Dissipative control for nonlinear Markovian jump systems with mixed time‐delays: The discrete‐time case

This article is concerned with the dissipative control problem for discrete‐time nonlinear Markovian jump systems subject to both discrete and distributed time‐delays. The purpose is to design a state feedback controller that is capable of guaranteeing the required closed‐loop stability and dissipativity performances simultaneously. By resorting to Lyapunov functional methodology and completing square technique, sufficient conditions are established for the existence of the desired state feedback controller in terms of certain Hamilton‐Jacobi inequalities (HJIs). Within the provided framework, the required controller parameters can be obtained by solving the corresponding HJIs. Finally, two numerical simulation examples are presented to demonstrate the correctness and effectiveness of the developed control paradigm.     

Stability and stabilization of nonlinear discrete‐time stochastic systems

This paper mainly studies the locally/globally asymptotic stability and stabilization in probability for nonlinear discrete‐time stochastic systems. Firstly, for more general stochastic difference systems, two very useful results on locally and globally asymptotic stability in probability are obtained, which can be viewed as the discrete versions of continuous‐time Itô systems. Then, for a class of quasi‐linear discrete‐time stochastic control systems, both state‐ and output‐feedback asymptotic stabilization are studied, for which, sufficient conditions are presented in terms of linear matrix inequalities. Two simulation examples are given to illustrate the effectiveness of our main results.     

Transient performance for discrete‐time singular systems with actuators saturation via composite nonlinear feedback control

This paper is concerned with the transient performance improvement in tracking control problems for linear multivariable discrete‐time singular systems subject to actuators saturation. A composite nonlinear feedback control strategy is considered, and the resulting controller consists of a linear feedback law and a nonlinear feedback law without any switching element. The nonlinear term leads to a varying damping ratio of the closed‐loop system and yields a small overshoot as the output approaches the target reference, whereas the linear component is designed to achieve a quick response of the closed‐loop system. Two composite nonlinear feedback control laws by both state feedback and measurement output feedback are addressed. An illustrative example is included to show the validity of the obtained results. Copyright © 2012 John Wiley & Sons, Ltd.     

Active disturbance rejection control approach to stabilization of lower triangular systems with uncertainty

In this paper, we apply the active disturbance rejection control (ADRC) to stabilization for lower triangular nonlinear systems with large uncertainties. We first design an extended state observer (ESO) to estimate the state and the uncertainty, in real time, simultaneously. The constant gain and the time‐varying gain are used in ESO design separately. The uncertainty is then compensated in the feedback loop. The practical stability for the closed‐loop system with constant gain ESO and the asymptotic stability with time‐varying gain ESO are proven. The constant gain ESO can deal with larger class of nonlinear systems but causes the peaking value near the initial stage that can be reduced significantly by time‐varying gain ESO. The nature of estimation/cancelation makes the ADRC very different from high‐gain control where the high gain is used in both observer and feedback. Copyright © 2015 John Wiley & Sons, Ltd.     

Feedback predictive control for constrained fuzzy systems with Markovian jumps

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete‐time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi‐Sugeno (T‐S) fuzzy model to represent a discrete‐time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on‐line optimization paradigm that utilizes the closed‐loop state feedback controller and is solved using the standard semi‐definite programming (SDP). To reduce the on‐line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Geometrically (Q,S, R)‐Incremental Dissipativity and Incremental Stability for Switched Time‐Varying Nonlinear Discrete‐Time Systems

This paper investigates geometrically (Q,S,R)‐incremental dissipativity and incremental stability for switched time‐varying nonlinear discrete‐time systems. A geometrically (Q,S,R)‐incremental dissipativity concept is proposed for switched nonlinear discrete‐time systems by using multiple storage functions and multiple incremental supply rate. Furthermore, the sufficient conditions of geometrically (Q,S,R)‐incremental dissipativity are given under the design of state‐dependent switching law. The incremental stability conditions are derived for geometrically (Q,S,R)‐incrementally dissipative switched systems. By designing of a composite state‐dependent switching law, the feedback interconnected switched systems are ensured to be geometrically (Q,S,R)‐incrementally dissipative. A numerical example is given to illustrate the validity of the proposed approach.     

