Guaranteed Cost State Feedback Controller Research Articles

Non‐fragile reliable guaranteed cost control and L2‐gain analysis for saturated switched nonlinear systems

AbstractFor the nonlinear continuous‐time saturated switched system, this article investigates the problem of non‐fragile reliable guaranteed cost control of the system. Due to the simultaneous occurrence of controller perturbation, actuator saturation and actuator failure, when designing the cost function, this article considers three scenarios affecting the system performance, controller perturbation, actuator saturation and actuator failure, simultaneously in the cost function, which has not been investigated in the existing literature. For nonlinear switched systems, we derive some sufficient conditions to satisfy simultaneously the stabilization of non‐fragile reliable guaranteed cost control and the performance index. In order to ensure the exponential stabilization of the nonlinear switched systems and minimize the upper bound of cost function, a switching law and the non‐fragile reliable guaranteed cost state feedback controllers are designed by using the minimum dwell‐time method. Furthermore, by solving optimization problems with linear matrix inequality constraints, the minimum upper bound of the cost function and the performance of the system are determined. At the end of the article, we give a numerical example to verify the effectiveness of the proposed approach.

Finite-Time Guaranteed Cost Control for Markovian Jump Systems with Time-Varying Delays

In this paper, the finite-time guaranteed cost control (FTGCC) problem is addressed for Itô Markovian jump systems with time-varying delays. The aim of this paper is to design a state feedback guaranteed cost controller, such that not only the resulting closed-loop systems are finite-time stable, but also cost performance has a minimum upper bound. First, new sufficient conditions for the existence of guaranteed cost controllers are presented via the linear matrix inequality (LMI) approach. Then, based on the established conditions, the desired controllers are designed and the upper bound of cost performance is provided. In the end, an example is employed to show the validity of the obtained results.

Guaranteed cost controller for discrete time-delayed systems with actuator saturation

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

A guaranteed cost strategy for speed-limit control of vehicles based on map information

This paper proposes a guaranteed cost strategy for longitudinal control of vehicles mainly considering speed-limit control based on map information. Firstly, a state-space model is developed to calculate the desired acceleration for the speed-limit control. Secondly, based on the formulated state-space model, a state-feedback guaranteed cost strategy is developed for the speed-limit control with system uncertainties considered. The stability of the proposed state-feedback guaranteed cost control system is discussed according to Lyapunov stability theory by means of linear matrix inequality approach and Schur complement. Moreover, with the proposed control law, it is proved that the defined cost function has an upper bound. Thirdly, to reduce potential unnecessary acceleration or deceleration caused by disturbances, an event-triggered filter is designed. Finally, to evaluate the performance of the proposed guaranteed cost controller, a switching PID controller, and a guaranteed cost controller without the proposed event-triggered filter are developed for comparisons. The effectiveness and the advantages of the proposed guaranteed cost strategy are proved by simulations where model uncertainties, disturbances, and the latency of the actuator are considered.

Robust Mixed H2/H∞ State Feedback Controller Development for Uncertain Automobile Suspensions with Input Delay

In order to achieve better dynamics performances of a class of automobile active suspensions with the model uncertainties and input delays, this paper proposes a generalized robust linear H2/H∞ state feedback control approach. First, the mathematical model of a half-automobile active suspension is established. In this model, the H∞ norm of body acceleration is determined as the performance index of the designed controller, and the hard constraints of suspension dynamic deflection, tire dynamic load and actuator saturation are selected as the generalized H2 performance output index of the designed controller to satisfy the suspension safety requirements. Second, a generalized H2/H∞ guaranteed cost state-feedback controller is developed in terms of Lyapunov stability theory. In addition, the Cone Complementarity Linearization (CCL) algorithm is employed to convert the generalized H2/H∞ output-feedback control problem into a finite convex optimization problem (COP) in a linear matrix inequality framework. Finally, a numerical simulation case of this half-automobile active suspension is presented to illustrate the effectiveness of the proposed controller in frequency-domain and time-domain.

Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks

Abstract Based on observer framework, this paper examines the reliable sampled-data actuator fault controller for stochastic neural networks of neutral-type along with Markovian jump parameters and time-varying delays. In particular, the main intention of this work is to obtain the reliable state feedback guaranteed cost controller with satisfactory mixed H∞ and passivity performance index. Particularly, a more generalized randomly occurring fault model is incorporated in the given quadratic cost function, where the faults of each and every actuator are represented by stochastic variables with some satisfactory probability conditions. By applying a proper Lyapunov-Krasovskii-functional along with neuron activation functions, a newly established conditions are captured to assure the stochastic stability of the considered model. Further an adequate performance index can be compared by solving the developed linear matrix inequalities. Furthermore, the effectiveness and the impact of the cost function based control scheme is tested through simulation results.

Mixed H2/H∞ guaranteed cost control for high speed elevator active guide shoe with parametric uncertainties

Aiming at the phenomenon that the elevator car system generates horizontal vibration due to the unevenness of the guide rail and the guide shoe modeling uncertainty caused by friction, wear and spring aging between the rolling guide shoe and the guide rail, a mixed H2/H∞ optimal guaranteed cost state feedback control strategy is proposed. Firstly, as the high-speed elevator car system always exist the phenomenon of stiffness and damping uncertainty in the guide shoe, the LFT method is adopted to construct the state space equation of the car system with parameter uncertainty. Secondly, considering the performance indexes of horizontal acceleration at the center of the car floor and the guide shoe vibration displacement system, an optimal guaranteed performance state feedback controller is designed based on the linear convex optimization method, which to minimize H2 performance index and achieve the specified H∞ performance level. Thirdly, the free matrix is introduced to reduce the conservatism of the controller. Finally, by comparing the simulation results with other control methods under the same conditions, it is verified that the control strategy can make the car system have better vibration suppression ability, and can significantly improve the ride comfort of the elevator.

Reliable Guaranteed Cost Control of Uncertain Systems with Nonlinear Perturbations

Network control system (NCS) is a distributed real-time feedback control system with the continuous development of network technology. It is generally composed of network, controller, actuator and sensor. It has brought great convenience to people in many fields, but it also has many problems, which makes the research of control system more complicated. Recently, there have been some efforts to tackle the reliable guaranteed cost controller design problem, and some good results have also been obtained for the continuous-time and for the discrete-time. However, there have been few results in the literature of an investigation for the reliable guaranteed cost controller design of nonlinear uncertain systems with time-varying state delay and actuator failure. This paper concerns the reliable guaranteed cost control problem of uncertain systems with time-varying state delay and nonlinear perturbations for a given quadratic cost function. The problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Firstly, the existence condition of reliable guaranteed cost control law is given by constructing Lyapunov stability function and using linear matrix inequality (LMI). Secondly, the design method of the optimal reliable guaranteed cost controller is given by solving the convex optimization problem with LMI constraints, which minimizes the upper bound of guaranteed cost for closed-loop systems. In the end, the numerical simulation result illustrates the effectiveness of the proposed method.

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.

Nonlinear robust state feedback control system design for nonlinear uncertain systems

SummaryThis paper presents a systematic approach to the design of a nonlinear robust dynamic state feedback controller for nonlinear uncertain systems using copies of the plant nonlinearities. The technique is based on the use of integral quadratic constraints and minimax linear quadratic regulator control, and uses a structured uncertainty representation. The approach combines a linear state feedback guaranteed cost controller and copies of the plant nonlinearities to form a robust nonlinear controller with a novel control architecture. A nonlinear state feedback controller is designed for a synchronous machine using the proposed method. The design provides improved stability and transient response in the presence of uncertainty and nonlinearity in the system and also provides a guaranteed bound on the cost function. An automatic voltage regulator to track reference terminal voltage is also provided by a state feedback equivalent robust nonlinear proportional integral controller. Copyright © 2016 John Wiley & Sons, Ltd.

State Feedback Guaranteed Cost Controller for Nonlinear Time-Varying Delay Systems

This paper considers the problem of designing state feedback guaranteed cost controllers for a class of nonlinear systems with time-varying delay. The time delay is a continuous function belonging to a given interval and not required to be differentiable. By applying Lyapunov function method and linear matrix inequality (LMI) technique, new delay-dependent sufficient conditions for designing the state feedback guaranteed cost controller are derived. The method is also extended to handle system uncertainties in a straightforward way. A numerical example is given to illustrate the design procedure.

