. We then propose a power signal model, that is based on pressure and flow measurements and optimal in a Bayesian sense within the class of C2 signals. Finally, we show how the proposed signal model can be used to create relevant simulation scenarios, and use this to illustrate why it is problematic to use the Windkessel model as a basis for designing a clinically relevant artificial afterload.

Keywords: Optimal control, Distributed control, Autonomous systems
Abstract: This paper presents a distance-based formation control of nonlinear agents on a plane. Due to mathematical complexity, the distance-based formation is mainly studied for linear single- and double-integrator models. Here, we introduce a novel control scheme for a distance-based control of a set of nonlinear agents. The formation topology is modeled as directed graphs where just one incident agent controls the corresponding edge (distance constraint). The proposed method is based on state-dependent Riccati equation (SDRE) theory, which can effectively be applied to nonlinear systems. The asymptotic stability of the formation is rigorously proven. Moreover, using the SDRE method and signed area constraints, the proposed controller guarantees collision avoidance and prevents flip ambiguity of the formation. Simulation results are presented that support theoretical results.

Keywords: Optimal control, Optimization
Abstract: The productivity and efficiency of port operations strongly depend on how fast a ship can be unloaded and loaded again. With this in mind, ship-to-shore cranes perform the critical task of transporting containers into and onto a ship and must do so as fast as possible. Though the problem of minimizing the time spent in moving the payload has been addressed in previous studies, the different heights of the container stacks have not been the focus. In this paper, we perform a change of variable and reformulate the optimization problem to deal with the constraints on the stack heights. As consequence, these constraints become trivial and easy to represent since they turn into bound constraints when the problem is discretized for the numerical solver. To validate the idea, we simulate a small-scale scenario where different stack heights are used. The results confirm our idea and the representation of the stack constraints become indeed trivial. This approach is promising to be applied in real crane operations and has the potential to enhance their automation.

Keywords: Optimal control, Optimization algorithms, Optimization
Abstract: A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed state-control constraint such that the constraint is expressed by variables at a certain previous time stage. It is showed that if the solution satisfies the second-order sufficient conditions of the OCP with the transformed mixed state-control constraints, it is a local minimum of the OCP with the original pure-state constraints. A Riccati recursion algorithm is derived to solve the OCP using the transformed constraints with linear time complexity in the grid number of the horizon, in contrast to a previous approach that scales cubically with respect to the total dimension of the pure-state equality constraints. Numerical experiments on the whole-body optimal control of quadrupedal gaits that involve pure-state equality constraints owing to contact switches demonstrate the effectiveness of the proposed method over existing approaches.

Keywords: Optimization, Optimization algorithms, Distributed control
Abstract: We study the problem of non-constrained, discrete-time, online distributed optimization in a multi-agent system where some of the agents do not follow the prescribed update rule either due to failures or malicious intentions. None of the agents have prior information about the identities of the faulty agents and any agent can communicate only with its immediate neighbours. At each time step, a locally Lipschitz strongly convex cost function is revealed locally to all the agents and the non-faulty agents update their states using their local information and the information obtained from their neighbours. We measure the performance of the online algorithm by comparing it to its offline version, when the cost functions are known apriori. The difference between the same is termed as regret. Under sufficient conditions on the graph topology, the number and location of the adversaries, the defined regret grows sublinearly. We further conduct numerical experiments to validate our theoretical results.

Keywords: Optimization algorithms, Optimal control, Hybrid systems
Abstract: This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous work, not only the size of the binary search tree is considered, but also the exact complexity of solving the relaxations in the nodes by using recent results from exact complexity certification of active-set QP methods. With the algorithm proposed in this paper, a total worst-case number of QP iterations to be performed in order to solve the MIQP problem can be determined as a function of the parameter in the problem. An important application of the proposed method is Model Predictive Control for hybrid systems, that can be formulated as an MIQP that has to be solved in real-time. The usefulness of the proposed method is successfully illustrated in numerical examples.

Keywords: Optimization, Lyapunov methods, Time-varying systems
Abstract: A time-varying (TV) optimization problem arises in many real-time applications, where the objective function or constraints change continuously with time. Consequently, the optimal points of the problem at each time instant form an optimal trajectory and hence tracking the optimal trajectory calls for the need to solve the TV optimization problem. A second-order continuous-time gradient-flow approach is proposed in this paper to track the optimal trajectory of TV convex optimization problems in fixed-time irrespective of the initial conditions. Later on we present a second-order nonsmooth dynamical system to solve the TV optimization problem in fixed time that does not require the exact information about the time rate of change of the cost function gradient. This makes the non-smooth dynamical system robust to the temporal variation in the gradient of the cost function. Two numerical examples are considered here for the simulation-based validation of the proposed approaches.

Keywords: Lyapunov methods, Nonlinear output feedback, Fluid flow systems
Abstract: In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of the system on the first sub-domain is measured along a given interval of time, and the state on the remaining sub-domain is measured along another interval of time. Under the proposed sensing scenario, we control the considered equation by designing the value of the state at three isolated spatial points, the two extremities of the spatial domain plus one inside point. Furthermore, we impose a null value for the spatial gradient of the state at these three locations. Under such a control loop, we propose two types of controllers and we analyze the stability of the resulting closed-loop system in each case. The paper is concluded with some discussions and future works.

