New results on non‐fragile H∞ controller design for uncertain linear systems

This paper deals with the non‐fragile H_∞ control problem for uncertain linear systems. The uncertainties are of a linear fractional form and appear in both the state and control input matrices. The purpose is to design a state feedback controller, which is subject to linear fractional parametric uncertainties, such that the resulting closed‐loop system is quadratically stable with an H_∞ norm bound. A sufficient condition for the solvability of the problem is obtained in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed design method. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A new approach to robust reliable H∞ control for uncertain nonlinear systems

This paper focuses on the optimal robust reliable H_∞ control for a class of uncertain nonlinear systems with actuator faults. A new method of annihilating uncertain matrix is proposed. Based on this approach, a new method of disposing of the phenomenon of uncertain matrices multiplication is provided. In accordance with the method, the optimal robust reliable H_∞ control problem for uncertain nonlinear systems is settled by employing state feedback, in terms of linear matrix inequality (LMI). Finally, two illustrative examples are given to show the feasibility and validity of the proposed method.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

Robust output-feedback control of linear discrete-time systems

The problem of designing H_∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H_∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.     

Chattering Elimination in the Hybrid Control of Constrained Manipulators via First/Second Order Sliding Mode Control

This paper deals with the hybrid position/force control problem for constrained manipulators subjected to uncertainties and disturbance of various natures. This problem can be formulated in terms of the solution to differential algebraic equations with a structure which allows the separation of the force and position control when the system is perfectly known. A solution for the uncertain case has been carried out based on sliding mode control theory which has been shown to be highly effective in counteracting uncertainties and disturbances for some classes of uncertain, nonlinear systems. Specific problems related to this technique are chattering elimination and the algebraic coupling between constraint forces and possibly discontinuous control signals. This paper presents a solution to the particular case of a manipulator with n degrees of freedom and n-1 holonomic constraints, leaving the solution to the general problem for further investigations. The main contribution is the use of a new second order sliding mode control algorithm which is proved to yield the solution of the problem after a transient of finite duration without requiring the availability of the acceleration vector.     

Robust adaptive learning control for nonlinear systems with extended matching unstructured uncertainties

The exponential output tracking problem for a class of single‐input, single‐output uncertain nonlinear systems, including systems with extended matching unstructured uncertainties and without a well‐defined global relative degree, is addressed. Conditions on the uncertain system dynamics are derived, which allow us to design a state‐feedback learning control achieving semi‐global exponential output tracking of sufficiently smooth and periodic reference signals of known period, while guaranteeing ??₂ and ??_∞ transient performances during the learning phase. The application of the proposed learning approach to the position tracking control problem for uncertain permanent magnet step motors with non‐sinusoidal flux distribution and uncertain position‐dependent load torque allows us to provide a solution to a yet unsolved problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Robust stabilization and H∞ control of uncertain stochastic time‐delay systems with nonlinear perturbation

This paper investigates the problem of delay‐dependent robust stochastic stabilization and H_∞ control for uncertain stochastic nonlinear systems with time‐varying delay. System uncertainties are assumed to be norm bounded. Firstly, by using novel method to deal with the integral terms, robustly stochastic stabilization results are obtained for stochastic uncertain systems with nonlinear perturbation, and an appropriate memoryless state feedback controller can be chosen. Compared with previous results, the new technique can sufficiently utilize more negative items information. Then, robust H_∞ control for uncertain stochastic system with time‐varying delay and nonlinear perturbation is considered, and the controller is designed, which will guarantee that closed‐loop system is robustly stochastically stable with disturbance attenuation level. Finally, two numerical examples are listed to illustrate that our results are effective and less conservative than other reports in previous literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized state-feedback stabilization and robust control of uncertain large-scale systems with integrally constrained interconnections

This paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems. A new class of uncertain large-scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints. The problem is to design a set of local (decentralized) controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem. The paper presents necessary and sufficient conditions for the existence of such a controller. The proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game-type Riccati algebraic equations arising in H_∞ control.     

