Robust sampled-data H ∞ output tracking control for a class of nonlinear networked systems with stochastic sampling

In this article, the problem of robust sampled-data H _∞ output tracking control is investigated for a class of nonlinear networked systems with stochastic sampling and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and can be extended to the case with multiple stochastic sampling periods. By the way of an input delay, the probabilistic system is transformed into a stochastic continuous time-delay system. A new linear matrix inequality-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H _∞. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H _∞ output tracking design.     

Decentralized H∞ control for large-scale interconnected nonlinear time-delay systems via LMI approach

In this paper, the problem of H_∞ control of nonlinear large-scale systems with interval time-varying delays in interconnection is considered. The time delays are assumed to be any continuous functions belonging to a given interval involved in both the state and observation output. 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 the existence of decentralized H_∞ control is established in terms of linear matrix inequalities (LMIs). The approach is applied to decentralized H_∞ control of uncertain linear systems with interval time-varying delay. Numerical examples are given to show the effectiveness of the obtained results.     

Robust H ∞ fuzzy control of nonlinear systems with multiple time delays

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and R_k of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H ^∞ control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.     

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.     

Robust nonlinear H∞ control of hyperbolic distributed parameter systems

A radial basis function (RBF) neural network model is developed for the identification of hyperbolic distributed parameter systems (DPSs). The empirical model is based only on process input–output data and is used for the estimation of the controlled variables at multiple spatial locations. The produced nonlinear model is transformed to a nonlinear state–space formulation, which in turn is used for deriving a robust H_∞ control law. The proposed methodology is applied to a long duct for the flow-based control of temperature distribution. The performance of the proposed method is illustrated by comparing it with conventional control strategies.     

On the design of a reduced-order H ∞ controller for nonlinear sampled-data systems

In this paper, the problem of designing reduced-order H ^∞ controllers is studied for nonlinear continuous-time systems with sampled measurements. Using the concepts of dissipativity and differential game, sufficient conditions are derived for the existence of such reduced-order H ^∞ controllers. These conditions are expressed in terms of the solutions of two Hamilton–Jacobi inequalities, comprising a standard Hamilton–Jacobi inequality and a differential Hamilton–Jacobi inequality with jumps. These Hamilton–Jacobi inequalities are exactly those used in the construction of full-order H ^∞ controllers. When these conditions hold, state-space formulae are also given for such reduced-order controllers. An illustrative example is also included.     

H ∞ control of networked control systems with state quantisation

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H _∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.     

H ∞ sampled data control of systems with time-delays

Sampled-data H _∞ control of linear systems with constant state, control and measurement delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input–output approach to stability and L ₂-gain analysis is applied to the resulting system. The discretised Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (those in the input and in the output), which are constant. Solutions to the state-feedback and the output-feedback H _∞ control problems are derived in terms of linear matrix inequalities (LMIs).     

H∞ output tracking fuzzy control for nonlinear systems with time-varying delay

This paper proposes an observer-based output tracking control via virtual desired reference model for a class of nonlinear systems with time-varying delay and disturbance. First, the Takagi–Sugeno fuzzy model represents the nonlinear system with time-varying delay and disturbance. Then we design an observer to estimate immeasurable states and controller to drive the error between estimated state and virtual desired variables (VDVs) to zero such that the overall control output tracking system has H_∞ control performance. Using Lyapunov–Krasovskii functional, we derive sufficient conditions for stability. The advantages of the proposed output control system are (i) systematic approach to derive VDVs for controller design; (ii) relaxes need for real reference model; (iii) drops need for information of equilibrium; (iv) relaxed condition is provided via three-step procedure to find observer and controller gain. We carry out simulation using a continuous stirred tank reactor system where the effectiveness of the proposed controller is demonstrated by satisfactory numerical results.     

Decentralised H ∞ filtering of interconnected discrete-time fuzzy systems with time delays

This article considers the decentralised H _∞ filtering of interconnected discrete-time fuzzy systems with time delays based on piecewise Lyapunov–Krasovskii functionals. The fuzzy system consists of J interconnected time-delay discrete-time Takagi–Sugeno fuzzy subsystems and the decentralised H _∞ filter is designed for each subsystem. It is shown that the stability with H _∞ performance of overall filtering error system can be established if a piecewise Lyapunov–Kroasovskii functional can be constructed, and moreover, the functional can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of the presented approach.     

H ∞ predictive control of networked control systems

This article is concerned with the problem of H _∞ predictive control of networked control system with random network delay. A new control scheme termed networked predictive control is proposed. This scheme mainly consists of the control prediction generator and network delay compensator. While designing the predictor, the control input to the actuator may be different due to networked induced time-delay and data dropout, and two cases are considered depending on the way that the observer obtains the plant control input u _t . The necessary and sufficient conditions are given for the closed-loop networked predictive control system to be stochastically stable for different u _t and random network delays in controller to actuator channel (CAC) and sensor to controller channel (SCC). A simulation study shows the effectiveness of the proposed scheme.     

On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H ^∞ control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L ^∞[0,∞) type system uncertainties with known bounding functions. H ^∞ control deals with unmatched disturbances of L ₂[0,∞) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H ^∞ control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H ^∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H ^∞ control, the resulting sliding manifold in the sliding phase possesses the desired L ₂ gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L ₂ gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.     

Reliable H ∞ control of a class of uncertain interconnected systems: an LMI approach

The aim of this work is to study the reliable control design problem for parameter-dependent interconnected systems in the presence of actuator failures. Moreover, the control ensures H _∞ performance in front of L ₂ perturbations. A more practical model of actuators or control channel failures than outage is adopted, considering partial achievement. The continuous H_∞ control problem is solved via elementary manipulations on linear matrix inequalities and the resulting control systems are robustly stable against plant uncertainties and failures.     

Robust sampled-data H∞ control of uncertain singularly perturbed systems using time-dependent Lyapunov functionals

In this paper, the problem of robust sampled-data H_∞ control of linear uncertain singularly perturbed systems is investigated. The parametric uncertainties are assumed to be time-varying and norm-bounded. Two types of controller design are considered: (1) with a fast sampling in the fast state and a slow one in the slow state, and (2) with a fast sampling in both states. For each type, a time-dependent Lyapunov functional associated with the sampling pattern is introduced to analyse the exponential stability and L₂-gain performance of the closed-loop system. Linear matrix inequalities based solutions of the robust sampled-data H_∞ control problem are derived. The new results are proved theoretically to be less conservative than the existing results. An illustrative example is given which substantiates the usefulness of the proposed method.