Robust decentralized adaptive control for uncertain large-scale delayed systems with input nonlinearities

The paper is concerned with the problem of robust stabilization for uncertain large-scale time-varying delayed systems with input nonlinearities. Based on the sliding mode control, a memoryless decentralized adaptive sliding mode controller (DASMC) is developed. The proposed controller ensures the occurrence of the sliding manifold of the composite system even subjected to input nonlinearity. It shows that the uncertain nonlinear large-scale system also possesses the property of insensitivity to uncertainties and disturbances as a linear system does. A numerical example is given to verify the validity of the developed memoryless DASMC.     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.     

Robust decentralized adaptive control for a class of uncertain neural networks with time-varying delays

This paper considers the robust control problem for a class of uncertain time-varying delayed neural networks, in which the activation function may be a discontinuous function. A robust decentralized adaptive sliding mode controller is proposed to guarantee the asymptotically stability of the system. The proposed controller, which does not dependent on the time delay, ensures the occurrence of the sliding manifold even when the system is undergoing parameter uncertainties and nonlinear input. Two numerical examples are given to show the effectiveness of the proposed controller.     

Non-fragile guaranteed cost control of uncertain large-scale systems with time-varying delays

The robust non-fragile guaranteed cost control problem is studied in this paper for a class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.     

Guaranteed cost control for uncertain large-scale systems with time-delays via delayed feedback

In this paper, we propose a design method for guaranteed cost controllers for uncertain large-scale systems with time-delays in subsystem interconnections using delayed feedback. Based on the Lyapunov method, an LMI (Linear Matrix Inequality) optimization problem is formulated to design the delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.     

Observer-based robust control for uncertain systems with time-varying delay

This paper is concerned with the function observer-based stabilizationfor time-varying delay systems with parameter uncertainties.The uncertain systems tackled in this paper involve uncertaintyin quadratic constrained form which includes the well-knownnorm-bounded time-varying uncertainty as a special case. Interms of Razumikhin-type stability theorem, we show that thefeasibility of several matrix inequalities guarantees the solvabilityof the addressed problem. Furthermore, we propose a parametricapproach for function observer-based robust stabilizer design.     

Decentralized stability for switched nonlinear large-scale systems with interval time-varying delays in interconnections

In this paper, the problem of decentralized stability of switched nonlinear large-scale systems with time-varying delays in interconnections is studied. The time delays are assumed to be any continuous functions belonging to a given interval. By constructing a set of new Lyapunov–Krasovskii functionals, which are mainly based on the information of the lower and upper delay bounds, a new delay-dependent sufficient condition for designing switching law of exponential stability is established in terms of linear matrix inequalities (LMIs). The developed method using new inequalities for lower bounding cross terms eliminate the need for overbounding and provide larger values of the admissible delay bound. Numerical examples are given to illustrate the effectiveness of the new theory.     

Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay

In this paper, we consider the problem of delay-dependent robust stability of a class of uncertain discrete-time systems with time-varying delay using Lyapunov functional approach. Two categories of time-varying uncertainties are considered for the robust stability analysis: viz., (i) nonlinear perturbations and (ii) norm-bounded uncertainties. In the proposed stability analysis, by exploiting a candidate Lyapunov functional, and using minimal number of slack matrix variables, less conservative stability criteria are developed in terms of linear matrix inequalities (LMIs) for computing the maximum allowable bound of the delay-range, within which, the uncertain system under consideration remains asymptotically stable in the sense of Lyapunov. The effectiveness of the proposed stability criteria is demonstrated using standard numerical examples.     

Decentralized robust control design for uncertain delay systems

We consider a class of large-scale uncertain delay systems. The uncertain parameter vector in the system is possibly fast time-varying. It may be nonlinear in the system dynamics. No statistical or fuzzy information of the uncertainty is known. Based on only the possible bound of the uncertain parameter, a decentralized linear robust control is proposed, which renders the system asymptotically stable.     

A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems

In this paper, a simple adaptive feedback control is proposed for full and reduced-order synchronization of time-varying and strictly uncertain chaotic systems. Our method uses only one feedback gain with parameter adaptation law and converges very fast even in the presence of noise. For full synchronization, a drive-response system consisting of two second-order identical parametrically excited oscillators achieve global synchronization; while for reduced-order synchronization, the dynamical evolution of a second-order parametrically driven oscillator is synchronized with the projection of a third-order time-varying chaotic system. The effectiveness of our approach is demonstrated using numerical simulations.     

An adaptive sliding mode control scheme for a class of chaotic systems with mismatched perturbations and input nonlinearities

This paper is concerned with the stabilization problem for a class of chaotic systems with mismatched perturbations and input nonlinearities. A novel sliding surface is specially designed so that when the system enters the sliding mode, the mismatched perturbations can be effectively overcome and achieve asymptotic stability. Then, an adaptive sliding mode controller (ASMC) is proposed to drive the controlled state trajectories into the designated sliding surface in finite time even subjected to input nonlinearities. Finally, the corresponding numerical simulations are demonstrated to verify the effectiveness of proposed method.     

An LMI approach to decentralized guaranteed cost control for a class of uncertain nonlinear large-scale delay systems

The guaranteed cost control problem via the decentralized robust control for nonlinear uncertain large-scale systems that have delay in both state and control input is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that the decentralized local state feedback controllers can be obtained by solving the LMI.     

Semi-global finite-time output feedback stabilization for a class of large-scale uncertain nonlinear systems

This paper addresses the problem of semi-global finite-time decentralized output feedback control for large-scale systems with both higher-order and lower-order terms. A new design scheme is developed by coupling the finite-time output feedback stabilization method with the homogeneous domination approach. Specifically, we first design a homogeneous observer and an output feedback control law for each nominal subsystem without the nonlinearities. Then, based on the homogeneous domination approach, we relax the linear growth condition to a polynomial one and construct decentralized controllers to render the nonlinear system semi-globally finite-time stable.     

Sliding mode variable structure control for parameter uncertain stochastic systems with time-varying delay

In this paper, the variable structure control problem for a class uncertain of stochastic system with time-varying delay is investigated. Firstly, a new concept of the subordinated reachability of the sliding motion is introduced to approach approximately the specified sliding surface. The variable structure control law is then proposed to ensure that the sliding motion is subordinated reachable. Furthermore, a sufficient condition for mean-square asymptotical stability of the sliding motion is given. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained results.     

Decentralized robust model reference adaptive control for interconnected time-delay systems

In this paper, the problem of decentralized robust model reference control for a class of interconnected time-delay systems is investigated. The interconnections with time-varying time delays considered are high order and the gains are not known. A class of decentralized adaptive feedback controllers are proposed, which can render the resulting closed-loop error system uniformly ultimately bounded stable. A numerical example is given to show the feasibility and effectiveness of the proposed design techniques.     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be (possibly fast) time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball can be made arbitrarily small by suitable choice of design parameters.     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.     

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

Email: chlien{at}mail.nkmu.edu.tw Received on August 10, 2006; Accepted on September 6, 2006 In this paper, delay-dependent guaranteed cost observer-basedcontrol for neutral systems with time-varying delays is considered.Control and observer gains will be given from the linear matrixinequality feasible solutions. Optimal guaranteed cost observer-basedcontrol which will minimize the guaranteed cost of the systemis provided.     

Algorithms for adaptive stochastic control for a class of linear systems

This paper is concerned with the control of linear, discrete-time, stochastic systems with unknown control gain parameters. Two suboptimal adaptive control schemes are derived: One is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single-input, third-order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.