H ∞ control of a Wiener-type system

A Wiener system is a system which can be modelled as a linear dynamic followed by a static gain. The goal of this paper is to develop a robust H _∞ compensator for controlling an SISO Wiener system. The controller also takes the form of a Wiener model. The design approach consists of the approximation of the non-linear gain using a piecewise linear (PWL) function and in using a linear controller for each sector obtained from this approximation. Therefore, the general controller structure can be stated as a linear dynamic compensator in series with a PWL static gain.

As an illustrative case, a neutralization pH reaction between a strong acid and a strong base in the presence of a buffer agent is dealt with. Computer simulations are developed for showing the performance of the proposed controller.     

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.     

Multi-objective H ∞ control for vehicle active suspension systems with random actuator delay

This article is concerned with the problem of multi-objective H _∞ control for vehicle active suspension systems with random actuator delay, which can be represented by signal probability distribution. First, the dynamical equations of a quarter-car suspension model are established for the control design purpose. Secondly, when taking into account vehicle performance requirements, namely, ride comfort, suspension deflection and the probability distributed actuator delay, we present the corresponding dynamic system, which will be transformed to the stochastic system for the problem of multi-objective H _∞ controller design. Third, based on the stochastic stability theory, the state feedback controller is proposed to render that the closed-loop system is exponentially stable in mean-square while simultaneously satisfying H _∞ performance and the output constraint requirement. The presented condition is expressed in the form of convex optimisation problems so that it can be efficiently solved via standard numerical software. Finally, a practical design example is given to demonstrate the effectiveness of the proposed method.     

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).     

Design of robust H ∞ controller for a half-vehicle active suspension system with input delay

This article is concerned with the problem of robust H _∞ control for a half-vehicle active suspension system with input delay. The delay is assumed to be interval time-varying delay with unknown derivative. The vehicle front sprung mass and the rear unsprung mass are assumed to be varying due to vehicle load variation and may result in parameter uncertainties being modelled by polytopic uncertainty. First of all, regarding the heave and pitch accelerations as the optimisation objectives, and suspension deflection and relative tire load constraints as the output constraints, we build the corresponding suspension systems. Then, by constructing a novel Lyapunov functional involved with the lower and upper bounds of the delay, sufficient condition for the existence of robust H _∞ controller is given to ensure robust asymptotical stability of the closed-loop system and also guarantee the constrained performance. The condition can be converted into convex optimisation problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.     

H∞ control of a gravity gradient stabilised satellite

This paper describes the attitude control of a small gravity gradient and reaction wheel stabilised satellite. Gravity gradient stabilised satellite have limited stability and pointing capabilities. Thus, H_∞ control has been applied, in order to improve the accuracy of the attitude control. The synthesis of a suitable H_∞ controller, using a composite weighting function is described. The trade-off between reaction wheel torque and possible disturbance rejection capability using H_∞ control is discussed. Also, the promising results using H_∞ control with antireset windup compensation are presented.     

Design of H ∞ control of neural networks with time-varying delays

This paper deals with the H _∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H _∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

     

LMI-based H ∞-optimal control with transients

In this article, the worst-case norm of the regulated output over all exogenous signals and initial states as a performance measure of the system is characterised in terms of linear matrix inequalities (LMIs). Optimal time-invariant state- and output-feedback controllers are synthesised as minimising this performance measure. The essential role in this synthesis plays a weighting matrix reflecting the relative importance of the uncertainty in the initial state contrary to the uncertainty in the exogenous signal. H _∞-optimal control with transients is shown to be actually a trade-off between H _∞-control, being optimal under unknown exogenous disturbances and zero initial state, and γ-control, being optimal under zero exogenous signal and unknown initial conditions, if and only if the weighting matrix satisfies a fundamental inequality. If this inequality is met, the performance measure is achieved and the explicit formulae for the worst-case disturbance and initial state are provided. If this inequality fails, the performance measure coincides with the H _∞-norm and the trade-off gets broken.     

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.     

Mixed H2/H∞ pitch control of wind turbine with a Markovian jump model

This paper proposes a Markovian jump model and the corresponding H₂/H_∞ control strategy for the wind turbine driven by the stochastic switching wind speed, which can be used to regulate the generator speed in order to harvest the rated power while reducing the fatigue loads on the mechanical side of wind turbine. Through sampling the low-frequency wind speed data into separate intervals, the stochastic characteristic of the steady wind speed can be represented as a Markov process, while the high-frequency wind speed in the each interval is regarded as the disturbance input. Then, the traditional operating points of wind turbine can be divided into separate subregions correspondingly, where the model parameters and the control mode can be fixed in each mode. Then, the mixed H₂/H_∞ control problem is discussed for such a class of Markovian jump wind turbine working above the rated wind speed to guarantee both the disturbance rejection and the mechanical loads objectives, which can reduce the power volatility and the generator torque fluctuation of the whole transmission mechanism efficiently. Simulation results for a 2 MW wind turbine show the effectiveness of the proposed method.     

Quantized H∞ control for a class of 2-D systems with missing measurements

In this paper, the problem of quantized H∞ control is investigated for a class of 2-D systems described by Roesser model with missing measurements. The measurement missing of system state is described by a sequence of random variables obeying the Bernoulli distribution. Meanwhile, the state measurements are quantized by logarithmic quantizer before being communicated. By introducing a new 2-D Lyapunov-like function, a sufficient condition is derived to guarantee stochastically stable and H∞ performance of the closed-loop 2-D system, where the method of sector-bounded uncertainties is utilized to deal with quantization error. Based on the condition, the quantized H∞ control can be designed by using linear matrix inequality technique. A simulation example is also given to illustrate the proposed method.

     

H∞ and H2 control of multi-agent systems with transient performance improvement

In this paper, the H_∞ consensus control and H₂ robust control synthesised with transient performance problems are investigated for a group of autonomous agents with linear or linearised dynamics. Based on the relative information between neighbouring agents and a subset of absolute information of the agents, distributed controllers are proposed for both H_∞ and H₂ cases. Compared with the existing protocols, the one presented in this article focuses on improving the transient performance of the consensus problem. By using the tools from matrix analysis and robust control theory, conditions for the existence of controllers to those problems under an undirected communication topology are provided. Then, it is shown that the H₂ performance limit of uncertain systems under a distributed controller equals the minimum H_∞ consensus index synthesised with transient performance of a single agent by using a state feedback controller, independent of the communication topology. Finally, a simulation example as an application in Raptor-90 helicopter is proposed to illustrate the effectiveness of the theoretical results.     

H∞ control of switched delayed systems with average dwell time

This paper considers the problems of stability analysis and H_∞ controller design of time-delay switched systems with average dwell time. In order to obtain less conservative results than what is seen in the literature, a tighter bound for the state delay term is estimated. Based on the scaled small gain theorem and the model transformation method, an improved exponential stability criterion for time-delay switched systems with average dwell time is formulated in the form of convex matrix inequalities. The aim of the proposed approach is to reduce the minimal average dwell time of the systems, which is made possible by a new Lyapunov–Krasovskii functional combined with the scaled small gain theorem. It is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature. Moreover, the exponential H_∞ controller can be constructed by solving a set of conditions, which is developed on the basis of the exponential stability criterion. Simulation examples illustrate the effectiveness of the proposed method.     

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.     

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.     

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.