Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks

In this paper, we show that a linear discrete-time system subject to input saturation is semi-globally exponentially stabilizable via linear state and/or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable, and has all its poles located inside or on the unit circle. Furthermore, the semi-globally stabilizing feedback laws are explicitly constructed. The results presented here are parallel to our earlier results on the continuous-time counterpart (Lin and Saberi, 1993).     

Semi-global stabilization of linear systems subject to output saturation

It is established that a SISO linear stabilizable and detectable system subject to output saturation can be semi-globally stabilized by linear output feedback if all its invariant zeros are in the closed left-half plane, no matter where the open loop poles are. This result complements a recent result that such systems can always be globally stabilized by discontinuous nonlinear feedback laws, and can be viewed as dual to a well-known result: a linear stabilizable and detectable system subject to input saturation can be semi-globally stabilized by linear output feedback if all its poles are in the open left-half plane, no matter where the invariant zeros are.     

Anti-windup design of output tracking systems subject to actuator saturation and constant disturbances

This paper considers the design of output tracking systems subject to actuator saturation and integrator windup. An optimization-based approach is developed to design feedback and anti-windup gains of a controller structure involving intelligent integrators. The design goal is to increase stability region and output tracking and disturbance rejection ability of the closed-loop system.     

Anti-windup strategies for discrete-time switched systems subject to input saturation

This paper deals with the design of anti-windup compensator for discrete-time switched systems subject to input saturation. The cases of static and dynamic anti-windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed-loop system. Two aspects of the switching law are taken into account during the design: either it is arbitrary or it is a part of the complete control law. Theoretical conditions allowing to synthesise the anti-windup compensator are mainly described through linear matrix inequalities. Computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution.     

Output regulation for linear discrete-time systems subject to input saturation

The purpose of this paper is to examine the problem of controlling a linear discrete-time system subject to input saturation in order to have its output track (or reject) a family of reference (or disturbance) signals produced by some external generator. It is shown that a semi-global framework, rather than a global framework, for this problem is a natural one. Within this framework, a set of solvability conditions are given and feedback laws which solve the problem are constructed. The theory developed in this paper parallels the one we developed earlier for the continuous-time system. © 1997 by John Wiley & Sons, Ltd.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Composite nonlinear feedback design for discrete-time switching systems with disturbances and input saturation

This paper addresses the problem of robust controller design for a class of discrete-time switching systems with input saturation. To this aim, the composite nonlinear feedback method is extended to design a robust controller with improved performances in terms of the response speed and overshoot in the presence of disturbances and input saturation. The proposed approach is theoretically analysed and its closed-loop stability is proved. Then, the performance of the proposed method is verified using numerical simulations.     

含状态和输入时滞的离散时间系统的近似最优跟踪控制

针对状 态和控制输入均含有时滞的离散时间系统, 提出最优跟踪控制的设计方法. 通 过引入一种新的状态向量, 将含有状态和控制输入时滞的离散时间系统转化为 含有虚拟扰动项的无时滞离散时间系统. 根据最优控制理论, 构造离散Riccati矩阵方 程和离散Stein矩阵方程的序列, 并证明该解序列一致收敛于变换后的离散时间系统的最优跟 踪控制策略. 利用最优控制的逐次逼近设计方法, 得到最优跟踪控制的近似 解, 并给出求解最优跟踪控制律的算法. 仿真算例表明了所提出最优跟踪控制 方法的有效性.     

Robust output tracking for uncertain/nonlinear systems subject to almost constant disturbances

In this paper, we consider uncertain/nonlinear systems subject to unknown constant disturbance inputs. We wish to design state feedback controllers which ensure that the system output asymptotically tracks a specified constant reference signal and all states are bounded. The controllers we consider are PI in the sense that they consist of a piece which depends linearly on the state and another piece which depends on the integral of the output tracking error. Our main result reduces the original problem to a stabilization problem for an associated augmented system which we call the derivative augmented system. We obtain controller design procedures for specific classes of uncertain/nonlinear systems. Then we extend these results to the situation in which the reference signal and the disturbance are not necessarily constant but asymptotically approach a constant.     

Dynamic output feedback robust MPC for LPV systems subject to input saturation and bounded disturbance

For linear parameter varying (LPV) systems with unknown scheduling parameters and bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with input saturation is investigated. By pre-specifying partial controller parameters, a main optimization problem is solved by convex optimization to reduce the on-line computational burden. The main optimization problem guarantees that the estimated state and estimation error converge within the corresponding invariant sets such that recursive feasibility and robust stability are guaranteed. The consideration of input saturation in the main optimization problem improves the control performance. Two numerical examples are given to illustrate the effectiveness of the approach.     