H∞ Control of Linear Discrete‐Time Systems With Norm‐Bounded Nonlinear Uncertainties

In this paper, robust H_∞ control of a class of discrete‐time uncertain systems in state‐space form with linear nominal parts and norm‐bounded nonlinear uncertainties in both state and output equations is discussed. Such systems have a unique characterisic; that is, the two norm‐bounded nonlinear uncertainties have the equivalent representation by means of time‐varying and norm‐bounded linear uncertainties. To overcome the conservativenss of [5], the two nonlinear uncertainty sets are considered to be different. Then, by converting such systems into related discrete‐time linear systems with time‐varying and norm‐bounded linear uncertainties, we obtain that a sufficient condition for robust H_∞ control of such systems is equivalent to the solvability of the same problem of the related linear uncertain systems, which is solvable by means of a linear algebraic Riccati inequality.     

具有时变状态滞后的非线性2-D 离散系统的稳定性与控制

考虑一类由局部状态空间Fornasini-Marchesini(FM LSS)第二模型描述的,具有时变状态滞后非线性二维(2-D)离散系统的稳定性分析和控制问题.时变状态滞后项的上、下界为正整数,非线性项满足Lipschitz条件.首先,通过引入一个含有时滞上、下界的新Lyapunov函数,给出了系统的稳定性准则;然后设计了状态反馈控制器以保证系统的稳定性,进而,状态反馈控制律可由线性矩阵不等式求得;最后通过数值算例表明了所得结果的有效性.     

Robust adaptive output feedback control of a class of discrete‐time nonlinear systems with nonlinear uncertainties and unknown control directions

In this paper, robust adaptive output feedback control is studied for a class of discrete‐time nonlinear systems with functional nonlinear uncertainties of the Lipschitz type and unknown control directions. In order to construct an output feedback control, the system is transformed into the form of a nonlinear autoregressive moving average with eXogenous inputs (NARMAX) model. In order to avoid the noncausal problem in the control design, future output prediction laws and parameter update laws with the dead‐zone technique are constructed on the basis of the NARMAX model. With the employment of the predicted future outputs, a constructive output feedback adaptive control is proposed, where the discrete Nussbaum gain technique and the dead‐zone technique are used in parameter update laws. The effect of the functional nonlinear uncertainties is compensated for, such that an asymptotic tracking performance is achieved, whereas other signals in the closed‐loop systems are guaranteed to be bounded. Simulation studies are performed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Stability analysis and output‐feedback stabilization of discrete‐time systems with a time‐varying state delay and nonlinear perturbation

This paper aims to derive stability conditions and an output‐feedback stabilization method for discrete‐time systems with a time‐varying state delay and nonlinear perturbation. With a new way of handling the Lyapunov stability criterion, linear matrix inequality conditions are obtained for estimating bounds on delay to ensure the asymptotic stability. Based on the conditions, a synthesis procedure is developed for finding stabilizing output‐feedback gains, which are formulated as direct design variables. Three numerical examples are employed to demonstrate the effectiveness and advantages of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Constrained robust sampled‐data control for nonlinear uncertain systems

In industrial process control, computer control, which makes the closed‐loop system a sampled‐data one containing both continuous‐ and discrete‐time signals, is widely used. In contrast with traditional approximation methods, sampled‐data synthesis, a direct digital controller design procedure without approximation, has received increasing attention during the past few years. However, many of the existing results cannot be applied to sampled‐data control design for the uncertain systems. In this paper, a result of robust asymptotic stability of sampled‐data systems with constraints on the state is presented based on a result on practical stability for these systems. Then the robust sampled‐data control for a class of uncertain nonlinear systems with constraints on the output is developed. The problem is formulated from vehicle steering control with constraint on the side slip angle of body. The result is described by some matrix inequalities which could be solved by an iterative algorithm based on the linear matrix inequality technique. Finally, a numerical example is presented to demonstrate the result. Copyright © 2002 John Wiley & Sons, Ltd.     

Compensation of time‐varying input delay for discrete‐time nonlinear systems

We consider general discrete‐time nonlinear systems (of arbitrary nonlinear growth) with time‐varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete‐time systems, an analogous restriction would be that the input delay is non‐increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous‐time case, the predictor feedback law in the discrete‐time case is explicit. We specialize the result to linear time‐invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges. Copyright © 2015 John Wiley & Sons, Ltd.     

ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS WITH TRACKING ERRORS SQUARE

In this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.     