Keywords: Stability of nonlinear systems
Abstract: This paper extends the existing singular perturbation results to a class of nonlinear discrete-time systems whose fast dynamics have limit cycles. By introducing the discrete-time reduced averaged system, the main result (Theorem 1) shows that for a given fixed time interval, the solutions of the original system can be made arbitrarily close to the solutions of the reduced averaged system and the boundary layer system. From this result, the stability properties of the original system are obtained from the stability properties of the reduced averaged system and the boundary layer system. Simulation results support the theoretical findings.

Keywords: Time-varying systems, Switched systems, Lyapunov methods
Abstract: Emerging advanced control applications, with increased complexity in software but limited computing resources, suggest that real-time controllers should have adaptable designs. These control strategies also should be designed with consideration of the run-time behavior of the system. One of such research attempts is to design the controller along with the task scheduler, known as control-scheduling co-design, for more predictable timing behavior as well as surviving system overloads. Unlike traditional controller designs, which have equal-distance sampling periods, the co-design approach increases the system flexibility and resilience by explicitly considering timing properties, for example using an event-based controller or with multiple sampling times (non-uniform sampling and control). Within this context, we introduce the first work on the discretization of an energy-based controller that can switch arbitrarily between multiple periods and adjust the control parameters accordingly without destabilizing the system. A digital controller design based on this paradigm for a DC motor with an elastic load as an example is introduced and the stability condition is given based on the proposed Lyapunov function. The method is evaluated with various computer-based simulations which demonstrate its effectiveness.

Keywords: Optimal control, Lyapunov methods, Optimization
Abstract: Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization problem. To address these challenges, we propose a duality-based safety-critical optimal control using nonsmooth control barrier functions for obstacle avoidance between polytopes, which can be solved in real-time with a QP-based optimization problem. A dual optimization problem is introduced to represent the minimum distance between polytopes and the Lagrangian function for the dual form is applied to construct a control barrier function. We validate the obstacle avoidance with the proposed dual formulation for L-shaped (sofa-shaped) controlled robot in a corridor environment. We demonstrate real-time tight obstacle avoidance with non-conservative maneuvers on a moving sofa (piano) problem with nonlinear dynamics.

Keywords: Adaptive control, Switched systems
Abstract: In this paper, we propose a novel indirect model reference adaptive control approach for uncertain piecewise affine systems. This approach exploits a barrier Lyapunov function to construct novel adaptation laws and average dwell time constraints for switching. Compared to the previous research, where closed-loop stability and asymptotic tracking can only be established with a common Lyapunov function, the current approach allows a multiple Lyapunov function setting and enables broader applications. Furthermore, the estimation errors of control gains and subsystem parameters are proved to converge to zero asymptotically if a persistent excitation condition is satisfied. A simulation example of the pitch control of a helicopter system shows the effectiveness of the proposed approach.

Keywords: Sampled-data control, Networked control systems, Hybrid systems
Abstract: In this paper, we implement model-based event-triggered control on a hybrid controller by exploiting finite-time attractivity of the sensor dynamics. We provide conditions for the following properties of the closed-loop system: 1) asymptotic stability of a compact set; 2) no Zeno solutions; 3) robustness against small perturbations. The versatility of the proposed approach is demonstrated by applying it on top of another event-triggered controller.

Keywords: Pattern recognition and classification, Statistical learning, Machine learning
Abstract: There is a need to perform offline anomaly detection in count data streams to identify both systemic changes and outliers, simultaneously. We propose a new algorithmic method, called the Anomaly Detection Pipeline, which leverages common statistical process control procedures in a novel way to accomplish this. The method we propose does not require user-defined control or phase I training data, automatically identifying regions of stability for improved parameter estimation to support change point detection. The method does not require data to be normally distributed, and it detects outliers relative to the regimes in which they occur. Our proposed method performs comparably to state-of-the-art change point detection methods, provides additional capabilities, and is extendable to a larger set of possible data streams than known methods.

Keywords: Stochastic systems, Kalman filtering, Control over communications
Abstract: In this paper, we have proposed a technique for Bayesian sequential detection of replay attacks on networked control systems with a constraint on the average number of watermarking (ANW) events used during normal system operations. Such a constraint limits the increase in the control cost due to watermarking. To determine the optimal sequence regarding the addition or otherwise of watermarking signals, first, we formulate an infinite horizon stochastic optimal control problem with a termination state. Then applying the value iteration approach, we find an optional policy that minimizes the average detection delay (ADD) for fixed upper bounds on the false alarm rate (FAR) and ANW. The optimal policy turns out to be a two thresholds policy on the posterior probability of attack. We derive approximate expressions of ADD and FAR as functions of the two derived thresholds and a few other parameters. A simulation study on a single-input single-output system illustrates that the proposed method improves the control cost considerably at the expense of small increases in ADD. We also perform simulation studies to validate the derived theoretical results.

