State Feedback Control Problem Research Articles

Co-design of adaptive event-triggered mechanism and controller for networked control systems with uncertainty and time-varying delay

ABSTRACT This paper investigates the co-design problem of event-triggered mechanisms and state feedback controllers for networked control systems with parameter uncertainty and network-induced delay. Firstly, to overcome the network bandwidth limitation, an adaptive event-triggered mechanism is used to filter the required sampling signals to reduce the network resource occupancy. Second, establish a unified model subject to event triggering mechanisms, parameter uncertainty, and network delay constraints, and derive the stability conditions of the system for the model by combining Lyapunov stability theory and the linear matrix inequality method. Then, the state feedback controller is designed to satisfy the event-triggering condition and certain robust performance requirements, and an optimisation method is proposed to compromise network resource consumption and control performance. Finally, the effectiveness of the proposed method is verified by a numerical example.

Density estimation based soft actor-critic: deep reinforcement learning for static output feedback control with measurement noise

ABSTRACT The state-of-the-art deep reinforcement learning (DRL) methods, including Deep Deterministic Policy Gradient (DDPG), Twin Delayed DDPG (TD3), Proximal Policy Optimization (PPO), Soft Actor-Critic (SAC), among others, demonstrate significant capability in solving the optimal static state feedback control (SSFC) problem. This problem can be modeled as a fully observed Markov decision process (MDP). However, the optimal static output feedback control (SOFC) problem with measurement noise is a typical partially observable MDP (POMDP), which is difficult to solve, especially for the continuous state-action-observation space with high dimensions. This paper proposes a two-stage framework to address this challenge. In the laboratory stage, both the states and the noisy outputs are observable; the SOFC policy is converted to a constrained stochastic SSFC policy, of which the probability density function is generally not analytical. To this end, a density estimation based SAC algorithm is proposed to explore the optimal SOFC policy by learning the optimal constrained stochastic SSFC. Consequently, in the real-world stage, only the noisy outputs and the learned SOFC policy are required to solve the optimal SOFC problem. Numerical simulations and the corresponding experiments with robotic arms are provided to illustrate the effectiveness of our method. The code is available at https://github.com/RanKyoto/DE-SAC.

Decentralized H2 Control for Discrete-Time Networked Systems With Positivity Constraint.

In this brief, we study the decentralized H2 state-feedback control problem for networked discrete-time systems with positivity constraint. This problem (for a single positive system), raised recently in the area of positive systems theory, is known to be challenging due to its inherent nonconvexity. In contrast to most works, which only provide sufficient synthesis conditions for a single positive system, we study this problem within a primal-dual scheme, in which necessary and sufficient synthesis conditions are proposed for networked positive systems. Based on the equivalent conditions, we develop a primal-dual iterative algorithm for solution, which helps prevent from converging to a local minimum. In the simulation, two illustrative examples are employed for verification of our proposed results.

An analytical approach to finite time H∞ event-triggered state feedback control of fractional order systems with delay

This paper investigates finite time H∞ event-triggered state feedback control problem of fractional-order systems with delay. Based on Laplace trasform and “inf-sup” norm, a delay-dependent sufficient condition for designing H∞ event-triggered control is established in terms of the Mittag-Leffler function and Linear matrix inequalities. A numerical example is given to show the effectiveness of the obtained result.

Adaptive tracking control for a class of stochastic nonlinear systems with full-state constraints and dead-zone

This paper seeks to address the problem of state-feedback tracking control for a class of stochastic systems whose states are constrained and input is perturbed by dead-zone. A tan-type barrier Lyapunov function (BLF) and a finite-time adaptive law are proposed such that all states of the system are constrained in the defined bounded compact sets. Based on stochastic Lyapunov theorem, an adaptive state-feedback tracking controller is designed to ensure that the considered stochastic system is semiglobally finite-time stable in probability (SGFSP) and the tracking error signal is bounded. Different from the existing control strategies for stochastic systems, the form of BLF can be used for asymmetric constraints without changing the controller, so the analysis of symmetric or asymmetric full-state constraints is unified. Finally, illustrative simulations are provided to verify the effectiveness of the proposed control strategy.

Dynamic event-triggered [formula omitted] control for markov jump systems with input saturation

This paper is mainly to explore H∞ state feedback control problem for Markov jump systems (MJSs) with input saturation. To avoid the waste of network resources, a dynamic event-triggered mechanism (DETM) is proposed from system plant to controller, which produces a larger interval between two consecutive events compared with the traditional static one. On the basis of this model, sufficient criteria for stochastic stability of the controlled MJSs are derived by linear matrix inequalities (LMIs) and the controllers are designed. Then the maximum estimate of the domain of attraction (DOA) is obtained by the optimization procedure. Finally, examples show that the proposed DETM has better properties of saving resources than static event-triggered mechanism (ETM) while maintaining the same performance.

