Asymptotic tracking in uncertain Volterra systems

This paper studies the robust tracking problem for an uncertain Volterra system via the frequency-domain approach. Based on the knowledge that the steady-state response of a Volterra system under the sinusoidal input contains possibly infinitely many frequency components, it is shown that (1) for any specified finitely many frequency components possibly contained in the steady-state tracking error, there exists a linear controller that robustly annihilates these components; and (2) robust tracking is possible by a linear controller provided that the Volterra system of the closed-loop system is polynomial. These results can be viewed as a nonlinear analog of the well-known linear robust servomechanism theory developed in the 1970s.     

Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust discrete-time sliding mode control for tracking and model following of uncertain nonlinear systems

This paper proposes a discrete-time controller for robust tracking and model following of a class of nonlinear, multi-input multi-output, systems. For this purpose, a discrete-time sliding mode controller (DTSMC) is used to ensure the stability, robustness and an output tracking against the modelling uncertainties, even at relatively large sampling periods. In this way, Takagi–Sugeno (T–S) fuzzy modelling is used to decompose the nonlinear system to a set fuzzy-blended locally linearised subsystems. Implementation of the second Lyapunov theory for mismatched uncertain nonlinear T–S fuzzy models results in a set of linear matrix inequalities, which is used to design the sliding surface. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show that the proposed method guarantees the stability of closed-loop system and achieves small tracking error in the presence of parametric uncertainties at large sampling periods.     

Robust tracking control of uncertain nonlinear systems with unknown control directions

A global robust tracking control design procedure is proposed for a class of uncertain nonlinear systems. The key point is that the signs of multiplicative uncertainties, the so-called control directions, are not assumed to be known a priori. The class of systems can be of arbitrary dynamic order and the unmatched additive uncertainties need not satisfy the global Lipschitz condition. It is proved that under the proposed control, all closed-loop states are bounded and the tracking error converges to any prescribed small neighborhood of the origin. The results of this paper enlarge the class of uncertain nonlinear systems for which global robust tracking control can be designed.     

具有不确定噪声的随机非线性系统的鲁棒自适应跟踪

研究了一类随机非线性系统的鲁棒自适应跟踪问题.文中利用随机控制Lyapunov设计方法,对于受方差不确定Wiener噪声干扰的参数严格反馈形式的系统,给出了参数自适应律和控制律,使得跟踪误差在4次均方意义下收敛到一个小范围内.     

Robust stability and performance of stochastic uncertain systems on an infinite time interval

In this paper, we consider a robust stability problem for continuous time stochastic uncertain systems. The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parametrized risk-sensitive performance analysis problem is used to estimate the level of guaranteed performance for the stochastic uncertain system under consideration. This solution is obtained by solving an algebraic Riccati equation. The corresponding performance bound holds for all admissible uncertainties and is nonconservative.     

Funnel‐like prescribed tracking control for uncertain nonlinear stochastic switched systems

This paper deals with the funnel‐like prescribed tracking control problem for a class of uncertain nonlinear stochastic switched systems. An improved performance technique is developed to restrain the fluctuation at the moment of switches and a new algorithm is proposed to address the funnel‐like prescribed tracking problem. First, a dynamic gain‐based switched K‐filter is constructed to estimate the unmeasured state information of the switched system. Subsequently, the performance technique is applied to prescribe output tracking error and restrain fluctuations of the system. Thereafter, the dynamic output feedback switched controller is designed by the use of the backstepping method. Moreover, based on the Lyapunov stability theory, it is proved strictly that all signals of the resulting closed‐loop system are bounded in probability if the switching signal satisfies the average dwell time. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed theoretical results.     

Robust tracking control for uncertain fuzzy systems with time delay and external disturbances

In this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional-integral controller with an enhanced equivalent-input-disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay-dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results.     

Robust adaptive tracking control of robotic systems with uncertainties

To deal with the uncertainty factors of robotic systems, a robust adaptive tracking controller is proposed. The knowledge of the uncertainty factors is assumed to be unidentified; the proposed controller can guarantee robustness to parametric and dynamics uncertainties and can also reject any bounded, immeasurable disturbances entering the system. The stability of the proposed controller is proven by the Lyapunov method. The proposed controller can easily be implemented and the stability of the closed system can be ensured; the tracking error and adaptation parameter error are uniformly ultimately bounded （UUB）. Finally, some simulation examples are utilized to illustrate the control performance.     

