Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts

This paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts, including modeled nonlinear dynamics, unmodeled dynamics, and dynamics modeled with unknown parameters. Also the virtual control directions of the system are unknown. The purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable. A novel observer and estimator are introduced for states and parameter estimates, respectively. A constructive procedure of design for an output feedback adaptive controller is given, by using the integrator backstepping approach and based on the proposed observer and parameter estimator. An example is given to show the effectiveness of the proposed scheme.     

Robust stabilization for uncertain switched impulsive control systems with state delay: An LMI approach

This paper deals with the problem of robust H_∞ state feedback stabilization for uncertain switched linear systems with state delay. The system under consideration involves time delay in the state, parameter uncertainties and nonlinear uncertainties. The parameter uncertainties are norm-bounded time-varying uncertainties which enter all the state matrices. The nonlinear uncertainties meet with the linear growth condition. In addition, the impulsive behavior is introduced into the given switched system, which results a novel class of hybrid and switched systems called switched impulsive control systems. Using the switched Lyapunov function approach, some sufficient conditions are developed to ensure the globally robust asymptotic stability and robust H_∞ disturbance attenuation performance in terms of certain linear matrix inequalities (LMIs). Not only the robustly stabilizing state feedback H_∞ controller and impulsive controller, but also the stabilizing switching law can be constructed by using the corresponding feasible solution to the LMIs. Finally, the effectiveness of the algorithms is illustrated with an example.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

具有不确定项的高阶非完整系统的反馈控制问题的研究

针对一类具有不确定性的高阶非完整系统,通过引入观测器,采用状态-输入转换、反推方法,设计了反馈控制器.同时为了处理初值为0的情况,提出了一种新的基于第一个子系统输出值的切换控制策略,提出的切换控制策略能有效的防止系统的状态发生有限时间逃逸现象.     

一类时滞非完整系统的反馈控制问题的研究

针对一类具有时滞项的非完整系统,研究了其反馈控制器的设计问题.采用状态转换技术和反推方法,设计了不依赖于时滞的反馈控制器.同时为了处理初值为零的情况,提出了一种新颖的基于第一个子系统输出值的切换控制策略,最后通过仿真算例说明了控制器的有效性.     

Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H _∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H _∞ performance. The derived methods can be applied to the robust H _∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).     

Robust Adaptive Finite-Time Stabilization of Nonlinearly Parameterized Nonholonomic Systems

This paper investigates the problem of adaptive finite-time stabilization of nonlinearly parameterized nonholonomic systems. By skilly using the parameter separation, input-state-scaling, and adding a power integrator techniques, an adaptive state feedback controller is obtained. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller can guarantee that the system states globally finite-time converge to the origin, while other signals remain bounded. Simulation examples demonstrate the effectiveness and the robust features of the proposed approach.     

Stability for uncertain nonlinear dissipative systems

This paper presents a technique for constructing a storage function for a broad class of nonlinear passive systems with mismatched uncertainties. And the problem for H_∞ disturbance attenuation with internal stability is studied by using robust adaptive output feedback controller which need not construct any state observer. The paper also shows how to explicitly design output feedback control that attenuates the disturbances effect on the output to an arbitrary degree of accuracy. Further, the results derived in this paper complement the previous work in the literature.     

Exponential H∞ synchronization for discrete‐time chaotic neural networks with time delays and stochastic perturbations via output feedback control

This paper investigates the problem of exponential H_∞ synchronization of discrete‐time chaotic neural networks with time delays and stochastic perturbations. First, by using the Lyapunov‐Krasovskii (Lyapunov) functional and output feedback controller, we establish the H_∞ performance of exponential synchronization in the mean square of master‐slave systems, which is analyzed using a matrix inequality approach. Second, the parameters of a desired output feedback controller can be achieved by solving a linear matrix inequality. Finally, 2 simulated examples are presented to show the effectiveness of the theoretical results.     

Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays

In this paper, we investigate the problems of robust delay-dependent ℒ₂ gain analysis and feedback control synthesis for a class of nominally-linear switched discrete-time systems with time-varying delays, bounded nonlinearities and real convex bounded parametric uncertainties in all system matrices under arbitrary switching sequences. We develop new criteria for such class of switched systems based on the constructive use of an appropriate switched Lyapunov-Krasovskii functional coupled with Finsler’s Lemma and a free-weighting parameter matrix. We establish an LMI characterization of delay-dependent conditions under which the nonlinear switched delay system is robustly asymptotically stable with an ℒ₂-gain smaller than a prescribed constant level. Switched feedback schemes, based on state measurements, output measurements or by using dynamic output feedback, are designed to guarantee that the corresponding switched closed-loop system enjoys the delay-dependent asymptotic stability with an ℒ₂ gain smaller than a prescribed constant level. All the developed results are expressed in terms of convex optimization over LMIs and tested on representative examples.     