Observer-based optimal output tracking for discrete-time systems with multiple state and input delays

The optimal output tracking control (OOTC) problem for a class of discrete-time systems with state and input delays is addressed. An augmented system is constructed such that the OOTC problem can be transformed into a two-point boundary value (TPBV) problem with both advance and delay terms from the necessary optimality conditions. The successive approximating method recently developed is extended to obtain an approximate solution of the TPBV problem, which is then used to obtain a feedforward and feedback tracking controller. An observer is designed for the uncertain reference input such that the feedforward controller is physically realizable. Simulations show the results are effective even with long time-delays. Recommended by Editorial Board member Poo Gyeon Park under the direction of Editor Young Il Lee. This research was supported by the National Natural Science Foundation of China (Grant No. 40776051), the Key Natural Science Foundation of Shandong Province (Grant No. Z2005G01), the Natural Science Foundation of Qingdao City (Grant No. 05-1-JC-94) and the research funds of QingDao University of Science and Technology. Hai-Hong Wang received the Ph.D. degree in Computer Science in July 2007 from Ocean University of China. She presently works in QingDao University of Science and Technology, Qingdao, P.R. China. Her current research interests include analysis and control for time-delay systems and nonlinear systems. Gong-You Tang received the Ph.D. degree in Control Theory and Applications from the South China University of Technology, P. R. China in 1991. He is a Professor at the College of Information Science and Engineering at the Ocean University of China, Qingdao, P. R. China. He is the Editor of the Journal of the Ocean University of China and Control and the Instruments in Chemical Industry. His research interests are in the areas of nonlinear systems, delay systems, large-scale systems, and networked control systems, with emphasis in optimal control, robust control, fault diagnosis and stability analysis.     

Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.     

Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation

For a linear system under a given saturated linear feedback, we propose feedback laws that achieve semi-global stabilization on the null controllable region while preserving the performance of the original feedback law in a fixed region. Here by semi-global stabilization on the null controllable region we mean the design of feedback laws that result in a domain of attraction that includes any a priori given compact subset of the null controllable region. Our design guarantees that the region on which the original performance is preserved would not shrink as the domain of attraction is enlarged by appropriately adjusting the feedback laws. Both continuous-time and discrete-time systems will be considered.     

Control of open‐loop neutrally stable systems subject to actuator saturation and external disturbances

In this paper, we study the disturbance response of open‐loop neutrally stable linear systems with saturating linear feedback controller. It is shown that the closed‐loop states remain bounded if the disturbances consists of those signals that do not have large sustained frequency components corresponding to the system's eigenvalues on the imaginary axis (continuous‐time) or on the unit circle (discrete‐time). Copyright © 2011 John Wiley & Sons, Ltd.     

考虑输入饱和的农用拖拉机路径跟踪有限时间控制

针对农用拖拉机的路径跟踪控制问题,提出基于有限时间和饱和技术的路径跟踪控制策略.首先,建立农机路径跟踪运动学模型,并通过有限时间控制技术,构造有限时间路径跟踪控制方法;其次,考虑到农用拖拉机的转向系统物理限制,将饱和技术与有限时间控制结合,给出复合的路径跟踪控制方法,通过严格的理论分析验证闭环系统在该控制器下的有限时间稳定性;最后,通过仿真结果表明,所设计的制导方法可以保证农用拖拉机快速、稳定地完成路径跟踪目标.     

Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.     

Improving transient performance in tracking control for linear multivariable discrete-time systems with input saturation

In this paper, we present a composite nonlinear feedback (CNF) control technique for linear discrete-time multivariable systems with actuator saturation. The CNF control law serves to improve the transient performance of the closed-loop system by adding an additional nonlinear feedback. The linear feedback can be designed to yield a quick response at the initial stage, then the nonlinear feedback is introduced to smooth out overshoots when the system output approaches the target reference. As such, the resulting closed-loop system typically has very fast transient response and small overshoots. The goal of this work is to complete the theory for general discrete-time systems. The technique is applied to a magnetic-tape-drive servo system design and yields a huge improvement in settling time compared to that of a purely linear controller.     

Analysis and design for discrete-time linear systems subject to actuator saturation

We present a method to estimate the domain of attraction for a discrete-time linear system under a saturated linear feedback. A simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant. Moreover, the condition can be expressed as linear matrix inequalities (LMIs) in terms of all the varying parameters and hence can easily be used for controller synthesis. The following surprising result is revealed for systems with single input: suppose that an ellipsoid is made invariant with a linear feedback, then it is invariant under the saturated linear feedback if and only if there exists a saturated (nonlinear) feedback which makes the ellipsoid invariant. Finally, the set invariance condition is extended to determine invariant sets for systems with persistent disturbances. LMI based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements.     

Simultaneous external and internal stabilization of linear systems with input saturation and non-input-additive sustained disturbances

In this paper, we study simultaneous external and internal stabilization of the linear system under input saturation and non-input additive sustained disturbances. For systems that are asymptotic null controllable with bounded control, it is shown that a nonlinear dynamic feedback controller can be designed so that the closed-loop states remain bounded for any initial condition and for two classes of sustained disturbances, and that the equilibrium in the absence of disturbances is globally asymptotically stable.