针对时变轨迹的非线性仿射系统的鲁棒近似最优跟踪控制

针对非线性连续系统难以跟踪时变轨迹的问题,本文首先通过系统变换引入新的状态变量从而将非线性系统的最优跟踪问题转化为一般非线性时不变系统的最优控制问题,并基于近似动态规划算法(ADP)获得近似最优值函数与最优控制策略.为有效地实现该算法,本文利用评价网与执行网来估计值函数及相应的控制策略,并且在线更新二者.为了消除神经网络近似过程中产生的误差,本文在设计控制器时增加一个鲁棒项;并且通过Lyapunov稳定性定理来证明本文提出的控制策略可保证系统跟踪误差渐近收敛到零,同时也验证在较小的误差范围内,该控制策略能够接近于最优控制策略.最后给出两个时变跟踪轨迹实例来证明该方法的可行性与有效性.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints, A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function, At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop svstems is guaranteed bv the proposed design method. A numerical example is given to illustrate the main results.     

Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

Robust disturbance attenuation for uncertain nonlinear networked control systems

This paper considers the problem of robust disturbance attenuation for a class of uncertain nonlinear networked control systems. Takagi-Sugeno fuzzy models are firstly employed to describe the nonlinear plant. Markov processes are used to model the random network-induced delays and data packet dropouts. The Lyapunov-Razumikhin method has been used to derive such a controller for this class of nonlinear systems such that it is stochastically stabilizable with a disturbance attenuation level. Sufficient conditions for the existence of such a controller are derived in terms of the solvability of bilinear matrix inequalities. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness of the proposed design methodology is verified by a numerical example.     

Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method

A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator (LQG) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle (AHFV) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.     

Decentralized tracking control for linear uncertain interconnected systems with time delays

This paper investigates the robust output tracking problem for a class of large‐scale linear uncertain systems with interactions and time delays. Time delays exist in both states and controls. Using the Riccati equation, a procedure for determining decentralized linear control laws is presented such that the closed‐loop system asymptotically tracks the reference output and rejects any constant but unknown disturbances. The main feature of this approach is that the uncertain systems may contain time delays in both states and controls as well as in interactions between subsystems. A numerical example is included to show the results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust finite horizon minimax filtering for discrete-time stochastic uncertain systems

We study a finite-horizon robust minimax filtering problem for time-varying discrete-time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which the stochastic noises, driving the system, are defined. The optimal minimax filter has been found by applying techniques of risk-sensitive LQG control. The structure and properties of resulting filter are analyzed and compared to H_∞ and Kalman filters.     

Robust model predictive control with guaranteed setpoint tracking

In this paper a novel robust model predictive control (RMPC) algorithm is proposed, which is guaranteed to stabilize any linear time-varying system in a given convex uncertainty region while respecting state and input constraints. Moreover, unlike most existing RMPC algorithms, the proposed algorithm is guaranteed to remove steady-state offset in the controlled variables for setpoints (possibly) different from the origin when the system is unknown linear time-invariant. The controller uses a dual-mode paradigm (linear control law plus free control moves to reach an appropriate invariant region), and the key step is the design of a robust linear state feedback controller with integral action and the construction of an appropriate polyhedral invariant region in which this controller is guaranteed to satisfy the process constraints. The proposed algorithm is efficient since the on-line implementation only requires one to solve a convex quadratic program with a number of decision variables that scale linearly with the control horizon. The main features of the new control algorithm are illustrated through an example of the temperature control of an open-loop unstable continuous stirred tank reactor.     

内模控制系统鲁棒跟踪控制器的参数化及优化

针对最常用的2自由度内模控制系统,利用基于传递函数互质分解的频域理论,推导了存在模型失配且参考输入和扰动为任意已知函数时,所有能实现稳态无差跟踪的前馈控制器和反馈滤波器的参数化表达式.所得结论同时适用干连续和离散时间系统,并可在参数化基础上实现频域的优化控制.     

不确定多重时滞随机中立系统鲁棒H∞控制

针对一类不确定多重时滞随机中立系统,研究了鲁棒H_∞控制设计问题．该随机中立系统的状态项、控制项、微分项、外部干扰输入项均含有时滞,系统中的不确定性满足广义匹配条件．首先,利用随机Lyapunov稳定性理论和Ito微分法则,推导出系统的随机鲁棒可镇定的充分条件．在此基础上,进一步给出了鲁棒H_∞控制器存在的充分条件．本文的研究结果以线性矩阵不等式的形式给出,仿真结果表明了此控制器设计方法的有效性．