Hybrid state-space fuzzy model-based controller with dual-ratesampling for digital control of chaotic systems

We develop a hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems. A Takagi-Sugeno (TS) fuzzy model is used to model the chaotic dynamic system and the extended parallel-distributed compensation technique is proposed and formulated for designing the fuzzy model-based controller under stability conditions. The optimal regional-pole assignment technique is also adopted in the design of the local feedback controllers for the multiple TS linear state-space models. The proposed design procedure is as follows: an equivalent fast-rate discrete-time state-space model of the continuous-time system is first constructed by using fuzzy inference systems. To obtain the continuous-time optimal state-feedback gains, the constructed discrete-time fuzzy system is then converted into a continuous-time system. The developed optimal continuous-time control law is finally converted into an equivalent slow-rate digital control law using the proposed intelligent digital redesign method. The main contribution of the paper is the development of a systematic and effective framework for fuzzy model-based controller design with dual-rate sampling for digital control of complex such as chaotic systems. The effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic Chua circuit     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.     

基于T-S模糊模型的转台鲁棒最优控制器设计

针对飞行器仿真转台系统的非线性以及不确定性问题,提出了基于T-S模糊模型的鲁棒最优控制器设计方法.首先,利用IF-THEN模糊规则将转台速度环系统的状态空间分成不同的区域,构建具有参数不确定性的T-S模糊模型;然后,根据给定的最优性能指标要求以及控制输入约束,通过求解一组线性矩阵不等式(LMIs)进行鲁棒最优控制嚣设计.仿真结果表明,该方法不仅具有比较好的控制效果,而且能有效地解决控制输入约束问题,并能很好地保证对参数变化的鲁棒稳定性.     

基于自适应动态规划的非线性鲁棒近似最优跟踪控制

为克服现有近似最优跟踪控制方法只能跟踪连续可微参考输入的局限,本文针对一类具有未知动态的连续时间非线性时不变仿射系统,提出了一种新的基于自适应动态规划的鲁棒近似最优跟踪控制方法.首先采用递归神经网络建立系统模型,然后建立评价神经网络对最优性能指标进行估计,从而得到最优性能指标偏导数的估计值,进而得到近似最优跟踪控制器,最后利用系统输出与参考输入之间的跟踪误差设计鲁棒项对神经网络建模误差进行补偿.分别针对两个非线性系统进行仿真实验,仿真结果表明了所提方法的有效性和优越性.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.     

一类非线性系统最大可控不变集求解

针对非线性系统线性化在状态约束下最优鲁棒控制求解问题,提出了一种基于混合系统的非线性系统最大鲁棒控制不变集的方法.对于一类非线性系统通过平衡点线性化的方法转化为多模态的混合系统,并进行了混合逻辑动态模型(MLD)的建模,在不变集基本理论的基础上,通过多参数规划的混合整数规划(MIQP)的方法迭代求解最大可控不变集,并求得不变集内的最优控制器,解决系统的状态约束问题.通过一个非线性系统的实例进行建模、仿真,证明了本方法的可行性.     

Optimal Control for a Class of Complex Singular System Based on Adaptive Dynamic Programming

This paper presents a new design approach to achieve decentralized optimal control of high-dimension complex singular systems with dynamic uncertainties. Based on robust adaptive dynamic programming (robust ADP) method, controllers for solving the singular systems optimal control problem are designed. The proposed algorithm can work well when the system model is not exactly known but the input and output data can be measured. The policy iteration of each controller only uses their own states and input information for learning, and do not need to know the whole system dynamics. Simulation results on the New England 10-machine 39-bus test system show the effectiveness of the designed controller.      

具有最优动态性能的鲁棒镇定控制器设计

针对ＳＩＳＯ线性离散系统,利用线性规划方法设计具有指定最优动态性能的鲁棒稳定控制器。当线性离散模型的零,极点已知时,将最优动态性能指标在指定输入信号下直接转化为线性规划问题。从而解出最优响应输出序列。最优动态性能指标与鲁棒稳定性的统一使该控制器的设计方法具备了工业应用条件。仿真实例验证了结果的正确性。     

Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation

Takagi-Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input-output submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear system subject to actuator saturation is presented. In our TS fuzzy representation, the modeling error is also captured by norm-bounded uncertainties. A set invariance condition for the system in the TS fuzzy representation is first established. Based on this set invariance condition, the problem of estimating the domain of attraction of a TS fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality (LMI) optimization problem. By viewing the state feedback gain as an extra free parameter in the LMI optimization problem, we arrive at a method for designing state feedback gain that maximizes the domain of attraction. A fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction. An inverted pendulum is used to show the effectiveness of the proposed fuzzy controller.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.     

