Non-fragile Guaranteed Cost Control Research Articles

Optimal non-fragile control design for linear systems under amplitude and rate saturation: An LMI approach

In this paper, the problem of optimal non-fragile guaranteed cost control design for linear systems subject to input amplitude and rate saturation is addressed. Sufficient conditions for the existence of a non-fragile state feedback are obtained by Lyapunov stability theory. The designed controller not only guarantees the asymptotic stability of the overall closed-loop system with a minimum upper bound of a cost function, but also ensures the actuator saturation avoidance. This problem is transformed into an optimization problem with linear matrix inequality (LMI) constraints. The proposed method guarantees that the control input amplitude and rate remain within the allowable ranges and do not exceed the considered bounds. The simulation results illustrate the effectiveness and superiority of the proposed theoretical results.

Non-fragile guaranteed cost control of microbial fuel cells

A microbial fuel cell (MFC), which is a new type of energy source, utilises electrogenic bacteria in sewage or soil to convert chemical energy into electrical energy. MFCs typically require an external controller to provide a stable output voltage to the external load. This study develops a non-fragile guaranteed cost (NFGC) controller to suppress the interference of the controller of an MFC and ensure that the quadratic cost function of the system satisfies certain performance indexes. First, for the convenience of controller design, a Takagi–Sugeno fuzzy model is established to approximate a single-chamber single-population MFC model. Subsequently, the linear matrix inequality method is used to design the NFGC controller. This control scheme can reduce the influence of controller disturbances on the system and ensure asymptotic stability of the closed-loop system under the specified upper bound of the provided cost function. The simulation results demonstrate that the developed control method has a shorter adjustment time and smaller steady-state error than traditional control methods such as sliding mode control (SMC), backstepping control, and fuzzy SMC

Non-fragile guaranteed cost control for networked nonlinear Markov jump systems under multiple cyber-attacks

This paper is concerned with the problem of non-fragile guaranteed cost control (GCC) for networked nonlinear Markov jump systems subject to multiple cyber-attacks, which are characterized by Takagi–Sugeno (T–S) fuzzy model with time-varying delay. Specifically, a variety of cyber-attacks, including deception attacks and Denial-of-Service (DoS) attacks, are considered, which occur in the forward and feedback communication links, respectively. To achieve stochastic stability under guaranteed cost function (GCF), the paper proposes a Lyapunov–Krasovskii (L–K) function approach. The approach derives sufficient conditions for stochastic stability, and obtains non-fragile controller gains and the uniform upper bound of the GCF using linear matrix inequalities (LMIs) technique. Finally, the effectiveness of the proposed algorithm is evaluated by simulation experiment.

Non-fragile guaranteed cost control of nonlinear switched systems with actuator saturation

This paper considers a non-fragile guaranteed cost control problem for a class of nonlinear switched systems with actuator saturation. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization and the performance index of guaranteed cost control. To ensure the asymptotic stability of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and non-fragile state feedback controllers are designed using the multiple Lyapunov functions method. On this basis, an optimization problem is solved by adopting linear matrix inequality (LMI) constraints, and the minimum upper bound of cost function is determined. At the end of the paper, a numerical example is given to prove the effectiveness of the proposed method.

Nonfragile Guaranteed Cost Control of Discrete-Time Takagi–Sugeno Fuzzy Systems with Multiple Quantizations

Nonfragile Guaranteed Cost Control of Discrete-Time Takagi–Sugeno Fuzzy Systems with Multiple Quantizations

Asynchronous Nonfragile Guaranteed Cost Control for Impulsive Switched Fuzzy Systems With Quantizations and Its Applications

This article investigates the nonfragile guaranteed cost (GC) control problem of discrete-time impulsive switched Takagi–Sugeno (T–S) fuzzy systems with input quantization and asynchronous switching. The model-dependent dynamic quantizers are applied to obtain the quantized input signal. To deeply study the GC performance analysis and GC control problems in the presence of quantization, asynchronous switching, and impulses, a novel piecewise cost function containing the quantized input instead of normal input is applied in this article. By using the mode-dependent average dwell time approach and introducing a class of Lyapunov-like functions allowing to increase during the asynchronous period, new sufficient conditions are established to guarantee the asymptotical stability with the GC performance index for the impulsive switched T–S fuzzy systems with quantized control input and asynchronous switching. Then, new design conditions about the nonfragile GC controllers and dynamic quantizers of impulsive switched T–S fuzzy systems are obtained in the form of linear matrix inequalities. Finally, a numerical example and a practical example are provided.

Robust Nonfragile Guaranteed Cost Control for Uncertain Fuzzy Markov Jump Systems with Time-Varying Delays

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain discrete-time Takagi–Sugeno fuzzy systems with Markov jumping parameters and time-varying delay. A nonfragile fuzzy-basis-dependent and mode-dependent controller is designed and a sufficient condition is developed to ensure that the resulting closed-loop system is robust asymptotically stable in mean square with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and minimum upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Compared with the existing literature, this paper enormously reduces the conservatism of the result obtained. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.

Synthesis of Formation Control Systems for Multi-Agent Systems under Control Gain Perturbations

This paper proposed a linear matrix inequality (LMI)-based design method of non-fragile guaranteed cost controllers for multi-agent systems (MASs) with leader-follower structures. In the guaranteed cost control approach, the resultant controller guarantees an upper bound on the given cost function together with asymptotical stability for the closed-loop system. The proposed non-fragile guaranteed cost control system can achieve consensus for MASs despite control gain perturbations. The goal is to develop an LMI-based sufficient condition for the existence of the proposed non-fragile guaranteed cost controller. Moreover, a design problem of an optimal non-fragile guaranteed cost controller showe that minimizing an upper bound on the given quadratic cost function can be reduced to constrain a convex optimization problem. Finally, numerical examples were given to illustrate the effectiveness of the proposed non-fragile controller for MASs.

Robust nonfragile guaranteed cost control for uncertain T-S fuzzy Markov jump systems with mode-dependent average dwell time and input constraint

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain Takagi-Sugeno fuzzy systems with Markov jump parameters, time-varying delay and input constraint. A nonfragile mode-dependent fuzzy controller with mode-dependent average dwell time (MDADT) is designed with input constraint. A sufficient condition is developed to ensure that the resulting closed-loop system is robust almost surely asymptotically stable with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.

Non-Fragile Control for Variable Sampling Period Network Control System with Actuator Failure

The guaranteed cost control problem is studied in this paper for a class of nonlinear discrete-time systems with both time-varying parametric uncertainty and actuator failures. At present, the researches on related fields of networked control systems are relatively mature, and many achievements have been made. But at the same time, most of the researches are focused on linear networked control systems, and the research on nonlinear networked control systems is relatively less. The goal is to design a non-fragile state feedback control law so that the closed-loop system is asymptotically stable and the closed-loop cost function value is no more than a specified upper bound for all admissible uncertainties. Firstly, the system model is established by using the method of variable sampling period. Secondly, the sufficient conditions for the asymptotic stability of the closed-loop system are given by using Lyapunov stability theory. Thirdly, based on the above researches, a non-fragile state feedback controller is designed by using linear matrix inequality (LMI). In the end, through the study of this paper, the cost function of the system under the designed non-fragile guaranteed cost controller does not exceed the given upper bound. This paper considers the actuator failure, and gives the design method of the non-fragile guaranteed cost controller of the nonlinear network control system, and makes a contribution to the field of network control system.

Comments on ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’

This paper points out some technical errors in a recent paper that appeared in Transactions of the Institute of Measurement and Control entitled ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’ by Akshata Tandon and Amit Dhawan ( http://dx.doi.org/10.1177/0142331216667476 ). We reveal that the upper bound of the closed-loop cost function provided by their Lemma 4 is erroneous. Some critical issues associated with the system initial conditions assumed in their paper are highlighted. The closed-loop cost bound claimed by their Theorem 1 is found to be incorrect. The optimization problem formulated in their Theorem 2 for the selection of an optimal guaranteed cost controller is erroneous. Finally, the corrections over their results are made available.

Fuzzy-Model-Based Nonfragile Guaranteed Cost Control of Nonlinear Markov Jump Systems

This paper investigates the problem of nonfragile guaranteed cost control for discrete-time Takagi–Sugeno fuzzy Markov jump systems with time-varying delays. With the help of the parallel distributed compensation, a nonfragile fuzzy controller is designed. Then via Lyapunov–Krasovskii functional approach, sufficient conditions are obtained ensuring that the resulting closed-loop system is asymptotically stable with an upper bound of the guaranteed cost index. The optimal upper bound of the guaranteed cost index and the controller gain can be achieved via the optimization technique. Finally, an example is presented to show the effectiveness of the proposed new design techniques.

Robust non-fragile guaranteed cost control for singular Markovian jump time-delay systems

This paper deals with the problem of robust non-fragile guaranteed cost control for a class of uncertain singular Markovian jump systems with time-varying delays. The time-varying and norm-bounded parameter uncertainties exist in both the state matrix and the derivative matrix. A non-fragile proportional-derivative state feedback controller is designed to guarantee the closed-loop singular Markovian jump system is normal and robustly stochastically stable. By proposing an optimization strategy in the framework of linear matrix inequalities, the upper bound of the cost function can be minimized. Finally, a numerical example is given to demonstrate the effectiveness of the results.

A Novel SHLNN Based Robust Control and Tracking Method for Hypersonic Vehicle under Parameter Uncertainty

Hypersonic vehicle is a typical parameter uncertain system with significant characteristics of strong coupling, nonlinearity, and external disturbance. In this paper, a combined system modeling approach is proposed to approximate the actual vehicle system. The state feedback control strategy is adopted based on the robust guaranteed cost control (RGCC) theory, where the Lyapunov function is applied to get control law for nonlinear system and the problem is transformed into a feasible solution by linear matrix inequalities (LMI) method. In addition, a nonfragile guaranteed cost controller solved by LMI optimization approach is employed to the linear error system, where a single hidden layer neural network (SHLNN) is employed as an additive gain compensator to reduce excessive performance caused by perturbations and uncertainties. Simulation results show the stability and well tracking performance for the proposed strategy in controlling the vehicle system.

Non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems

ABSTRACTThis paper is concerned with the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model with norm-bounded uncertainties. Our attention is focused on the design of non-fragile state feedback controllers such that the resulting closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is established under the linear matrix inequality framework. Moreover, a convex optimisation problem is proposed to select a non-fragile robust optimal guaranteed cost controller stabilising the 2-D discrete state-delayed system as well as achieving the least guaranteed cost for the resulting closed-loop system. The proposed method is compared with the previously reported criterion. Finally, illustrative examples are given to show the potential of the proposed technique.

A generalized multiple Lyapunov functions method based non-fragile guaranteed cost control for uncertain switched fuzzy systems

This paper is concerned with a non-fragile guaranteed cost control problem for a class of uncertain switched fuzzy systems which are described by switched Takagi–Sugeno (T–S) fuzzy models. By employing the generalized multiple Lyapunov functions method, we present a sufficient condition to guarantee the closed-loop system asymptotically stable and possess an upper bound of the non-fragile guaranteed cost function. Meanwhile, a non-fragile state feedback control law and a switching law are designed. Moreover, an optimization problem, in which the minimal non-fragile guaranteed cost can be obtained, is solved. Finally, a simulation example is given to verify the feasibility and effectiveness of the proposed method.

Nonfragile Guaranteed Cost Control of Discrete-Time Fuzzy Bilinear System With Time-Delay

This paper focuses on the problem of nonfragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS) with time-delay in both states and inputs. Based on the parallel distributed compensation approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations.

An LMI approach to non-fragile robust optimal guaranteed cost control of 2D discrete uncertain systems

This paper addresses the problem of non-fragile robust optimal guaranteed cost control for a class of two-dimensional discrete systems described by the general model with norm-bounded uncertainties. Based on Lyapunov method, a new linear matrix inequality (LMI)-based criterion for the existence of non-fragile state feedback controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select a non-fragile robust optimal guaranteed cost controller, which minimizes the upper bound of the closed-loop cost function. The merit of the proposed criterion in aspect of conservativeness over a recently reported criterion is demonstrated with the help of illustrative examples.

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.

Non-Fragile Guaranteed Cost Control for a Class of Uncertain Time-Delay Switched Singular Systems

The problem of robustly non-fragile guaranteed cost control for a class of uncertain time-delay switched singular systems under arbitrary switching laws is considered. By means of matrix equivalent transformation and the relationship between the norm and the matrix, based on linear matrix inequality tools, a sufficient condition on the existence of non-fragile guaranteed cost state feedback controllers is derived, which ensures that uncertain time-delay switched singular system is admissible, and a corresponding cost index can be guaranteed. The design problem of the non-fragile guaranteed cost controller can be turned into the feasibility problem of a set of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of proposed method.