Robust H ∞ control for singular systems with time-varying uncertainties

In this paper, we investigate the problem of robust H _∞ control for singular systems with polytopic time-varying parameter uncertainties. By introducing the notion of generalized quadratic H _∞ performance, the relationship between the existence of a robust H _∞ dynamic state feedback controller and that of a robust H _∞ static state feedback controller is given. By using matrix inequalities, the existence conditions of robust H _∞ static state feedback and dynamic output feedback controllers are derived. Moreover, the design methods for such controllers are provided in terms of the solutions of matrix inequalities. An example is also presented to demonstrate the validity of the proposed methods. __________ Translated from Journal of Northeastern University (Natural Science), 2004, 25(2): 110–113     

Observer-based robust adaptive variable universe fuzzy control for chaotic system

A novel observer-base output feedback variable universe adaptive fuzzy controller is investigated in this paper. The contraction and expansion factor of variable universe fuzzy controller is on-line tuned and the accuracy of the system is improved. With the state-observer, a novel type of adaptive output feedback control is realized. A supervisory controller is used to force the states to be within the constraint sets. In order to attenuate the effect of both external disturbance and variable parameters on the tracking error and guarantee the states to be within the constraint sets, a robust controller is appended to the variable universe fuzzy controller. Thus, the robustness of system is improved. By Lyapunov method, the observer-controller system is shown to be stable. The overall adaptive control algorithm can guarantee the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. In the paper, we apply the proposed control algorithms to control the Duffing chaotic system and Chua’s chaotic circuit. Simulation results confirm that the control algorithm is feasible for practical application.     

Toward unified analysis and controller synthesis for a class of hybrid systems

This work defines a new class of hybrid systems called state-based switched (SBS) systems that have numerous important engineering applications. The characterizing feature of these systems is that the discrete-event dynamics are associated with the continuous-time state making a specific function be equal to zero. The choice of this function is application specific and for the closed-loop SBS systems defined in this paper it is related to the execution of a desired set of tasks from a pre-specified mission plan. For this broad class of SBS systems, the paper presents a unified analysis and controller synthesis methodology based on Lyapunov theory. Depending on the details of the mission plan, the closed-loop hybrid system will be divided into two subclasses: sequential and non-sequential. The controller design procedure for both subclasses consists of the same two steps: finding a control law and finding a stabilizing switching rule. For static state and output feedback of sequential hybrid systems, the paper proposes a new hybrid sequential sliding-mode controller. It is proven that the control mission can be accomplished for sequential hybrid systems under static state and output feedback using this new controller. A similar framework is investigated for the more complex class of nonsequential hybrid systems and a systematic procedure for designing the switching rule is presented for some specific instances of these systems.     

Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system

This paper presents some simple feedback control laws to study global stabilization and global synchronization for a special chaotic system described in the generalized Lorenz canonical form (GLCF) when τ = −1 (which, for convenience, we call Shimizu–Morioka system, or simply SM system). For an arbitrarily given equilibrium point, a simple feedback controller is designed to globally, exponentially stabilize the system, and reach globally exponent synchronization for two such systems. Based on the system’s coefficients and the structure of the system, simple feedback control laws and corresponding Lyapunov functions are constructed. Because all conditions are obtained explicitly in terms of algebraic expressions, they are easy to be implemented and applied to real problems. Numerical simulation results are presented to verify the theoretical predictions.     

Output-feedback synchronization of chaotic systems based on sum-of-squares approach

This paper investigates the synchronization of chaotic systems using an output feedback polynomial controller. As only output system states are considered, it makes the controller design and system analysis more challenging compared to the full-state feedback control schemes. To study the system stability and synthesize the output feedback polynomial controller, Lyapunov stability theory is employed. Sufficient stability conditions are derived in terms of sum of squares (SOS) conditions to guarantee the system stability and aid the controller synthesis. A genetic algorithm-based SOS technique is proposed to find the solution to the SOS conditions and the parameter values of the output feedback polynomial controller. A simulation example is employed to illustrate the effectiveness of the proposed approach.     

基于快速输出采样反馈技术的无抖振离散滑模控制

针对一类单输入单输出的离散时间系统,提出了一种基于快速输出采样反馈技术(FOS)的无抖振滑模控制器.该控制策略避免了在控制器中采用切换模式,从而消除了切换面附近的抖振.理论分析和仿真结果表明该方法不仅能保证闭环系统的稳定性,而且能提高系统的稳态精度.     

Decentralized Reliable Control of Interconnected Systems with Time-Varying Delays

In this paper, we study the problem of designing decentralized reliable feedback control methods under a class of control failures for a class of linear interconnected continuous-time systems having internal subsystem time-delays and additional time-delay couplings. These failures are described by a model that takes into consideration possible outages or partial failures in every single actuator of each decentralized controller. The decentralized control design is performed through two steps. First, a decentralized stabilizing reliable feedback control set is derived at the subsystem level through the construction of appropriate Lyapunov-Krasovskii functional and, second, a feasible linear matrix inequalities procedure is then established for the effective construction of the control set under different feedback schemes. Two schemes are considered: the first is based on state measurement and the second utilizes static output feedback. The decentralized feedback gains in both schemes are determined by convex optimization over LMIs. We characterize decentralized linear matrix inequalities (LMIs)-based feasibility conditions such that every local closed-loop subsystem of the linear interconnected delay system is delay-dependent robustly asymptotically stable with a γ-level ℒ₂-gain. The developed results are tested on a representative example.     

Delay-dependent robust control for uncertain discrete-time singular systems with time-delays

The robust memoryless state feedback H_∞ control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback H_∞ control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given.     

Adaptive stabilization of high order nonholonomic systems with strong nonlinear drifts

This paper investigates the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts, including unmodeled dynamics, and dynamics modeled with unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterized system into a linear-like parameterized system. Then, by the use of input-state scaling technique and adding a power integrator backstepping approach, an adaptive state feedback controller is obtained. The adaptive control based switching strategy is proposed to eliminate the phenomenon of uncontrollability. Global asymptotic regulation of the closed-loop system states and the boundedness of other signals are guaranteed. Simulation examples demonstrate the effectiveness of the proposed scheme.     

Boundary output feedback stabilization for a class of coupled parabolic systems

In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L²norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme.