Guaranteed Cost Stabilization Research Articles

Adaptive guaranteed cost control for nonlinear systems with unknown parameters and time delays based on fully actuated system approaches

This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov–Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method.

Guaranteed cost stabilization control of discrete‐time switched systems

Guaranteed cost stabilization control of discrete‐time switched systems

Guaranteed Cost Anti-windup Stabilization of Discrete Delayed Cellular Neural Networks

This paper studies the problem of guaranteed cost anti-windup stabilization of discrete delayed cellular neural networks. Saturation degree function is initially presented and the convex hull theory is applied to handle the saturated terms of discrete delayed cellular neural networks. Accordingly, after choosing a common quadratic performance function, the paper designs a guaranteed cost stabilization controller in the absence of input saturation on the basis of Lyapunov–Krasovskii theorem and linear matrix inequality formulation. Then a static state feedback anti-windup compensation is derived, which guarantee a guaranteed cost and the estimation of the asymptotic stability region for the closed-loop system. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed design technique.

Guaranteed cost consensus protocol design for linear multi-agent systems with sampled-data information: An input delay approach

To investigate the energy consumption involved in a sampled-data consensus process, the problem of guaranteed cost consensus for sampled-data linear multi-agent systems is considered. By using an input delay approach, an equivalent system is constructed to convert the guaranteed cost consensus problem to a guaranteed cost stabilization problem. A sufficient condition for guaranteed cost consensus is given in terms of linear matrix inequalities (LMIs), based on a refined time-dependent Lyapunov functional analysis. Reduced-order protocol design methodologies are proposed, with further discussions on determining sub-optimal protocol gain and enlarging allowable sampling interval bound made as a complement. Simulation results illustrate the effectiveness of the theoretical results.

Membership-Function-Dependent Stability Analysis and Control Synthesis of Guaranteed Cost Fuzzy-Model-Based Control Systems

This paper focuses on the guaranteed cost stability analysis of fuzzy-model-based (FMB) control systems. Representing the nonlinear plant using a Takagi–Sugeno (T–S) fuzzy model, a fuzzy controller is employed to close the feedback loop. A weighted linear quadratic cost function is considered as the cost index to measure the performance of the closed-loop fuzzy system in terms of the system states, system outputs, and control signals. The stability of the FMB control system is investigated by the Lyapunov stability theory subject to the minimization of cost index for performance realization. A membership-function-dependent approach using the piecewise-linear membership functions is employed to include the information of membership functions into the stability analysis. Membership-function-dependent stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and feedback gains with the consideration of the system performance measured by the cost function. A simulation example is provided to illustrate the effectiveness and merits of the proposed approach.

Guaranteed Cost Stabilization of Cellular Neural Networks with Time‐Varying Delay

AbstractGuaranteed cost stabilization of cellular neural networks with time‐varying delay (DCNNs) is considered in this paper. Via applying the zoned discussion and maximum synthesis (ZDMS) in DCNNs and Lyapunov–Krasovskii functional, a less conservative feedback control law in the form of quadratic matrix inequality (QMI) is derived to achieve globally asymptotic stability of the system.

Guaranteed Cost Stabilization of Time-varying Delay Cellular Neural Networks via Riccati Inequality Approach

This letter deals with the guaranteed cost stabilization of time---varying delay cellular neural networks (DCNNs). Based on the Razumikhin theorem and via applying the zoned discussion and maximax synthesis method in DCNNs, the quadratic Riccati matrix inequality criterion for the guaranteed cost stabilization controller is designed to stabilize the given chaotic DCNNs. The minimization of the guaranteed cost of stabilization for the DCNNs is also given. Finally, numerical examples are given to show the effectiveness of proposed guaranteed cost stabilization control and its corresponding minimization problem.

Decentralized guaranteed cost stabilization of time-delay large-scale systems based on reduced-order observers

This paper addresses the problem of decentralized guaranteed cost stabilization (DGCS) of large-scale systems with delays both in the isolated subsystems and interconnections based on reduced-order observers. Sufficient conditions for the existence of delay-independent decentralized guaranteed cost controller (DGCC) are given in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMIs constraints is formulated to design the optimal DGCC which minimizes the guaranteed cost of the closed-loop large-scale systems. Finally, a simulation is performed to show the effectiveness of the proposed control scheme.

