A novel predictor feedback design approach for dynamical systems with input delay

International audience

Predictor-based stabilisation results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal controller for the delay-free case. The control scheme is applicable even to the case where the measurement is sampled and possibly delayed. The input and measurement delays can be arbitrarily large but both of them must be constant and accurately known. The closed-loop system is shown to have the properties of global asymptotic stability and exponential convergence in the disturbance-free case, robustness with respect to perturbations of the sampling schedule, and robustness with respect to measurement errors. In contrast to existing predictor feedback laws, the proposed control scheme utilises an approximate predictor of a dynamic type that is expressed by a system described by integral delay equations. Additional results are provided for systems that can be transformed to systems with a compact absorbing set by means of a preliminary predictor feedback.

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

This study investigates the prediction-based (dynamic) stabilization of linear systems with input delay in the presence of external disturbances and multiplicative noise modelled as Itô type stochastic differential equations. Conventional memory-less (static) controllers are widely used for the stabilization of both deterministic and stochastic delayed systems. However, using these methods the upper bound for delay is strongly restricted. Motivated by acceptable performances of dynamic controllers for deterministic delayed systems, the extension of these methods for stochastic delayed systems is considered in this paper. The structure of the dynamic controller for stabilization of stochastic delayed systems is firstly derived utilizing the prediction vector. Then two sufficient conditions are given in the form of linear matrix inequalities that in the case of feasibility provide the stabilizing gain of the controller. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

This paper addresses the stability analysis and dynamic output feedback control for a class of T–S fuzzy networked control systems with mixed time-varying delays and interval distributed time-varying delays. Firstly, the T–S fuzzy model is employed to approximate the networked control system based on the system model. Secondly, the dynamic output feedback controller with hybrid intermittent feedback control law is designed for the T–S fuzzy networked control system. Thirdly, the delay-dependent stability conditions are derived by introducing the Lyapunov functional with Leibniz–Newton formula. Compared with previous works, both the mixed time-varying delays and interval distributed time-varying delays are considered in the T–S fuzzy networked control system. The control design conditions are relaxed because of the proposed controller. By introducing the Lyapunov functional with Leibniz–Newton formula, the linear matrix inequalities are solved effectively by the standard convex optimization algorithm. Finally, the simulation examples and some computing results are given to show the effectiveness and advantage of the proposed method, respectively.

Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model

This paper considers the design problem of dynamic output feedback control for fractional-order (FO) Takagi-Sugeno fuzzy systems with uncertain parameters. Via the application of FO system stability theory, robust control method and the linear matrix inequality techniques, sufficient conditions are given for the stability analysis and the existence of the dynamic fuzzy output feedback controllers. The dynamic output feedback controller designed here guarantees the robust stability of the closed-loop system. Finally, a fractional order chaotic system simulation example is given to illustrate the effectiveness of the design approach here.

SummaryIn this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.

Control of time-delay systems represents one important class of control problems. A lot of work has been done in recent years. Much of the research work has been focused on the stability analysis and stabilization of time-delay systems based on the Lyapunov functional and linear matrix inequality (LMI) approaches. While the LMI approach does provide an e±cient tool, the results are mostly only su±cient and only numerical solutions are available. Our research aims to present analytical solutions by some algebraic approaches, which can provide an insightful understanding of control problem of time-delay systems. On the other hand, there has also been significant recent interest in networked multi-agent system (MAS) where unavoidably there exist delays in information acquisition as well as information exchange between agents in addition to possible input/state delays in each agent. This motivates the study of MASs with input and communication delays. The thesis is divided into two parts: Part I is focused on optimal control of single agent systems with multiple input delays; Part II is on distributed consensus control of MAS with communication and input delays. More specifically, in Part I, we shall study the linear quadratic regulation (LQR) and tracking for a single agent with linear dynamics. We first focus on LQR for linear discrete-time systems with multiple delays in a single input channel. By introducing a backward stochastic system, we establish a relationship between the LQR problem for the original system and optimal estimation for a backward stochastic system which can be solved by using projection approach. The explicit optimal controllers are developed for both finite time and infinite time horizon cases. A parallel result for linear continuous-time systems is also established, where the optimal feedback gain is given in terms of the solution of Riccati-type partial differential equations (PDEs).

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

The design of delay-dependent wide-area DOFC with prescribed degree of stability α for damping inter-area low-frequency oscillations in power system

A dynamic output feedback controller for NCS based on delay estimates

This paper presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for local exponential stabilization of hybrid periodic orbits. The properties of the Poincare map are investigated to show that the Jacobian linearization of the Poincare map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.

ABSTRACTThis paper investigates the robust control of discrete‐time switched systems in the presence of parametric uncertainty and time‐varying delays. To accommodate a more general model, nonlinear Lipschitz functions are incorporated. Additionally, the system is modeled with constraints on both control inputs and outputs. To achieve the control objectives, static and dynamic output feedback controllers are designed using the robust model predictive control (RMPC) framework. The underlying optimization problem is formulated and solved, leveraging Lyapunov‐Krasovskii functionals (LKF) and switched Lyapunov functions (SLF). The asymptotic stability of the closed‐loop system under arbitrary switching signals is ensured by satisfying sufficient conditions expressed as linear matrix inequalities (LMIs). A key advantage of the proposed method lies in its low conservatism. Moreover, the time delay and state variables are assumed unknown, and they ensure an acceptable transient response of the closed‐loop system. To demonstrate the effectiveness of the designed controllers, simulation results are provided and compared against prior related works, highlighting the improvements achieved.

In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.