Keywords: Modeling, Linear parameter-varying systems, Kalman filtering
Abstract: A digital twin is a computer-based digital representation that simulates the behavior of a physical system. Digital twins help users to interact with real-world processes digitally. Time-variant modeling is critical to preserving the accuracy of digital twin models as the process dynamics change with time. Kalman filter is a well-known recursive algorithm that adjusts the process state estimates using real-time measurements. Sparse identification of nonlinear dynamics (SINDy) is an algorithm that automatically identifies system models from large data sets using sparse regression so as to prevent overfitting and find an ideal trade-off between model complexity and accuracy. In this paper, the SINDy approach is first extended to the generalized SINDy (GSINDy). Then, the GSINDy is integrated with Kalman filter to automatically identify time-variant digital twin models for online applications. The effectiveness of the algorithm is revealed through a simulation example based on Lorenz system and an industrial diesel hydrotreating unit example.

Keywords: Uncertain systems, Optimization, Randomized algorithms
Abstract: In this paper, we consider the optimal controller design problem against data injection attacks on actuators for an uncertain control system. We consider attacks that aim at maximizing the attack impact while remaining stealthy in the finite horizon. To this end, we use the Conditional Value-at-Risk to characterize the risk associated with the impact of attacks. The worst-case attack impact is characterized using the recently proposed output-to-output gain (OOG). We formulate the design problem and observe that it is non-convex and hard to solve. Using the framework of scenario-based optimization and a convex proxy for the OOG, we propose a convex optimization problem that approximately solves the design problem with probabilistic certificates. Finally, we illustrate the results through a numerical example.

Keywords: Large-scale systems, Network analysis and control, Stochastic systems
Abstract: In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing its corresponding safety controller. We then utilize dissipativity theory to compositionally construct barrier certificates for interconnected systems based on storage certificates of individual subsystems. The proposed dissipativity-type compositional conditions can leverage the structure of the interconnection topology and be fulfilled independently of the number or gains of subsystems. We eventually employ the constructed barrier certificate and quantify upper bounds on the probability that the interconnected system reaches certain unsafe regions in a finite time horizon. We apply our results to a room temperature network of 200 rooms with Markovian switching signals while accepting multiple storage certificates. We compositionally synthesize safety controllers to maintain the temperature of each room in a comfort zone for a bounded time horizon.

Keywords: Stochastic systems, Lyapunov methods, Control applications
Abstract: Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness and approximate completeness guarantees. However, for continuous-time stochastic dynamical systems, probabilistic reach-avoid-stay problems are viewed as challenging tasks. Motivated by the recent surge of applications in characterizing safety-critical properties using Lyapunov-barrier functions, we aim to provide a stochastic version for the probabilistic reach-avoid-stay problems in consideration of robustness. To this end, we first establish a connection between stochastic stability with safety constraints and reach-avoid-stay specifications. We then prove that stochastic Lyapunov-barrier functions provide sufficient conditions for the target objectives. We apply Lyapunov-barrier conditions in control synthesis for reach-avoid-stay specifications, and show its effectiveness in a case study.

Keywords: Delay systems, Observers for nonlinear systems, Filtering
Abstract: In this paper, a novel structure of a Filtered high-gain Observer is proposed for a class of nonlinear systems subject to delayed measurements, bounded disturbances and noise measurements effects. The structure of the proposed observer is able to obtain a larger bound of the Maximum Allowable Value of Time Delay (MAVTD) that ensures the convergence of the observer in comparison with the one obtained by standard High Gain methodology. The convergence of the proposed observer is provided by means of Lyapunov-Krasovskii functional. The efficiency of the proposed observer has been validated experimentally on real UAV systems.

Keywords: Observers for nonlinear systems
Abstract: This paper shows the existence of robust functional observers for autonomous dynamical systems that verify a backward-distinguishability condition with respect to the functional to be estimated. The proof leverages on the theory of Kazanzis-Kravaris/Luenberger (KKL) observer design, which is adapted to the functional context. Then, we show how those results can be exploited to show existence of asymptotic observers for controlled systems under appropriate distinguishability conditions, when the input is known to be generated by some finite-dimensional autonomous dynamical system. This is done by considering an extended system made of the plant and the input generator. Applications include state estimation in presence of known/unknown inputs, unknown input observers and input reconstruction/estimation. On the other hand, when the input can only be approximated by such signals, practical functional estimation may be achieved by exploiting the observer robustness.

Keywords: Robotics, Predictive control for nonlinear systems
Abstract: This paper presents a model predictive control (MPC)-based planning and control approach for catching objects in flight with a robotic arm. The core of the approach is to combine the three elementary tasks of the catching process, namely predicting the flight trajectory, determining the catching pose and the motion planning and control of the robot in one optimization problem. Thereto, a time-optimal problem formulation is chosen with additional robot-specific inequality constraints. Based on a parametric description of the flight parabola, terminal equality constraints are defined ensuring that the end effector position lies on the flight parabola with an orientation in tangential direction of the trajectory. The approach is successfully applied in simulation and experiments in real-time for a 7-degrees-of-freedom (DOF) robot arm with the nonlinear model predictive control toolbox GRAMPC.

Keywords: Maritime control, Control applications, Optimization
Abstract: The plan of rudder roll stabilization controllers for underactuated vessels is complicated by model coupling, non-minimum phase dynamics in rudder to roll response and the limitation of rudder angle. A factorized form of the Nonlinear Generalized Minimum Variance (NGMV) control is applied for a rudder roll damping system. For the basic NGMV controller, the non-minimum phase subsystem is unstable when control costing approaches to zero. The factorization method can be used on this problem and provides a unique relatively simple controller. Since, the NGMV and FNGMV controllers require square system, the underactuated ship control system is simplified to a single-input-single-output (SISO) system, firstly. Then, the FNGMV based roll damping controller is presented and an energy consumption index (ECI) is proposed to evaluate the fuel efficiency of ship motion. Finally, simulations are shown to illustrate the validity of the roll stabilization control scheme and the effect of weightings on the energy measure.

Keywords: Modeling, Energy systems
Abstract: In this paper, a novel electrochemical model for LiFePO4 battery cells that accounts for the positive particle lithium intercalation and deintercalation dynamics is proposed. Starting from the enhanced single particle model, mass transport and balance equations along with suitable boundary conditions are introduced to model the phase transformation phenomena during lithiation and delithiation in the positive electrode material. The lithium-poor and lithium-rich phases are modeled using the core-shell principle, where a core composition is encapsulated with a shell composition. The coupled partial differential equations describing the phase transformation are discretized using the finite difference method, from which a system of ordinary differential equations written in state-space representation is obtained. Finally, model parameter identification is performed using experimental data from a 49Ah LFP pouch cell.

Keywords: Energy systems, Machine learning, Optimization
Abstract: The fast charging of lithium-ion batteries while minimizing battery degradation is a key challenge to battery community. Difficulties in this optimization are the high dimensionality of parameter space of charging strategies, significant variability between batteries, and limited quantitative information on battery degradation mechanisms. Current approaches to addressing these challenges are model-based optimization and grid search. Model-based methods are limited by the insufficient complexity and accuracy of electrochemical models – especially in the early stage of development when a new battery chemistry is being introduced to the market – and grid search methods are expensive in terms of testing time and cells. This article proposes a data-driven Bayesian optimization (BO) approach for minimum charging time problem, in which an acquisition function of constrained expected improvement is employed to explicitly handle constraints that limit degradation. In addition, continuous-varied-current charging protocols are introduced into the proposed BO approach by utilizing the technique of polynomial function expansions. The effectiveness of the proposed approach is demonstrated on the LIONSIMBA, a porous electrode theory-based battery simulator. The simulation results show that the proposed BO-based charging approach with continuous current profile outperforms the commonly used constant current constant voltage (CC-CV) method for the minimum charging time problem. Moreover, the decrease in the minimum charging time and increase in its variance with increasing number of degrees of freedom used in charging protocols is also quantified.

Keywords: Energy systems, Cooperative control, Optimization
Abstract: Wind turbines in an offshore wind farm usually operate individually to maximize the power output for each turbine. However, this is not an optimal configuration for a wind farm with inner wake interactions, as they not only affect the overall power output but also introduce extra fatigue on the turbine structures. Recently, wind farm level coordinated control, such as coordinated yaw and axial-induction control, has been regarded as a promising solution to improve the overall performance of a wind farm. In this work, an offshore wind farm wake redirection control scheme is proposed for both power maximization and load reduction, which is achieved by a multi-objective optimization process. In particular, a fatigue assessment model is established for fast fatigue evaluation under yaw-misalignment and wake effects based on a large number of aero-elastic simulations. It is accomplished by calculating the Damage Equivalent Loads (DELs) on the tower and the blade with the rain-flow counting method. To verify the effectiveness of the proposed method, the medium-fidelity wind farm simulation code WFSim is used in the optimization and analysis process. Numerical results have shown that the overall power output can be increased by up to 12.5%, while the fatigue loads of critical structures are reduced by up to 15.3% with the proposed wind farm control strategy. In contrast, a power-only optimization design may lead to increased fatigue loads.

Keywords: Identification for control, Modeling, Fluid flow systems
Abstract: The wind preview provided by a nacelle-based lidar system allows the wind turbine controller to react to the wind disturbance prior to its impact on the turbine. This technology, commonly referred to as lidar-assisted wind turbine control, has been shown to be beneficial in reducing wind turbine structural loads. The wind preview quality defines how the lidar estimated disturbance is correlated with the actual one. In practice, the preview quality can vary following the change in atmospheric conditions and lidar operating states.

When assessing the benefits of lidar-assisted control, previous studies mainly focused on the freestream turbulence where the turbine wake has not been included. In reality, wind turbines sometimes operate within the wake caused by upstream situated turbines, which happens more often in a narrowly spaced wind farm. Based on existing literature, the wake turbulence has three main phenomena compared with the freestream turbulence, i.e. (1) the reduced wind speed region (wake deficit), (2) the meandering (wake deficit moves in the lateral and vertical directions), and (3) the smaller-scale added turbulence caused by the interaction between rotor and the flow. The extent to which these phenomena affect the quality of lidar wind preview still needs to be investigated.

In this paper, we use the dynamic wake meandering model, which covers the three wake characteristics mentioned above, and analyze its impact on lidar wind preview qualities. The most representative turbine layout where two turbines lie in a row will be considered. Frequency-domain analysis will be carried out to assess the measurement coherence of the lidar and the results will be compared to the freestream case.