Stabilization of Stochastic Coupled Systems With Time Delay Via Feedback Control Based on Discrete‐Time State Observations

In this paper, the stabilization of stochastic coupled systems (SCSs) with time delay via feedback control based on discrete‐time state observations is investigated. We use the discrete‐time state feedback control to stabilize stochastic coupled systems with time delay. Moreover, by employing Lyapunov method and graph theory, the upper bound of the duration between two consecutive state observations is obtained and some criteria are established to guarantee the stabilization in sense of ‐stability and mean‐square asymptotic stability of SCSs with time delay via feedback control based on discrete‐time state observations. In addition, to verify the theoretical results, stochastic coupled oscillators with time delay are performed. At last, a numerical example is given to illustrate the applicability and effectiveness of our analytical results.     

Robust ℋ︁∞ sliding mode control for nonlinear stochastic systems with multiple data packet losses

In this paper, an ??_∞ sliding mode control (SMC) problem is studied for a class of discrete‐time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state‐feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete‐time system considered is also subject to norm‐bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete‐time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ??_∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete‐time SMC controller is designed capable of guaranteeing the discrete‐time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

Neural network‐based adaptive dynamic surface control of uncertain nonlinear pure‐feedback systems

In this paper, by incorporating the dynamic surface control technique into a neural network‐based adaptive control design framework, we have developed a backstepping‐based control design for a class of nonlinear systems in pure‐feedback form with arbitrary uncertainty. The circular design problem which may exist in pure‐feedback systems is overcome. In addition, our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. A stability analysis is given, which shows that our control law can guarantee the semi‐global uniformly ultimate boundedness of the solution of the closed‐loop system, and makes the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict‐feedback nonlinear systems with arbitrary uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.     

A nonlinear state‐feedback state‐feedforward tracking control strategy for a boiler‐turbine unit

A boiler‐turbine unit is a primary module for coal‐fired power plants, and an effective automatic control system is needed for the boiler‐turbine unit to track the load changes with the drum water level kept within an acceptable range. The aim of this paper is to develop a nonlinear tracking controller for the Bell‐Åström boiler‐turbine unit. A Takagi‐Sugeno fuzzy control system is introduced for the nonlinear modeling of the Bell‐Åström boiler‐turbine unit. Based on the Takagi‐Sugeno fuzzy models, a nonlinear tracking controller is developed, and the proposed control law is comprised of a state‐feedforward term and a state‐feedback term. The stability of the closed‐loop control system is analyzed on the basis of Lyapunov stability theory via the linear matrix inequality approach and Schur complement. Moreover, model uncertainties are also considered, and it is proved that with the proposed control law the tracking error converges to zero. To assess the performance of the proposed nonlinear state‐feedback state‐feedforward control strategy, a nonlinear model predictive control strategy and a linear strategy are presented as comparisons. The effectiveness and the advantages of the proposed nonlinear state‐feedback state‐feedforward control strategy are demonstrated by simulations.     

Stationary policies for lower bounds on the minimum average cost of discrete‐time nonlinear control systems

The paper deals with the control problem of discrete‐time nonlinear systems. The main contribution of this note is to present conditions that assure the existence of stationary policies that generate lower bounds for the minimal long‐run average cost. These lower bounds coincide with the optimal solution when a mild convergence assumption holds. To illustrate the results, the paper presents an application for the simultaneous state‐feedback control problem, and the derived strategy is used to design a real‐time simultaneous control for two direct current motor devices. The dynamics of these two devices are written in terms of a nonlinear algebraic matrix recurrence, which in turn represents a particular case for our general nonlinear approach. The optimal gain for the corresponding simultaneous state‐feedback problem is obtained, and such a gain was implemented in a laboratory testbed to control simultaneously the two direct current motors. Copyright © 2013 John Wiley & Sons, Ltd.     

Static output feedback sliding mode control for time‐varying delay systems with time‐delayed nonlinear disturbances

In this paper, a robust stabilization problem for a class of linear time‐varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time‐varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds which are employed for the control design. A sliding surface is designed and the stability of the corresponding sliding motion is analysed based on the Razumikhin Theorem. Then a static output feedback sliding mode control with time delay is synthesized to drive the system to the sliding surface in finite time. Conservatism is reduced by using features of sliding mode control and systems structure. Simulation results show the effectiveness of the proposed approach. Copyright © 2009 John Wiley & Sons, Ltd.