Distributed Adaptive Control with Momentum for Synchronization of Linear Agents

This paper studies the problem of learning-based adaptive state feedback control for networks of heterogeneous agents with input and matched uncertainties. We propose a control strategy that guarantees that the closed-loop synchronization error of all agents in the network is bounded. Adaptive control laws are designed via matching conditions to approximate the dynamics of each agent, which are partially unknown. Uncertainty parameters in the model are suppressed using adaptive optimal modification theory. Moreover, a momentum-based technique is also introduced in our framework for improving the convergence behavior of the adaptive control law parameters computation. Finally, a simulation example for Cooperative Adaptive Cruise Control (CCAC) is presented to validate the effectiveness of the control scheme. Numerical examples show that momentum-based techniques reach the bounded error set faster than gradient-based techniques.

Stability analysis and design of cooperative control for linear delta operator system

<abstract><p>This paper investigates the cooperative state feedback control problem for delta operator-based large-scale systems with independent subsystems. First, the state feedback controller is introduced to interconnect the adjacent subsystems into a closed-loop system. Second, the Lyapunov function in delta domain is constructed, and the linear matrix inequality method is used to design the cooperative state feedback stability controller for the whole large-scale interconnected system. Third, a performance index is introduced for the design of the optimal cooperative state feedback controller. Finally, stability of the closed-loop system is proved on the basis of stability theory, and simulation examples are given for showing the effectiveness of the design method.</p></abstract>

State-feedback memory control for uncertain cyber-physical systems under Denial-of-Service attacks*

This paper tackles the problem of state-feedback control for uncertain cyber-physical systems with the presence of Denial-of-Service attacks. The closed-loop stability is guaranteed through a new state-feedback packet-based strategy that utilizes past states (memory) to artificially enrich the control dynamics. The presence of an energy-bounded attacker is assumed and the closed-loop system under attack is modeled as an uncertain switched system. A less conservative stability analysis condition based on the Lyapunov theory is used as starting point for the synthesis conditions, which are formulated in terms of Linear Matrix Inequalities. Numerical experiments are conducted to illustrate the technique's effectiveness and perform comparisons with packet-based methods from the literature.

Reliable induced [formula omitted] control for polytopic uncertain continuous-time singular systems with dynamic quantization

This paper considers the problem of state feedback control for a class of polytopic uncertain continuous-time singular systems with input quantization and actuator faults. The aim of this paper is to design the reliable controller and dynamic quantizer that ensure the considered closed-loop system is asymptotically stable and satisfies the prescribed induced L∞ performance constraint. The introduced proportional plus derivative state feedback controller can eliminate the structural restrictions of the system matrices, thus a more general sufficient condition is obtained for the problem. Finally, the four-mesh circuit is provided to demonstrate the effectiveness of the proposed induced L∞ control approach.

State-Feedback Control for Cyber-Physical Discrete-Time Systems under Replay Attacks: An LMI Approach

This paper addresses the state-feedback control problem for cyber-physical discrete-time linear systems. The main goal is to design state-feedback controllers that can mitigate the interference of replay attacks in the stability of the closed-loop system. The system under replay attack is modeled as a switched linear system, and a packet-based approach is employed for control design. New conditions in the form of Linear Matrix Inequalities are presented to provide stabilizing controllers. Numerical experiments illustrate the effectiveness of the proposed method.

Integral-based robust LPV control of nonlinear flight systems

This paper presents a novel speed control method for an unmanned flight system. A Polytopic Linear Parameter Varying model is generated by linearization of the nonlinear dynamic model around several trim points. As a novelty of this paper, an Integral action over the tracking error is added to a conventional state-feedback to form the proposed control law. Augmenting the proposed control action to the system dynamic, the proposed control law is reassigned as a common state-feedback control problem. An attenuation level for the tracking error under external disturbances is guaranteed by solving the related linear matrix inequalities to compute the control gains. In the end, the designed controller has been implemented for different scenarios in order to maintain the speed in different modes with the ability to control the longitudinal, Lateral, and altitude velocities simultaneously. The simulation results show the effectiveness of the proposed control against the system uncertainties, external disturbances, and the interactions between different channels.

Discrete-time control for highly nonlinear neutral stochastic delay systems

This work explores the discrete-time state feedback control problem for neutral stochastic delay systems(NSDSs) in which coefficients satisfy highly nonlinear. Due to the highly nonlinear, the neutral term and discrete time observation value, many conventional methods are not applicable. A more general Lyapunov function is constructed to prove that the designed controller can stabilize the corresponding systems. In addition, H∞-stable, asymptotically stable and exponentially stable of the corresponding studied systems are presented. Then, a numerical case is demonstrated to verify the correctness and validity of the proposed theoretical results.

Formula omitted] state-feedback control for discrete-time cyber-physical uncertain systems under DoS attacks

This paper investigates the packet-based state-feedback control problem for uncertain discrete-time cyber-physical systems. The presence of Denial of Service (DoS) attacks is considered, and the dynamics of the closed-loop system under attacks is modeled as a switched uncertain system. The H2 performance criteria is employed to assess the robustness of the system. Moreover, three strategies are considered in the control design: i) the use of a full packet of controllers, ii) the zero-input strategy, which sets the control to zero in the presence of an attacker, and iii) the hold strategy, that keeps the same control input during the DoS attack. The conditions are formulated as parameter-dependent linear matrix inequalities, and the Lyapunov theory was employed to derive the conditions. Numerical experiments are employed to illustrate the efficacy of the method when considering the H2 performance criteria.