Adaptive output rejection of unmatched input disturbances

To adaptively reject the effect of certain unmatched input disturbances on the output of a linear time-invariant system, a transfer function matching condition is needed. A lemma which presents a novel basic property of linear systems is derived to characterize system conditions for such transfer function matching. An adaptive disturbance rejection control scheme is developed for such systems with uncertain dynamics parameters and disturbance parameters. This adaptive control technique is applicable to control of systems with actuator failures whose failure values, failure time instants, and failure patterns are unknown. A solution is presented to this adaptive actuator failure compensation problem, which ensures closed-loop stability and asymptotic output tracking, in the presence of any up to m−1 uncertain failures of the total m actuators. Desired adaptive system performance is verified by simulation results.     

ROBUST H∞ CONTROL FOR UNCERTAIN STOCHASTIC SYSTEMS WITH MARKOVIAN SWITCHING AND TIME‐VARYING DELAYS

This paper is concerned with the problem of robust H_∞ control for uncertain stochastic systems with Markovian jump parameters and time‐varying state delays. A linear matrix inequality approach is developed and state feedback controllers are designed, which guarantee mean square asymptotic stability of the closed‐loop system and a prescribed H_∞ performance level for all modes and admissible uncertainties. A numerical example is provided to demonstrate the application of the proposed method.     

Output feedback adaptive DSC for nonlinear systems with guaranteed L-infinity tracking performance

In this paper, the problem of output tracking for a class of uncertain nonlinear systems is considered. First, neural networks are employed to cope with uncertain nonlinear functions, based on which state estimation is constructed. Then, an output feedback control system is designed by using dynamic surface control (DSC). To guarantee the L-infinity tracking performance, an initialization technique is presented. The main feature of the scheme is that explosion of complex- ity problem in backstepping control is avoided, and there is no need to update the unknown parameters including control gains as well as neural networks weights, the adaptive law with one update parameter is necessary only at the first design step. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the L-infinity performance of system tracking error can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

Stabilisation and L 2-gain analysis for a class of uncertain switched non-linear systems

This article is concerned with the problem of stabilisation and L ₂-gain analysis for a class of switched non-linear systems with norm-bounded time-varying uncertainties. A system in this class is composed of two parts: an uncertain linear switched part and a non-linear part, which are also switched systems. When all the subsystems are stabilisable and have an L ₂-gain, the switched feedback control law and the switching law are designed respectively using average dwell-time method such that the corresponding closed-loop switched system is exponentially stable and achieves a weighted L ₂-gain.     

Robust H 2 control of Markovian jump systems with uncertain switching probabilities

This article deals with the robust H ₂ control problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration appear both in the system parameters and in the mode transition rates. First, a new criterion based on linear matrix inequalities is established for checking the robust H ₂ performance of the uncertain system. Then, a sufficient condition for the existence of the state-feedback controllers is established such that the closed-loop system is quadratically mean square stable and has a certain level of robust H ₂ performance in terms of linear matrix inequalities with equality constraints. A globally convergent algorithm is also presented to construct such controllers effectively. Finally, an illustrative numerical example is used to demonstrate the developed theory.     

Robust passivity‐based H∞ control for uncertain switched nonlinear systems

In this paper, we investigate the H_∞ control problem for uncertain switched nonlinear systems with passive and non‐passive subsystems. For any given average dwell time, any given passivity rate and any given disturbance attenuation level, we design feedback controllers of subsystems, which may depend on the pre‐given constants, to solve the H_∞ control problem for the uncertain switched nonlinear systems for all admissible uncertainties. For linear systems, the exponential small‐time norm‐observability is shown to be preserved under disturbance. Two examples are provided to demonstrate the effectiveness of the proposed design method. Copyright © 2016 John Wiley & Sons, Ltd.     

L 2-gain analysis and control synthesis of uncertain switched linear systems subject to actuator saturation

This article addresses the L ₂-gain analysis and control synthesis problem for a class of uncertain switched linear systems with saturating actuators and external disturbances. First, when the controllers are pre-given, an analysis condition on disturbance tolerance is established under which the state trajectory starting from the origin will remain inside a bounded set. By this condition, the problem of estimating disturbance tolerance capability is formulated as a constrained optimisation problem. Then, the restricted L ