Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

In this work, sampled‐data iterative learning control (ILC) method is extended to a class of continuous‐time nonlinear systems with iteration‐varying trial lengths. In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled‐data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant. To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases.     

Iterative Learning Control for Nonlinear Systems: A Bounded‐Error Algorithm

This paper presents a nonlinear iterative learning control (NILC) for nonlinear time‐varying systems. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory‐tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. A special feature of the algorithm is that the trial‐time interval is finite but not fixed as it is for the other iterative learning algorithms. A sufficient condition for convergence and robustness of the bounded‐error learning procedure is derived. With respect to the bounded‐error and standard learning processes applied to a virtual robot, simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control.     

High‐precision formation control of nonlinear multi‐agent systems with switching topologies: A learning approach

Arbitrary high precision is considered one of the most desirable control objectives in the relative formation for many networked industrial applications, such as flying spacecrafts and mobile robots. The main purpose of this paper is to present design guidelines of applying the iterative schemes to develop distributed formation algorithms in order to achieve this control objective. If certain conditions are met, then the control input signals can be learned by the developed algorithms to accomplish the desired formations with arbitrary high precision. The systems under consideration are a class of multi‐agent systems under directed networks with switching topologies. The agents have discrete‐time affine nonlinear dynamics, but their state functions do not need to be identical. It is shown that the learning processes resulting from the relative output formation of multi‐agent systems can converge exponentially fast with the increase of the iteration number. In particular, this work induces a distributed algorithm that can simultaneously achieve the desired relative output formation between agents and regulate the movement of multi‐agent formations as desired along the time axis. The illustrative numerical simulations are finally performed to demonstrate the effectiveness and performance of the proposed distributed formation algorithms. Copyright © 2014 John Wiley & Sons, Ltd.     

High‐order internal model‐based iterative learning control design for nonlinear distributed parameter systems

This article deals with the problem of iterative learning control algorithm for a class of nonlinear parabolic distributed parameter systems (DPSs) with iteration‐varying desired trajectories. Here, the variation of the desired trajectories in the iteration domain is described by a high‐order internal model. According to the characteristics of the systems, the high‐order internal model‐based P‐type learning algorithm is constructed for such nonlinear DPSs, and furthermore, the corresponding convergence theorem of the presented algorithm is established. It is shown that the output trajectory can converge to the desired trajectory in the sense of (L²,λ) ‐norm along the iteration axis within arbitrarily small error. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Sliding mode learning control of non‐minimum phase nonlinear systems

In this paper, a novel robust sliding mode learning control scheme is developed for a class of non‐minimum phase nonlinear systems with uncertain dynamics. It is shown that the proposed sliding mode learning controller, designed based on the most recent information of the stability status of the closed‐loop system, is capable of adjusting the control signal to drive the sliding variable to reach the sliding surface in finite time and remain on it thereafter. The closed‐loop dynamics including both observable and non‐observable ones are then guaranteed to asymptotically converge to zero in the sliding mode. The developed learning control method possesses many appealing features including chattering‐free characteristic, strong robustness with respect to uncertainties. More importantly, the prior information of the bounds of uncertainties is no longer required in designing the controller. Numerical examples are presented in comparison with the conventional sliding mode control and backstepping control approaches to illustrate the effectiveness of the proposed control methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust stabilization of nonlinear stochastic 2‐D systems: LaSalle‐type theorem approach

LaSalle theorem (also known as the LaSalle invariance principle) plays an essential role in the systems and control theory. Recently, it has been extensively studied and developed for various types of one‐dimensional (1‐D) systems including deterministic and stochastic 1‐D systems in discrete‐ and continuous‐time domains. For two‐dimensional (2‐D) systems, such studies have received considerably less attention. In this article, based on discrete martingale theory, a LaSalle‐type theorem is first developed for a class of discrete‐time nonlinear stochastic 2‐D systems described by a Roesser model. The proposed result can be regarded as an extension of stochastic Lyapunov‐like theorem, which guarantees the convergence almost surely of system state trajectories. Extensions to the problem of optimal guaranteed cost control of nonlinear stochastic 2‐D systems are also presented. The proposed schemes are then utilized to derive tractable synthesis conditions of a suboptimal state‐feedback controller for uncertain 2‐D systems with multiplicative stochastic noises. The effectiveness of the obtained results is illustrated by given numerical examples and simulations.     

Nonlinear adaptive learning control for unknown time‐varying parameters and unknown time‐varying delays

A new adaptive learning control approach is proposed for a class of first‐order nonlinear systems with two unknown time‐varying parameters and an unknown time‐varying delay. By reconstructing the system equation, all unknown time‐varying terms, including the time‐varying delay, are combined into an unknown periodic time‐varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov–Krasovskii‐like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high‐order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust monotone gradient‐based discrete‐time iterative learning control

This paper considers the use of matrix models and the robustness of a gradient‐based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data‐dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean‐square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well‐known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non‐causal controller dynamics. The results are compared with recently published results for robust inverse‐model‐based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high‐frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic intermittent Q‐learning–based model‐free suboptimal co‐design of ‐stabilization

This paper proposes an intermittent model‐free learning algorithm for linear time‐invariant systems, where the control policy and transmission decisions are co‐designed simultaneously while also being subjected to worst‐case disturbances. The control policy is designed by introducing an internal dynamical system to further reduce the transmission rate and provide bandwidth flexibility in cyber‐physical systems. Moreover, a Q‐learning algorithm with two actors and a single critic structure is developed to learn the optimal parameters of a Q‐function. It is shown by using an impulsive system approach that the closed‐loop system has an asymptotically stable equilibrium and that no Zeno behavior occurs. Furthermore, a qualitative performance analysis of the model‐free dynamic intermittent framework is given and shows the degree of suboptimality concerning the optimal continuous updated controller. Finally, a numerical simulation of an unknown system is carried out to highlight the efficacy of the proposed framework.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.