Dynamic output feedback H ∞ control for networked control systems with quantisation and random communication delays

This article is concerned with the dynamic output feedback H _∞ control problem for networked control systems with quantisation and random communication delays, where the random communication delays from the sensor to the controller and from the controller to the actuator are considered simultaneously. A novel quantised random delay model is proposed, and by using this model, the relationship of the quantisations, delays and the system performance is studied. The quantiser considered here is dynamic and composed of an adjustable zoom parameter and a static quantiser. With the condition on the quantisation range and the error bound satisfied, a quantised H _∞ control strategy is derived such that the closed-loop system is exponentially mean-square stable and with a prescribed H _∞ performance bound. An example is presented to illustrate the effectiveness of the proposed method.     

H∞Fuzzy State‐Feedback Control Plus State‐Derivative‐Feedback Control Synthesis for Photovoltaic Systems

This paper addresses the problem of designing an H_∞fuzzy state‐ feedback (SF) plus state‐derivative‐feedback (SDF) control system for photovoltaic (PV) systems based on a linear matrix inequality (LMI) approach. The TS fuzzy controller is designed on the basis of the Takagi‐Sugeno (TS) fuzzy model. The sufficient condition is found such that the system with the fuzzy controller is asymptotically stable and an H_∞performance is satisfied. First, a dc/dc buck converter is considered to regulate the power output by controlling state and state‐derivative variables of PV systems. The dynamic model of PV systems is approximated by the TS fuzzy model in the form of nonlinear systems. Then, based on a well‐known Lyapunov functional approach, the synthetic is formulated of an H_∞fuzzy SF plus SDF control law, which guarantees the L₂‐gain from an exogenous input to the regulated output to be less than or equal to some prescribed value. Finally, to show effectiveness, the simulation of the PV systems with the proposed control is assessed by the computer programme. The proposed control method shows good performance for power output and high stability for the PV system.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Robust H∞ control for uncertain discrete-time systems with time-varying delays via exponential output feedback controllers

This paper considers the problem of robust H_∞ control for uncertain discrete systems with time-varying delays. The system under consideration is subject to time-varying norm-bounded parameter uncertainties in both the state and measured output matrices. Attention is focused on the design of a full-order exponential stable dynamic output feedback controller which guarantees the exponential stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. In terms of a linear matrix inequality (LMI), a sufficient condition for the solvability of this problem is presented, which is dependent on the size of the delay. When this LMI is feasible, the explicit expression of the desired output feedback controller is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.     

output feedback control for uncertain stochastic systems with time-varying delays

This paper deals with the problem of H_∞ output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed H_∞ performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given.     

The H∞ control problem using static output feedback

In this paper we shall consider the H_∞ control problem using static output feedback. The approach uses some recent results from linear algebra. The main result shows that the H_∞ control problem is solvable by a static output feedback controller if and only if there exists a positive definite matrix satisfying two certain quadratic matrix inequalities. A parametrization of all static output feedback H_∞ controllers is given.     

H∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.     

Simultaneous robust normalization and delay‐dependent robust H∞ stabilization for singular time‐delay systems with uncertainties in the derivative matrices

This paper investigates the problem of simultaneous robust normalization and delay‐dependent H_∞ control for a class of singular time‐delay systems with uncertainties. Not only the state and input matrices but also the derivative matrices of the considered systems are assumed to have uncertainties. New sufficient conditions for the existence of a proportional plus derivative state feedback H_∞ controller are derived as LMIs such that the closed‐loop singular system is normal, stable, and guarantee a specific level of performance. Specially, a static state feedback H_∞ controller alone or a state‐derivative feedback H_∞ controller alone can unite to be dealt with by applying our proposed method. Two simulation examples are provided to demonstrate the effectiveness of the proposed approach in this paper. Copyright © 2014 John Wiley & Sons, Ltd.     

A Simultaneous Mixed LQR/H∞ Control Approach to the Design of Reliable Active Suspension Controllers

This paper is concerned with the synthesis of reliable controllers for quarter‐car active suspension systems. By a simultaneous mixed LQR/H_∞ control approach, a static output feedback controller is derived for guaranteeing good suspension performance under possible sensor fault or suspension component breakdown. The considered simultaneous mixed LQR/H_∞ control problem is a nonconvex optimization problem; therefore, the linear matrix inequality approach is not applicable. Based on the barrier method, we solve an auxiliary minimization problem to get an approximate solution for the simultaneous mixed LQR/H_∞ control problem. Necessary conditions for the local optimum of the auxiliary minimization problem are derived. Moreover, a three‐stage solution algorithm is developed for solving the auxiliary minimization problem. The simulation shows that the obtained static output feedback suspension controllers can improve suspension performance in nominal mode and all considered failure modes.     

Novel Optimal Design Approach for Output‐Feedback H∞ Control of Vehicle Active Seat‐Suspension System

In this paper, the output‐feedback control problem of a vehicle active seat‐suspension system is investigated. A novel optimal design approach for an output‐feedback H_∞ controller is proposed. The main objective of the controller is to minimize the seat vertical acceleration to improve vehicle ride comfort. First, the human body and the seat are considered in the modeling of a vehicle active suspension system, which makes the model more precise. Other constraints, such as tire deflection, suspension deflection and actuator saturation, are also considered. Then the output‐feedback control strategy is adopted since some state variables, such as body acceleration and body deflection, are unavailable. A concise and effective approach for an output‐feedback H_∞ optimal control is presented. The desired controller is obtained by solving the corresponding linear matrix inequalities (LMIs) and by the calculation of equations proposed in this paper. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed controller design approach.     