Keywords: Smart grid, Optimization, Power systems
Abstract: State estimation is crucial to the reliable operation of the power grid. Hence, various cyber-physical attacks take advantage of manipulating the state estimation outcome to threaten grid reliability. Such cyber-physical attacks include fuzzing, malware injection and false data injection attack (FDIA). While the traditional residual-based error detection could prevent certain attacks, FDIA is not one of them. This study notices that matrix separation is a powerful tool in terms of FDIA detection. Thus, we cast FDIA detection into the matrix separation framework, embedding two types of structural knowledge. The first one highlights that only some rows in the attack matrix have nonzero values, while the second one emphasizes that the temporal variability of data collected by the same meter is usually small. Our proposed framework yields a structure embedding detection method, and numerical studies highlight its remarkable performance.

Keywords: Distributed parameter systems, Optimal control, Observers for Linear systems
Abstract: In this work, we are interested in the boundary control of a counter-current heat exchanger. This system is governed by two hyperbolic partial differential equations that characterize the dynamics of temperatures. First the properties of the dynamic system are studied. The existence and uniqueness of positive solutions are established. Next an observer-based state feedback control law with integral action is designed, in order to guarantee the stability, regulation and robustness of the closed-loop system. In particular, the proportional gains of the controller and of the observer are obtained by solving the LQ-optimal problem of the system and its dual.

Keywords: Iterative learning control, Control applications, Identification for control
Abstract: Although effective low-level control configurations of quadrotors are already known, the tuning of such controllers requires extensive expert knowledge which can impede their design and deployment. Considering the growing demand for quadrotors in different environments, the importance of an automated approach to designing the controller cannot be neglected. For this purpose, recently, a successful implementation of a model-based reinforcement learning technique was demonstrated by training a neural network using only flight data. In this paper, as an alternative to the neural network approach, we employ a structured model parameterized by a set of bases to identify the governing dynamics of quadrotors. The model accompanied by a value function defined in the product space of the bases leads to an analytical update rule for the controller that can be effectively solved by ODE solvers. The runtime results confirm that the controller together with a recursive least squares identifier can be used as a lightweight framework for learning to stabilize an unknown quadrotor at a given position. In the simulation results, a nonlinear model of the quadrotor is exploited that replaces the real unknown quadrotor. The flight data and 3D graphical simulation are generated to verify the presented learning approach.

Keywords: Autonomous robots, Neural networks, Learning
Abstract: We embark on a hitherto unreported problem of an autonomous robot (self-driving car) navigating in dynamic scenes in a manner that reduces its localization error and eventual cumulative drift or Absolute Trajectory Error, which is pronounced in such dynamic scenes. With the hugely popular Velodyne-16 3D LIDAR as the main sensing modality, and the accurate LIDAR-based Localization and Mapping algorithm, LOAM, as the state estimation framework, we show that in the absence of a navigation policy, drift rapidly accumulates in the presence of moving objects. To overcome this, we learn actions that lead to drift-minimized navigation through a suitable set of reward and penalty functions. We use Proximal Policy Optimization, a class of Deep Reinforcement Learning methods, to learn the actions that result in drift-minimized trajectories. We show by extensive comparisons on a variety of synthetic, yet photo-realistic scenes made available through the CARLA Simulator the superior performance of the proposed framework vis-à-vis methods that do not adopt such policies.

Keywords: Robotics
Abstract: Passive dynamic walking is a form of locomotion generated by a dynamical interaction between environments and passive legged robots. Its dynamics at foot strike are governed by impact forces. The impulsive dynamics have been modeled in several approaches, where all the approaches assume that the stance leg instantaneously loses contact with the ground at foot strike; however, it is unclear when the assumption is satisfied. This paper derives a loss-of-contact condition in closed-form as follows. A compass-like biped robot is considered in this paper. Its impulsive dynamics at foot strike are modeled by using a modeling framework for multibody dynamics with impact. Examining the validity of foot velocities and impact forces in the impulsive model provides a necessary and sufficient condition for the impulsive model to be valid in closed-form. The condition includes a loss-of-contact condition. The derived condition is also a necessary condition for smooth passive dynamic walking.

Keywords: Mechatronics, Control applications, Mechanical systems/robotics
Abstract: In this paper, an input shaping-based control law is designed for an overhead crane system with time-varying cable length. The proposed method employs a zero vibration (ZV) input shaper. It is well-known that the ZV input shaper is not robust to modeling errors causing by the time-varying dynamics, which leads to the fact that a direct application of ZV input shaper on time-varying systems often results in poor vibration suppression performance. Therefore, we first apply the standard ZV input shaper on an undamped linear time-invariant (LTI) second-order system. This step provides us a reference oscillation function that is exactly zero after the trolley stops. The real control input is then devised to perfectly match the real vibration of the crane system with the reference oscillation, and hence a vibration-free transportation can be achieved. The unshaped command is parameterized and its coefficients are designed to deal with control objectives other than the vibration elimination. The simulation results are provided to validate the efficacy of the proposed approach.

