A robust H ∞ control approach for a class of networked control systems with sampling jitter and packet-dropout

This paper is concerned with the robust H _∞ control problem for a class of networked control systems (NCSs) with sampling jitter, short time-varying delays and packet-dropouts. By considering state feedback controller, the close-loop NCS is described as a discrete-time linear switched system model with uncertainties. Based on the linear matrix inequality (LMI) approach, a robust H _∞ condition is proposed to solve the H _∞ stability and stabilization problems for the considered NCS. An illustrative example is provided to demonstrate the effectiveness of the proposed theoretical results.     

H∞control of interconnected nonlinear sampled-data systems with parametric uncertainty

This paper studies the problem of robust control design for a class of interconnected uncertain systems under sampled measurements. The class of system under consideration is described by a state space model containing unknown cone bounded nonlinear interaction and time-varying norm-bounded parameter uncertainties in both state and output equations. Our attention is focused on the design of linear dynamic output feedback controllers using sampled measurements. We address the problem of robust H_∞ control in which both robust stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainties and nonlinearities. The H_∞ performance measure involves both continuous-time and discrete-time signals. It has been shown that the above problems can be recast into H_∞ syntheses for related N decoupled linear sampled-data systems without parameter uncertainties and unknown nonlinearities, which can be solved in terms of Riccati differential equations with finite discrete jumps. A numerical example is given to show the potential of the proposed technique.     

Robust H ∞ networked control for discrete-time fuzzy systems with state quantisation

The problem of robust H _∞ control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) with state quantisation is investigated. A new model of network-based control with simultaneous consideration of network-induced delays and packet dropouts is proposed. By using a fuzzy Lyapunov–Krasovskii functional (LKF), we derive a less conservative delay-dependent stability condition for the closed-loop NCSs. Robust H _∞ fuzzy controller is developed for the asymptotical stabilisation of the NCSs. Since it is not expressed as strict LMI conditions, the cone complementary linearisation procedure is exploited to solve the nonconvex feasibility problem. A numerical example shows the feasibility applications of the proposed technique.     

Robust H ∞ control for a class of uncertain mechanical systems

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.     

Robust H∞ control for uncertain discrete stochastic time-delay systems

This paper deals with the problems of robust stabilization and robust H_∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H_∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H_∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach.     

Decentralised indirect adaptive output feedback fuzzy H ∞ tracking design for a class of large-scale nonlinear systems

A novel decentralised indirect adaptive output feedback fuzzy controller with a compensation controller and an H _∞ tracking controller is presented for a class of uncertain large-scale nonlinear systems in this article. The compensator adaptively compensates for interconnections between subsystems as well as mismatched errors, while the H _∞ controller suppresses the effect of external disturbances. Based upon the combination of fuzzy inference systems, a state observer, H _∞ tracking technique and the strictly positive real condition, the proposed overall observer-based decentralised algorithm guarantees not only asymptotical tracking of reference trajectories but also an arbitrary small attenuation level of the unmodelled error dynamics including the disturbances on the tracking control. Simulation results substantiate the effectiveness of the proposed scheme.     

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.     

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.     

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.     

Adaptive practical output tracking of a class of nonlinear systems

Focus is hid on the adaptive practical output-tracking problem of a chss of nonlinear systems with high-order lower-triangular structure and uncontrollable unstable linearization. Using the modified adaptive addition of a power integrator technique as a basic tool, a new smooth adaptive state feedback controller is designed. This controller can ensure all signals of the closed-loop systems are globally bounded and output tracking error is arbitrary small.     

Robust H∞ containment control for uncertain multi-agent systems with inherent nonlinear dynamics

This article considers the distributed containment control problem of nonlinear multi-agent systems subject to parameter uncertainties and external disturbances. An appropriate controlled output function is defined to quantitatively analyse the effect of external disturbances on the containment control problem. By employing robust H_∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H_∞ performance under fixed topology. Moreover, the unknown feedback matrix of the proposed protocol is determined by solving only two LMIs with the same dimensions as a single agent. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

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.     

Robust H ∞ reliable control for a class of uncertain neutral delay systems

This paper deals with the problem of robust reliable control for a class of uncertain neutral delay systems. The aim was to design a state feedback controller such that the plant remained stable for all admissible uncertainties as well as actuator faults among a prespecified subset of actuators or sector-type actuator non-linearity, independently of the delay time. A linear matrix inequality approach was developed to solve the problem addressed with an H X norm bound constraint on disturbance attenuation.     

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.     

Dual-terminal event-triggered dynamic output feedback H∞ control for aero engine networked control systems with quantization

This study deals with the problem of dual-terminal event-triggered dynamic output feedback (DOF) control for aero engine networked control systems (NCSs) subject to network-induced delay, external disturbance, and quantization effects. First, we established a generalized mathematical model of the aero engine. Second, a dual-terminal dynamic event-triggered mechanism (DETM) was designed to reduce the utilization of the network bandwidth. In addition, a DOF controller with a compensation function was proposed to stabilize the system. By utilizing the Lyapunov-Krasovskii (LK) method, the stability criteria were determined. Accordingly, the design conditions of the DOF controller and DETMs were presented. Furthermore, based on a genetic algorithm (GA), a parameter tuning method was proposed to obtain the allowable delay upper bound with less conservatism. Finally, some examples were presented to show the effectiveness and superiority of the presented scheme.     

Quantized H ∞ fault-tolerant control for networked control systems

Quantized H_∞ fault-tolerant control for networked control systems (NCSs) with partial actuator fault with respect to actuators is concerned in this paper. Considering transmission delay, packet dropout and quantization, a synthesis model with partial actuator fault is established. The piecewise constant controller is adopted to model NCS with the transmission delay and packet dropout. Due to data transmitted in practical NCSs should be quantized before they are sent to the next network node, the logarithmic static and time-invariant quantizers at the sensor and controller sides are proposed in the paper. For the established model, an appropriate type of Lyapunov functions is provided to investigate the delay-dependent H_∞ control problem. According to an optimal problem, the controller that makes the system achieve the best performance is designed. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Robust H∞ control for stochastic systems with nonlinearity,uncertainty and time-varying delay

This paper deals with the problems of robust stochastic stabilization and $H_{\infty }$ control for uncertain stochastic systems with time-varying delay and nonlinear perturbation. System uncertainties are assumed to be norm bounded and time delay is assumed to be bound and time varying with delay-derivative bounded by a constant, which may be greater than one. First, new delay-dependent criterion is proposed by exploiting delay-partitioned Lyapunov–krasovskii functional and by employing tighter integral equalities to estimate the upper bound of the stochastic differential of Lyapunov–krasovskii functional without ignoring some useful terms. Second, based on the criterion obtained, a delay-dependent criterion for the existence of a state feedback $H_{\infty }$ controller that ensures robust stochastic stability and a prescribed $H_{\infty }$ performance level of the closed-loop system for all admissible uncertainties is proposed. These developed results have advantages over some previous ones, in that they involve fewer matrix variables but have less conservatism and they also enlarge the application scope. New sufficient conditions are presented in terms of linear matrix inequality. Numerical examples are used to illustrate the effectiveness and feasibility of the proposed method.