Analysis and synthesis of nonlinear time-delay systems via fuzzycontrol approach

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller     

Robust anti-windup controller design of time-delay fuzzy systems with actuator saturations

This study presents a robust anti-windup fuzzy control approach for uncertain nonlinear time-delay systems with actuator saturations. The discussed system dynamics is presented by the Takagi-Sugeno (T-S) fuzzy model. To facilitate the design process, the nonlinearity of input saturation is characterized by a specific sector condition. Given a stabilizing dynamic output feedback fuzzy controller, an anti-windup control approach is then developed to maximize the size of estimate of the domain of attraction. Significantly, the convergence of all admissible initial states within this region could be ensured. Based on the Lyapunov-Krasovskii delay-independent and delay-dependent analyses, sufficient conditions for the robust stabilization are derived. These conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities, allowing the fuzzy controller to be synthesized more efficiently. Finally, numeric simulations are given to validate the proposed approach.     

Gain-phase margin analysis of dynamic fuzzy control systems

In this paper, we apply some effective methods, including the gain-phase margin tester, describing function and parameter plane, to predict the limit cycles of dynamic fuzzy control systems with adjustable parameters. Both continuous-time and sampled-data fuzzy control systems are considered. In general, fuzzy control systems are nonlinear. By use of the classical method of describing functions, the dynamic fuzzy controller may be linearized first. According to the stability equations and parameter plane methods, the stability of the equivalent linearized system with adjustable parameters is then analyzed. In addition, a simple approach is also proposed to determine the gain margin and phase margin which limit cycles can occur for robustness. Two examples of continuous-time fuzzy control systems with and without nonlinearity are presented to demonstrate the design procedure. Finally, this approach is also extended to a sampled-data fuzzy control system.     

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.     

Data-Driven Global Robust Optimal Output Regulation of Uncertain Partially Linear Systems

In this paper, a data-driven control approach is developed by reinforcement learning (RL) to solve the global robust optimal output regulation problem (GROORP) of partially linear systems with both static uncertainties and nonlinear dynamic uncertainties. By developing a proper feedforward controller, the GROORP is converted into a global robust optimal stabilization problem. A robust optimal feedback controller is designed which is able to stabilize the system in the presence of dynamic uncertainties. The closed-loop system is ensured to be input-to-output stable regarding the static uncertainty as the external input. This robust optimal controller is numerically approximated via RL. Nonlinear small-gain theory is applied to show the input-to-output stability for the closed-loop system and thus solves the original GROORP. Simulation results validates the efficacy of the proposed methodology.      

基于观测器的不确定T-S模糊系统鲁棒镇定

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件. 该条件用来设计模糊控制器和模糊观测器. 为了设计模糊控制器和模糊观测器, 用T-S模糊模型来表示非线性系统, 并运用平行分布补偿观念. 充分条件基于二次Lyapunov函数, 通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式, 比以往文献中列出的条件具有更小的保守性. 该不等式为双线性矩阵不等式, 可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益. 最后, 通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.     

H/sub /spl infin// fuzzy output feedback control design for nonlinear systems: an LMI approach

Addresses the problem of stabilizing a class of nonlinear systems by using an H/sub /spl infin// fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an H/sub /spl infin// fuzzy output feedback control law which guarantees the L/sub 2/ gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an H/sub /spl infin// fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H/sub /spl infin// fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.     

Robust Quadratic-Optimal Control of TS-Fuzzy-Model-Based Dynamic Systems With Both Elemental Parametric Uncertainties and Norm-Bounded Approximation Error

This paper considers the design problem of the robust quadratic-optimal parallel-distributed-compensation (PDC) controllers for Takagi–Sugeno (TS) fuzzy-model-based control systems with both elemental parametric uncertainties and norm-bounded approximation error. By complementarily fusing the robust stabilizability condition, the orthogonal functions approach (OFA), and the hybrid Taguchi genetic algorithm (HTGA), an integrative method is presented in this paper to design the robust quadratic-optimal PDC controllers such that 1) the uncertain TS-fuzzy-model-based control systems can be robustly stabilized, and 2) a quadratic integral performance index for the nominal TS-fuzzy-model-based control systems can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). By using the OFA and the LMI-based robust stabilizability condition, the robust quadratic-optimal PDC control problem for the uncertain TS-fuzzy-model-based dynamic systems is transformed into a static constrained-optimization problem represented by the algebraic equations with constraint of LMI-based robust stabilizability condition, thus greatly simplifying the robust optimal PDC control design problem. Then, for the static constrained-optimization problem, the HTGA is employed to find the robust quadratic-optimal PDC controllers of the uncertain TS-fuzzy-model-based control systems. Two design examples of the robust quadratic-optimal PDC controllers for an uncertain inverted pendulum system and an uncertain nonlinear mass–spring–damper mechanical system are given to demonstrate the applicability of the proposed integrative approach.      

Robust decentralized adaptive fuzzy control for a class of large‐scale MIMO nonlinear systems

In this paper, a novel decentralized robust adaptive fuzzy control scheme is proposed for a class of large‐scale multiple‐input multiple‐output uncertain nonlinear systems. By virtue of fuzzy logic systems and the regularized inverse matrix, the decentralized robust indirect adaptive fuzzy controller is developed such that the controller singularity problem is addressed under a united design framework; no a priori knowledge of the bounds on lumped uncertainties are being required. The closed‐loop large‐scale system is proved to be asymptotically stable. Simulation results confirmed the validity of the approach presented. Copyright © 2011 John Wiley & Sons, Ltd.