Keywords: Variable-structure/sliding-mode control
Abstract: This paper extends previous results on constrained optimization control problems of uncertain robot systems based on sliding modes generation. An equivalent linear parameter varying (LPV) state-space representation of the nonlinear robot model is considered to design a stabilizing state-feedback control law by solving linear matrix inequalities (LMI) with structural constraints. The finite-time regulation of the state trajectory to a desired reference, while minimizing a pre-specified cost function with state constraints, is then solved by a sliding mode approach relying on the considered parameter-dependent structure of the robot system. Stability conditions of the proposed approach are provided, and a realistic numerical example verifies the effectiveness of the proposed technique.

Keywords: Control education, Mechanical systems/robotics, Feedback linearization
Abstract: The swirling pendulum is an underactuated, two-link, two-degree-of-freedom mechanism consisting of a pair of swirling and swinging links, that on account of its unusual out-of-the plane inertial coupling exhibits interesting dynamics and dynamical properties like multiple (eight) isolated equilibria (both stable as well as unstable), regions with loss of relative degree, loss of controllability and loss of inertial coupling. This work is an attempt to highlight the utility of the swirling pendulum as an attractive as well as a simple system for demonstrating a range of concepts/notions a learner would typically encounter in academic courses related to controls and dynamics. To achieve this goal, we start by presenting a (yet incomplete) summary of modeling, analysis, and control design concepts that can be studied in linear or nonlinear frameworks in various courses. We discuss as examples, the problems of input-output linearization and partial feedback linearization picked up from this summary. Furthermore, we also present inversion-based selective tracking control for tracking trajectories on the swirling pendulum outputs. In doing so, we explain how the problem of system zeros on the imaginary axis (that results in an unstable inversion-based feedforward controller) is avoided. We conclude by mentioning the problems that can be taken up as future work.

Keywords: Network analysis and control, Game theory
Abstract: In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Because players' actions are constrained by local feasible sets, one of the most popular methods is to employ projection operators. However, it may be hard to get the exact projection points in practice due to complex set constraints. Inspired by the advantage of the projection on hyperplanes, we promote to use inscribed polyhedrons to approximate players' local sets, which yields a related approximate game model. Then we propose a distributed algorithm to seek the Nash equilibrium of the approximate game. The projection in the algorithm is replaced by a standard quadratic program with linear constraints, which can reduce the computational complexity. Moreover, we show that the equilibrium of the proposed algorithm induces an ϵ-Nash equilibrium of the original game.

Keywords: Optimal control, Agents-based systems, Game theory
Abstract: We study pursuit-evasion differential games be- tween a faster pursuer moving in 3D space and an evader moving in a plane. We first extend the well-known Apollonius circle to 3D space, by which we construct the isochron for the considered two players. Then both cases with and without a static target are considered and the corresponding optimal strategies are derived using the concept of isochron. In order to guarantee the optimality of the proposed strategies, the value functions are given and are further proved to be the solution of Hamilton-Jacobi-Isaacs equation. Simulations with comparison between the proposed strategies and other classical strategies are carried out and the results show the optimality of the proposed strategies.

Keywords: Fault tolerant systems, Estimation, LMIs
Abstract: The purpose of this work is to design a failure-tolerant observer that meets pole position constraints to enhance the observer's response under various sensor failure scenarios while optimizing the nominal performance, measured by a disturbance rejection metric. A failure-tolerant observer design methodology based on the regional pole placement (RPP) technique is provided. The number of sensors m and a minimum number of assumed functional sensors p define the range of failure situations. Thus, p specifies a failure tolerance level for the observer design. A semi-definite relaxation (SDR) technique is presented to alleviate the computational burden imposed by a large number of evaluated failure situations. The SDR method results in only a few linear matrix inequality sufficient conditions to solve the problem, but at the expense of reduced optimal performance. To compensate, the Hadamard and block Hadamard product approaches are suggested to provide more degrees of freedom in searching for the optimal solution. To demonstrate the efficacy of the failure-tolerant observer design, two illustrative examples are provided.

Keywords: Robust control, Stability of nonlinear systems, Variable-structure/sliding-mode control
Abstract: A novel switched state feedback is proposed to stabilize an arbitrary order chain of integrators in prescribed time regardless of matched external disturbances with an a priori known magnitude bound. The design recast a HOSM (high order sliding mode) controller with finite-time convergence to the origin, especially developed for a system composed of diagonal and over-diagonal forms, and it is based on the scaling technique. The proposed hybrid control algorithm operates with time-varying gains, uniformly bounded on an infinite horizon, thereby yielding an attractive implementation opportunity compared to the original design by Song et al. with time-varying gains, which escape to infinity as time goes to the prescribed time instant. Capabilities of the present hybrid control algorithm are supported in a numerical study, performed for a perturbed triple integrator, and are compared with existing prescribed-time and fixed-time controllers.

Keywords: Delay systems, Linear systems, LMIs
Abstract: The strong delay independent stability (DIS) for commensurate multiple time delay systems (CMTDSs) is studied in this paper. The necessary and sufficient strong DIS condition is derived for an augmented time delay system (TDS) originated from the original multiple time delay system (MTDS). A linear matrix inequality (LMI) condition is used to deal with the strong DIS, whose solution is derived by means of Kalman-Yakubovich-Popov (KYP) lemma and Kronecker properties. Two numerical examples are given to demonstrate the advantages and applicability of the proposed approach.

