Iterative learning control for discrete-time switched singular systems

This paper deals with the problem of iterative learning control for a class of discrete-time switched singular systems with arbitrary switching rules. According to the characteristics of the systems, two types of iterative learning algorithms are proposed and the corresponding convergence conditions of the algorithms are established. Under some given assumptions, the algorithms can ensure the system state converges to the desired state trajectory on a finite time interval. Finally, two numerical examples are constructed to support the theoretical analysis.     

线性定常广义系统的D型迭代学习控制收敛性

给出了线性定常广义系统在D型学习律作用下的迭代控制收敛性结果,这一结果是全新的,其对时变系统也成立,而且,本文结果和方法大部分可以移植到线性定常广义离散时间系统.     

Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty

A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method.     

Nonlinear control of systems with multiple equilibria and unknown sinusoidal disturbance

In this paper, nonlinear systems having multiple equilibrium points and low order dynamics are investigated. Roll motions of ships are studied by means of modern nonlinear techniques to exemplify the behavior of such nonlinear systems in the case when they are under the influence of external sinusoidal disturbances with unknown amplitudes. The main objective is to analyze the performance of this system at different operating conditions, including those giving rise to chaos, and to design a controller with an overparameterized structure to stabilize the system at the origin. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Lyapunov-based techniques are used to force systematic following of a reference model while introducing a nonlinear parameter estimator to guarantee adaptivity. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.     

Iterative learning control design of nonlinear multiple time-delay systems

Most available results on iterative learning control address trajectory tracking problem for systems without multiple time-delay. This paper is concerned with iterative learning control design for nonlinear systems with multiple delays, in which external disturbances and output measurement noises are involved. We obtain some new and interesting criteria to guarantee the convergence of the tracking error in the sense of the λ − norm. It will be shown that the convergence of the system outputs to the desired trajectory is ensured in the absence of disturbances and output measurement noises. In the presence of disturbance and measurement noises, we estimate the upper bound of the tracking error. In order to confirm the validity of the present results, numerical simulation is also presented.     

一类非线性中立型系统的渐近稳定性

基于李雅普诺夫泛函方法,本文讨论了一类非线性中立型系统渐近稳定性的充分条件,推广了中立型系统稳定性结果。最后,通过实例及其仿真数值模拟验证了上述理论结果。     

Iterative identification algorithm for Wiener nonlinear systems using the Newton method

The Wiener system is an important class of output nonlinear systems. This paper presents a Newton iterative parameter estimation algorithm for Wiener nonlinear systems. The simulation results show that the proposed algorithm is effective. The proposed algorithm can be combined with other iterative methods to identify other linear or nonlinear systems with colored noises.     

线性滞后广义系统的二阶滑模控制方法

讨论了时滞广义系统在不同条件下的变结构控制,根据终端滑模控制的特点,提出了一种由线性滑模与终端滑模构成的二阶终端滑模及相应控制策略.研究结果表明,该方法能够有效地清除系统的高频抖振,同时保证闭环系统的渐近稳定,实现滑模运动.举例说明了设计的合理性和有效性.     

Non-coercive Lyapunov functions for infinite-dimensional systems

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with Lipschitz continuous nonlinearities these additional assumptions become especially simple. The results encompass some recent results on linear switched systems on Banach spaces. Finally, we derive new non-coercive converse Lyapunov theorems and give some examples showing the necessity of our assumptions.     

A new control method and its robustness for a class of nonlinear systems

For a class of time-varying nonlinear systems described by the equation , the precalculating control is not available if the input matrixg(x,t) is not invertible. With Lyapunov's second method, a stabilizing controller which makes the system practically stable is constructed in this paper. It is shown that the implementation of this scheme depends on some so-called posi-invertibility conditions forg(x,t). In case the system is partly stable, the method, named part-calculating control, can simplify the on-line computations. Without the assumption that the nominal system is asymptotically stable, the method is applied to the problems of control for the corresponding uncertain system that satisfies the matching condition. When the matching condition is not satisfied, the mismatching control problem is also studied with Lyapunov's second method.This work was supported by the Science Fund of the Chinese Academy of Science.     

A generic design methodology for sliding mode control of switched systems

The aim of this paper is to present a generic methodology to design sliding mode controllers for multivariable switched systems affine in control such as dc–dc power converters. An original formulation of the so-called reachability condition, suitable for this class of systems, is established. Based on the choice of a Lyapunov-like function and parameterized by a single weighting matrix, it allows several kinds of control strategies to be derived, namely conventional piecewise continuous strategies as well as discrete (Boolean) strategies. Its application to the important subclass of linear time invariant systems is investigated more specifically. In the Boolean case, the present approach is also compared to another hybrid one called the stabilizing approach. Eventually, its efficiency as a design methodology, as well as the performance of the resulting control, are shown by simulating it on non-trivial examples of power converters.     