A BMI approach to guaranteed cost control of discrete-time uncertain system with both state and input delays

SUMMARY In this study, the guaranteed cost control of discrete time uncertain system with both state and input delays is considered. Sufficient conditions for the existence of a memoryless state feedback guaranteed cost control law are given in the bilinear matrix inequality form, which needs much less auxiliary matrix variables and storage space. Furthermore, the design of guaranteed cost controller is reformulated as an optimization problem with a linear objective function, bilinear, and linear matrix inequalities constraints. A nonlinear semi-definite optimization solver—PENLAB is used as a solution technique. A numerical example is given to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.

Guaranteed cost control of linear uncertain discrete-time impulsive systems

The guaranteed cost control problem for a class of linear uncertain discrete-time impulsive systems is considered. The parametric uncertainties are assumed to be time-varying and norm-bounded. The problem is to design a robust state feedback controller such that the resulting closed-loop system is robustly exponentially stable, and the closed-loop value of a specified quadratic cost function is not more than a certain upper bound for all admissible uncertainties and for all admissible impulse time sequences. A sufficient condition for the existence of guaranteed cost state feedback controllers is derived via a time-varying Lyapunov function approach. This condition is expressed in terms of linear matrix inequalities. Furthermore, the problem of selecting a suboptimal guaranteed cost controller is formulated as a convex optimization problem. An example is provided to demonstrate the effectiveness of the proposed results.

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.

Sevorel Conclusions of Guaranteed Cost for Uncertain Discrete Singular System

In this papar we research the guaranteed cost control for a class of norm bounded uncertain discrete singular systems was considered in this paper. The objective is to design state-feedback controllers such that the closed-loop systems is regular, causal, stable and the corresponding cost function have a certain upper bound minimized for all admissible uncertainties. Two sufficient conditions for the existence of state-feedback guaranteed cost controllers are obtained in terms of algebraic Riccati equation and linear matrix inequalities, respectively. And the numerical examples show the validity of our inclusion.

Robust Quantized Guaranteed Cost Control

In this paper, the robust state feedback guaranteed cost control problem for discrete-time systems with signal quantization is studied. A dynamic quantization control strategy is proposed with updating the quantizer’s parameter such that the system is asymptotically stable and the performance index is with a upper bound.

Guaranteed Cost Control for a Class of Switched Descriptor Systems

This paper deals with the problem of guaranteed cost control for a class of switched descriptor systems. State feedback guaranteed cost controller is adopted to make the resulting closed-loop system stable and cost function have an upper bound. Based on single Lyapunov function and convex combination technique, a switching law is designed and a sufficient condition of the existence of such controller is presented. By means of variables substitution and linear matrix inequality, the condition can be turned to LMI. The advantage of method presented in this paper is illustrated by an example.

NON-FRAGILE GUARANTEED COST CONTROL OF T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH LOCAL BILINEAR MODELS

This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bi- linear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.

Robust guaranteed cost control for singular Markovian jump systems with time-varying delay

This paper is concerned with the guaranteed cost control for continuous-time singular Markovian jump systems with time-varying delay. Without using the free weighting matrices method, a delay-range-dependent condition is derived in terms of strict linear matrix inequality (LMI), which guarantees that the singular system is regular, impulse free and mean-square exponentially stable with an H∞ performance. Based on this, the existence condition of the guaranteed cost state feedback controller is proposed. A numerical example is given to illustrate the effectiveness and less conservatism of the proposed design method.

An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

This paper deals with the problem of optimal guaranteed cost control via memory state feedback for a class of two-dimensional (2-D) discrete shift-delayed systems in Fornasini–Marchesini (FM) second model with norm-bounded uncertainties. A new criterion for the existence of memory state feedback guaranteed cost controllers is derived, based on the linear matrix inequality (LMI) approach. Moreover, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers which minimize the upper bound of the closed-loop cost function. Illustrative examples demonstrate the merit of the proposed method in the aspect of conservativeness over a previously reported result.