H∞ control of networked control systems based on Markov jump unified model

This paper focuses on a new H_∞ controller design issue for networked control systems with external disturbance as well as random time delays and packet dropouts in forward and feedback channels, which are modeled by multiple Markov chains in a unified style. The output feedback controller is designed to stabilize the networked control system and also achieves the prescribed H_∞ disturbance attenuation level. The addressed controller design problem is transformed into a nonlinear minimization problem with LMI constraints. An illustrative example is provided to show the effectiveness of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Delay-dependent H ∞ controller design for linear neutral systems with discrete and distributed delays

This article considers the delay-dependent H _∞ control problem for linear neutral systems with both discrete and distributed delays. The problem we address is to design a state feedback controller such that the resulting closed-loop system is asymptotically stable and satisfies a prescribed H _∞ performance level. First, a delay-dependent sufficient condition for the solvability of the problem is obtained in terms of matrix inequalities. Then, by using the cone complementarity linearization approach, an H _∞ controller is developed based on the solvability condition. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Dynamic output feedback control synthesis for stochastic time-delay systems

This article deals with the dynamic output feedback control synthesis problem for Itô-type stochastic time-delay systems. Our aim is to design a full order dynamic output feedback controller to achieve the desired control objectives. We will formulate the controller design problem as an H _∞ optimisation problem in the mean-square sense. The main contributions of this article are as follows: (i) for stochastic systems, the design of a controller with multiple objectives can be addressed without employing a unique Lyapunov function; (ii) using an inequality technique and Finsler Lemma, we provide convex controller synthesis conditions described by linear matrix inequalities (LMIs). Some examples are presented to show the effectiveness of the developed theoretical results.     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

Observer-based H∞ fuzzy control for discrete-time Takagi–Sugeno fuzzy mixed delay systems with random packet losses and multiplicative noises

This paper investigates the observer-based H_∞ fuzzy control problem for a class of discrete-time fuzzy mixed delay systems with random communication packet losses and multiplicative noises, where the mixed delays comprise both discrete time-varying and distributed delays. The random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer-based fuzzy feedback controller are derived, such that the closed-loop control system is asymptotically mean-square stable and preserves a guaranteed H_∞ performance. Then a linear matrix inequality approach for designing such an observer-based H_∞ fuzzy controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results.     

Receding horizon H∞ control problems for sampled-data systems§

In this article, the receding horizon H_∞ control problems for sampled-data systems are considered. Since sampled-data systems can be rewritten as equivalent jump systems, the receding horizon H_∞ control problems for time-varying jump systems are considered first and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Then the obtained results are applied to sampled-data systems and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Two numerical examples are given to illustrate the theory.     

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T–S fuzzy approach

By utilising Takagi–Sugeno (T–S) fuzzy set approach, this paper addresses the robust H_∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics’ enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T–S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H_∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T–S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.     

Asynchronous H∞ Dynamic Output Feedback Control for Markovian Jump Neural Networks with Time-varying Delays

In this paper, the problem of asynchronous robust H_∞ dynamic output feedback control for Markovian jump neural networks with norm-bounded parameter uncertainties and mode-dependent time-varying delays is investigated. The improved delay-dependent stochastic stability conditions and bounded real lemma are obtained by introducing the relaxation variables, which reduces the conservatism caused by boundary technology and model transformation. An improved Lyapunov-Krasovskii functional is constructed using linear matrix inequalities. On this basis, the solution of robust H_∞ dynamic output feedback problem and sufficient conditions for solving the problem of asynchronous dynamic output feedback controller are given respectively. Asynchronous dynamic output feedback controller is constructed to ensure that the closed-loop mode-dependent time-varying delays Markovian jump neural networks achieve different convergence speeds. The given H_∞ performance index is satisfied for the delays not bigger than a given upper bound. Numerical examples are employed to show the effectiveness and correctness of the method presented in this paper.

     

Observer‐based H ∞ control for networked systems with bounded random delays and consecutive packet dropouts

This paper is concerned with the H _∞ control problem for a class of systems with bounded random delays and consecutive packet dropouts that exist in both sensor‐to‐controller channel and controller‐to‐actuator channel during data transmission. A new model is developed to describe possible random delays and packet dropouts by two groups of Bernoulli distributed stochastic variables. To avoid the state augmentation, a full‐order observer‐based feedback controller is designed via LMI approach. Based on the Lyapunov theory, a sufficient condition is provided to guarantee the closed‐loop networked system to be asymptotically mean‐square stable and achieve the prescribed H _∞ disturbance‐rejection‐attenuation level. The simulation examples illustrate the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Design of stochastic fault tolerant control for H2 performance

In this paper, the controller synthesis problem for fault tolerant control systems (FTCS) with stochastic stability and H₂ performance is studied. System faults of random nature are modelled by a Markov chain. Because the real system fault modes are not directly accessible in the context of FTCS, the controller is reconfigured based on the output of a fault detection and identification (FDI) process, which is modelled by another Markov chain. Then state feedback and output feedback control are developed to achieve the mean square stability (MSS) and the H₂ performance for both continuous‐time and discrete‐time systems with model uncertainties. Copyright © 2006 John Wiley & Sons, Ltd.