Keywords: Game theory, Stochastic optimal control, Stochastic systems
Abstract: In this paper, we consider a discrete-time stochastic Stackelberg game where there is a defender (also called leader) who has to defend a target and an attacker (also called follower). The attacker has a private type that evolves as a controlled Markov process. The objective is to compute the stochastic Stackelberg equilibrium of the game where defender commits to a strategy. The attacker’s strategy is the best response to the defender strategy and defender’s strategy is optimum given the attacker plays the best response. In general, computing such equilibrium involves solving a fixed-point equation for the whole game. In this paper, we present an algorithm that computes such strategies by solving smaller fixed-point equations for each time t. Based on this algorithm, we compute the Stackelberg equilibrium of a security example.

Keywords: Transportation networks, Optimization algorithms, Optimization
Abstract: Fixed pickup and delivery times can strongly limit the performance of freight transportation. Against this backdrop, fleet operators can use compensation mechanisms such as monetary incentives to buy delay time from their customers, in order to improve the fleet efficiency and ultimately minimize the costs of operation. To make the most of such an operational model, the fleet activities and the incentives should be jointly optimized accounting for the customers’ reactions. Against this backdrop, this paper presents an incentive-aware electric vehicle routing scheme in which the fleet operator actively provides incentives to the customers in exchange of pickup or delivery time flexibility. Specifically, we first devise a bi-level model whereby the fleet operator optimizes the routes and charging schedules of the fleet jointly with an incentive rate to reimburse the delivery delays experienced by the customers. At the same time, the customers choose the admissible delays by minimizing a monetarily-weighted combination of the delays minus the reimbursement offered by the operator. Second, we tackle the complexity resulting from the bi-level and nonlinear problem structure with an equivalent transformation method, reformulating the problem as a single- level optimization problem that can be solved with standard mixed-integer linear programming algorithms. We demonstrate the effectiveness of our framework via extensive numerical experiments using VRP-REP data from Belgium. Our results show that by jointly optimizing routes and incentives subject to the customers’ preferences, the operational costs can be reduced by up to 5%, whilst customers can save more than 30% in total delivery fees.

Keywords: Networked control systems, Human-in-the-loop control, Control applications
Abstract: This paper studies a safe interaction between a platoon of autonomous vehicles and a set of human-driven vehicles. Considering the longitudinal motion of the vehicles in the platoon, the problem is to ensure a safe emergency braking by the autonomous platoon considering the actions of human-driven vehicles, which may vary based on the driver type. We consider two types of platoon topologies, namely unidirectional and bidirectional. Safe emergency braking is characterized by a specific type of platoon stability, called head-to-tail stability (HTS). We present system-theoretic necessary and sufficient conditions for the combination of the autonomous platoon and human-driven vehicles to be HTS for two-platoon control laws, namely the velocity tracking and the platoon formation. Modeling the input-output behavior of each vehicle via a transfer function, the HTS conditions restrict the human-driven vehicles’ transfer functions to have H1 norms below certain thresholds. A safe interaction algorithm first identifies the transfer functions of the human-driven vehicles. Then, it tunes the platoon control gains such that the overall system meets HTS conditions. Theoretical results are validated with both experimental data with human subject studies and simulation studies.

Keywords: Delay systems, Control of networks, Stability of linear systems
Abstract: Several sources of delay in an epidemic network might negatively affect the stability and robustness of the entire network. In this paper, a multi-delayed Susceptible-Infectious-Susceptible (SIS) model is applied on a metapopulation network, where the epidemic delays are categorized into local and global delays. While local delays result from intra-population lags such as symptom development duration or recovery period, global delays stem from inter-population lags, e.g., transition duration between subpopulations. The theoretical results for a network of subpopulations with identical SIS dynamics and different types of time-delay show that depending on the type of the time-delay in the network, different eigenvalues of the underlying graph should be evaluated to obtain the feasible regions of stability. The delay-dependent stability of such epidemic networks has been analytically derived, which eliminates potentially expensive computations required by current algorithms. The effect of time-delay on the H2 norm-based performance of a class of epidemic networks with additive noise inputs and multiple delays is studied and the closed-form of their performance measure is derived using the solution of delayed Lyapunov equations. As a case study, the theoretical findings are implemented on a network of United States' busiest airports, where the results highlight the difference of local and global delays.

Keywords: Traffic control, Mean field games, Robust control
Abstract: Historically, traffic modeling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there has not been a rigorous framework to facilitate passage between controls for the microscopic models and the macroscopic models. We begin this work with a particle-based model of autonomous vehicles subject to drag, unknown disturbances, noise, and a speed limit in addition to the control.

We formulate a robust stochastic differential game on the particles. We pass formally to the infinite-particle limit to obtain a robust mean-field game PDE system. We solve the mean-field game PDE system numerically and discuss the results. In particular, we obtain an optimal control which increases the bulk velocity of the traffic flow while reducing congestion.