Optimal guaranteed cost stabilization of networked systems with bounded random packet losses

SUMMARYThis paper is concerned with the optimal guaranteed cost stabilizing controller design problem for a class of networked control systems (NCSs) with random packet losses. The number of consecutive packet losses is assumed to be upper bounded, and the closed‐loop NCS is described as a discrete‐time stochastic delay system with a time‐varying input delay and a stochastic parameter. A sufficient condition is derived for the closed‐loop NCS to be exponentially stable and achieve an optimal guaranteed cost performance level. The relationships among the exponential decay rate, the guaranteed cost performance level, and two parameters characterizing the random packet losses, namely, the packet loss probability and the maximal number of consecutive packet losses, are simultaneously established in the obtained condition. Furthermore, design procedures for the state feedback stabilizing controllers are also presented. Finally, an illustrative example is given to show the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.

Robust H2 guaranteed cost fuzzy control for uncertain discrete-time fuzzy systems via poly-quadratic Lyapunov functions

In this paper, new approaches regarding H2 guaranteed cost stability analysis and controller synthesis problems for a class of discrete-time fuzzy systems with uncertainties are investigated. The state-space Takagi-Sugeno fuzzy model with norm-bounded parameter uncertainties is adopted. Based on poly-quadratic Lyapunov functions, sufficient conditions for the existence of the robust H2 fuzzy controller can be obtained in terms of linear matrix inequalities (LMIs). Furthermore, a convex optimization problem with LMI constraints is formulated to design a suboptimal fuzzy controller which minimizes the upper bound on the quadratic cost function. The effectiveness of the proposed design approach is illustrated by two examples. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Delay-dependent guaranteed cost stabilization criterion for neutral delay-differential systems: matrix inequality approach

In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral delay-differential systems with a given quadratic cost function. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be easily solved by various efficient optimization algorithms.

On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach

In this paper, we consider a design problem of dynamic output feedback controller for guaranteed cost stabilization of discrete-delay systems with norm-bounded time-varying parameter uncertainties. A linear-quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov second method, several stability criteria for the existence of the controller are derived in terms of linear matrix inequalities (LMIs). The solutions of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.

On design of dynamic output feedback controller for GCS of large-scale systems with delays in interconnections: LMI optimization approach

This paper considers the dynamic output feedback controller design problem for decentralized guaranteed cost stabilization (GCS) of large-scale systems with time delays in subsystem interconnections. Based on the Lyapunov method, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function.

Decentralized dynamic output feedback controller design for guaranteed cost stabilization of large-scale discrete-delay systems

In this paper, we discuss how to solve dynamic output feedback controller design problem for decentralized guaranteed cost stabilization of large-scale discrete-delay system by convex optimization. Based on Lyapunov second method, an linear matrix inequality optimization problem is formulated to design the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. A numerical example is given to illustrate the proposed method.

Guaranteed cost stabilization of neutral differential systems with parametric uncertainty

In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function. The parametric uncertainties are real time-varying norm bounded and state delay is a constant. The problem is to design the 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 uncertainty and delay. Two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the Lyapunov method. The developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities.

Guaranteed-cost stabilization of non-linear stochastic systems

The control of uncertain non-linear discrete-time systems having stochastic cone-bounded non-linearities is considered. First, a quadratic performance bound and a guaranteed-cost optimal state feedback controller are derived. Then, an auxiliary system is introduced. It is shown that the quadratic optimal control for this auxiliary system is the same as the guaranteed-cost control for the original system, and, therefore, the existence of the infinite-horizon guaranteed-cost controller can be based on the stabilizability and observability properties of the auxiliary system. Finally, the stochastic boundedness of the controlled uncertain system is proved based on the properties of the auxiliary system. © 1998 John Wiley & Sons, Ltd.

Guaranteed cost stabilization for a class of uncertain discrete-time systems

A technique to design stabilizing state feedback controllers is presented for a class of linear discrete-time systems subject to possibly time-varying uncertainties that affect the system and input matrices. The controller design procedure is based on the solution of one of three modified algebraic Riccati matrix equations. Stability considerations rely on the second method of Lyapunov. To evaluate the system's performance degradation due to uncertainly, an upper bound (guaranteed cost) is derived for the cost of the controlled uncertain system with respect to a designer-chosen quadratic cost function. An example adapted from the literature is used to illustrate the method.