Indirect adaptive synchronization for a heterogeneous multiagent network

SummaryThis article studies the problem of indirect adaptive state feedback control for a heterogeneous MIMO network with input and matched uncertainties. A mechanical network composed of two‐wheeled robots is proposed to validate the developed methodology. Within the network, a reference system is defined, and each robot has wireless communication between them. Likewise, for control design, specific adaptive laws are adopted through matching conditions to approximate the dynamics of each agent, which are partially unknown and constructed. The inclusion of an optimal adaptive modification is considered for the suppression of input uncertainties. This methodology, along with the distributed adaptive control and identification, is validated with Lyapunov‐based stability analysis. The presented control scheme guarantees that all closed‐loop signals are bounded and ensures that synchronization errors converge asymptotically to zero. Finally, simulations oriented to the application problem mentioned are presented to validate the effectiveness of the control scheme.

Optimal Control Strategies for Systems with Input Delay using the PIE Framework

The Partial Integral Equation (PIE) framework provides a unified algebraic representation for use in analysis, control, and estimation of infinite-dimensional systems. However, the presence of input delays results in a PIE representation with dependence on the derivative of the control input, u˙. This dependence complicates the problem of optimal state-feedback control for systems with input delay – resulting in a bilinear optimization problem. In this paper, we present two strategies for convexification of the H∞-optimal state-feedback control problem for systems with input delay. In the first strategy, we use a generalization of Young's inequality to formulate a convex optimization problem, albeit with some conservatism. In the second strategy, we filter the actuator signal – introducing additional dynamics, but resulting in a convex optimization problem without conservatism. We compare these two optimal control strategies on four example problems, solving the optimization problem using the latest release of the PIETOOLS software package for analysis, control and simulation of PIEs.

Online optimal estimation and control for a common class of activated sludge plants

In this work, we design an output predictive controller that operates a common class of activated sludge plants. The controller solves a state-feedback model predictive control problem in which the process state and disturbances are determined by a moving horizon estimator. We illustrate the behaviour of the controller when operating the plant to produce an effluent water of varying nitrogen content. The close tracking of the effluent profiles is enforced by stabilizing the system around optimal steady-state points that satisfy the output reference trajectories. Considering the generality of the formulation, the predictive controller can be configured to operate this class of activated sludge plants to achieve alternative objectives.

State-Feedback Control in Descriptor Discrete-Time Fractional-Order Linear Systems: A Superstability-Based Approach

In this article, the superstabilizing state-feedback control problem in descriptor discrete-time fractional-order linear (DDFL) systems with a regular matrix pencil is studied. Methods for investigating the stability and superstability of the considered class of dynamical systems are presented. Procedures for the computation of the static state-feedback (SSF) and dynamic state-feedback (DSF) gain matrices such that the closed-loop DDFL (CL-DDFL) system is superstable are presented. A numerical example is used to show the efficacy of the presented approach. Our considerations were based on the Drazin inverse matrix method.

ON L∞-INDUCED STABILIZATION OF POSITIVE LINEAR SYSTEMS WITH DISTRIBUTED DELAYS

The problem of L∞-gain control is studied for positive linear systems with distributed time delays. By a novel comparison technique involving the monotonicity of the so-called upper scaled systems with peak values of exogenous disturbances, a characterization of L∞-induced norm is first reformulated. Then, necessary and sufficient LP-based conditions subject to L∞-induced performance with prescribed level are derived and utilized to address the design problem of state-feedback controllers that make the closed-loop systems positive, stable and have prescribed L∞-gain performance level. A numerical example is given to illustrate the effectiveness of the proposed method.

Online Kernel Learning With Adaptive Bandwidth by Optimal Control Approach.

Online learning methods are designed to establish timely predictive models for machine learning problems. The methods for online learning of nonlinear systems are usually developed in the reproducing kernel Hilbert space (RKHS) associated with Gaussian kernel in which the kernel bandwidth is manually selected and remains steady during the entire modeling process in most cases. This setting may make the learning model rigid and inappropriate for complex data streams. Since the bandwidth appears in a nonlinear term of the kernel model, it raises substantial challenges in the development of learning methods with an adaptive bandwidth. In this article, we propose a novel approach to address this important open issue. By a carefully casted linearization scheme, the nonlinear learning problem is reasonably transformed into a state feedback control problem for a series of controllable systems. Then, by employing optimal control techniques, an effective algorithm is developed, and the parameters in the learning model including kernel bandwidth can be efficiently updated in a real-time manner. By taking advantage of the particular structure of the Gaussian kernel model, a theoretical analysis on the convergence and rationality of the proposed method is also provided. Compared with the kernel algorithms with a fixed bandwidth, our novel learning framework can not only achieve adaptive learning results with a better prediction accuracy but also show performance that is more robust with a faster convergence speed. Encouraging numerical results are provided to demonstrate the advantages of our new method.