Keywords: Automotive control, Predictive control for nonlinear systems, Simulation
Abstract: With the advent of autonomous vehicles on public roads imminent in the near future, special emphasis needs to be placed on addressing scenarios pertaining to mixed-traffic settings, comprised of human-driven and autonomous vehicles. In this paper, we address the problem of autonomous vehicle overtaking in a bidirectional mixed-traffic setting. We design a mixed-integer model predictive controller that maximizes the ego vehicle’s velocity while prioritizing safety and accounting for driver comfort. The proposed approach: (i) operates in a limited sensing range while accounting for occlusion; (ii) is able to retract the overtake decision through a receding horizon approach; (iii) is robust to the variations in sensory input and driving behaviors of external agents due to behavior-dependent safety margins; and (iv) reduces to a mixed-integer optimization problem with linear constraints, yielding low computational complexity. We demonstrate the behavior of the proposed approach in a realistic traffic simulation environment.

Keywords: Adaptive control, Algebraic/geometric methods, Flight control
Abstract: A planar 4R-foldable quadrotor, i.e., foldable quadrotor with four independent revolute joints for wings rotation has the edge over conventional quadrotor in confined space navigation due to its morphing capability and multi-modal behaviors. However, the morphing induced inertial and center of gravity variations cause attitude destabilization, which impedes the trajectory tracking efficiency and reduces the flight stability in confined environments. In this paper, we propose an adaptive flight stabilization framework for a planar 4R-foldable morphing quadrotor that comprises the adaptive control and geometric tracking control. The adaptive control laws are developed to estimate the morphing induced inertial and center of gravity variations with respect to the desired attitude dynamics. These adaptive laws are then used to develop the feedback component of geometric tracking control which improves the trajectory tracking efficiency. Together with the controller design, the boundness of the attitude tracking errors is proved. Moreover, the simulations were conducted to validate the effectiveness of the proposed control framework in confined environments. Initial results show that the adaptive stabilization framework is effective in attitude stabilization and enhancing the trajectory tracking performance of a planar 4R-foldable morphing quadrotor.

Keywords: Estimation, Kalman filtering, Robust control
Abstract: It is well known that the Kalman filter (KF) performance is clearly degraded in real-life applications where the system model is misspecified to a certain extent, that is, when the assumed knowledge does not perfectly match the true system dynamics. A possible way to mitigate the impact of a system model mismatch is to resort to linear constraints. In that perspective, a general linearly constrained KF (LCKF) formulation has been recently derived and shown to provide an effective robust filtering solution. In this contribution, we extend the LCKF framework to linear smoothers. Adapting the Fixed-Interval (FI) smoother is easy with sequential state augmentation, but the obtained linearly constrained FI (LCFI) has quadratic complexity in the interval length. Hence the need for an efficient alternative: the linearly constrained Rauch-Tung-Striebel (LCRTS) smoother. Introduced in an intuitive manner, its consistency is proved by showing that the LCFI and LCRTS coincide. The mismatch mitigation capabilities and performance of the LCRTS, with respect to unconstrained smoothers, are shown through illustrative examples with different types of mismatch in both measurement and process equations.

Keywords: Estimation, Observers for Linear systems, Fault detection
Abstract: In this paper, we propose a Virtual Distributed Observer (VDO) which is built by virtually excluding some redundant sensors from conventional distributed observers.

By using the VDO, we can construct not only robust estimators against sensor attacks but detectors of attacks by malicious agents.

We also consider the new framework of estimation problem which is more useful to adapt under distributed conditions. This relaxed problem makes it possible to estimate partial state under sensor attacks even if the whole observer system is not detectable.

Finally, we confirm the effectiveness of our proposed method through numerical simulations in the presence of measurement attacks.

Keywords: Subspace methods, Estimation, Identification for control
Abstract: In this work, a fast subspace identification method for estimating LTI state-space models corresponding to large input-output data is proposed. The algorithm achieves lesser RAM usage, reduced data movement between slow (RAM) and fast memory (processor cache), and introduces a novel method to estimate input (B) and feedforward (D) matrices. By design, the proposed algorithm is specially well-suited to identify multi-scale systems with both fast and slow dynamics. Identification of these systems require high-frequency data recordings over prolonged periods, leading to large input-output data sizes. For such large data sizes, the proposed algorithm outperforms the MATLAB-MOESP method in terms of memory cost, flop-count, and computation time. The effectiveness of the proposed algorithm is established by theoretical computations and various case studies.

Keywords: Optimal control, Linear systems, Learning
Abstract: In this paper, we analyze the optimization landscape of gradient descent methods for static output feedback (SOF) control of discrete-time linear time-invariant systems with quadratic cost. The SOF setting can be quite common, for example, when there are unmodeled hidden states in the underlying process. We first establish several important properties of the SOF cost function, including coercivity, L-smoothness, and M-Lipschitz continuous Hessian. We then utilize these properties to show that the gradient descent is able to converge to a stationary point at a dimension-free rate. Furthermore, we prove that under some mild conditions, gradient descent converges linearly to a local minimum if the starting point is close to one. These results not only characterize the performance of gradient descent in optimizing the SOF problem, but also shed light on the efficiency of general policy gradient methods in reinforcement learning.