A new proof of a theorem on optimal control of switched systems

Recently Sorin C. Bengea and Raymond A. DeCarlo [Sorin C. Bengea, Raymond A. DeCarlo, Optimal control of switching systems, Automatica J. IFAC 41 (2005) 11-27] have offered a key result that the set of trajectories of the two-switched system is dense in the set of trajectories of the embedded system. This result was proven by means of relaxed controls and the Chattering Lemma. In this paper we use the Lyapunov theorem to give a new simple proof.     

Pattern-forming systems for control of large arrays of actuators

Summary. We consider an approach for coordinating the activity of a large array of microactuators via diffusive (i.e., nearest-neighbor) coupling combined with reactive growth and decay, implemented via interconnection templates which have been artificially engineered into the system (for example, in collocated microelectronic circuitry, or through the formulation of active material layers). Such coupled systems can support interesting spatiotemporal patterns, which in turn determine the actuation patterns. Generating such spatiotemporal patterns typically involves stressing the interconnections by raising or lowering a parameter resulting in the crossing of stability thresholds. The possibility of making such parametric adjustments via feedback on a slower timescale offers a solution to the problem of communicating effectively within a large array: The communication is achieved through the interconnection template. The mathematics behind this idea leads us into the rich domain of nonlinear partial differential equations (PDEs) with spatiotemporal pattern solutions. We present a global nonlinear stability analysis that applies to certain model pattern-forming systems. The nonlinear stability analysis could serve as a starting point for control system design for systems containing large microactuator arrays. Received August 1, 2000; accepted August 16, 2001 Online publication November 5, 2001     

非线性系统的高阶迭代学习控制算法

本文对一般非线性系统,提出了三种高阶迭代学习控制算法:(Ⅰ)u_(h 1)=sum from j=1 to r(P_ju_(k-j 1) Г_je_(h-j 1));(Ⅱ)u_(k 1)=sum from j=1 to r(P_ju_(k-j 1) F_je_(k-j 1));(Ⅲ)u_(k 1)=sum from j=1 to r{P_ju_(k-j 1) (Г_j F_jd/(dt))e_(k-j 1)},其中u_(k 1)=u_(k 1)(t)表示系统第k 1次运行时的输入;e_k=y_k-y_d;y_d是系统所期望的输出;y_k是系统第k次运行时的输出;P_j,Г_j,F_j(j=1,…,r)是常数阵;进而给出了比较弱的收敛性条件。     

Composite nonlinear feedback based discrete integral sliding mode controller for uncertain systems

In this paper, a discrete integral sliding mode (ISM) controller based on composite nonlinear feedback (CNF) method is proposed. The aim of the controller is to improve the transient performance of uncertain systems. The CNF based discrete ISM controller consists of a linear and a nonlinear term. The linear control law is used to decrease the damping ratio of the closed-loop system for yielding a quick transient response. The nonlinear feedback control law is used to increase the damping ratio with an aim to reduce the overshoot of the closed-loop system as it approaches the desired reference position. It is observed that the discrete CNF-ISM controller produces superior transient performance as compared to the discrete ISM controller. The closed-loop control system remains stable during the sliding condition. Simulation results demonstrate the effectiveness of the proposed controller.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Some computational issues in optimal control by nonlinear programming

The Roppenecker [11] parameterization of multi-input eigenvalue assignment, which allows for common open- and closed-loop eigenvalues, provides a platform for the investigation of several issues of current interest in robust control. Based on this parameterization, a numerical optimization method for designing a constant gain feedback matrix which assigns the closed-loop eigenvalues to desired locations such that these eigenvalues have low sensitivity to variations in the open-loop state space model was presented in Owens and O'Reilly [8]. In the present paper, two closely related numerical optimization methods are presented. The methods utilize standard (NAG library) unconstrained optimization routines. The first is for designing a minimum gain state feedback matrix which assigns the closed-loop eigenvalues to desired locations, where the measure of gain taken is the Frobenius norm. The second is for designing a state feedback matrix which results in the closed-loop system state matrix having minimum condition number. These algorithms have been shown to give results which are comparable to other available algorithms of far greater conceptual complexity.     

General theorems for stability and boundedness for nonlinear functional discrete systems

We consider the nonlinear functional discrete system

     

Complicated version of a robust control scheme

The omission of four references from Page 642 of Ref. 1 is corrected.     

Multirate sampling and input-to-state stable receding horizon control for nonlinear systems

In this paper, a robust receding horizon control for multirate sampled-data nonlinear systems with bounded disturbances is presented. The proposed receding horizon control is based on the solution of Bolza-type optimal control problems for the approximate discrete-time model of the nominal system. “Low measurement rate” is assumed. It is shown that the multistep receding horizon controller that stabilizes the nominal approximate discrete-time model also practically input-to-state stabilizes the exact discrete-time system with disturbances.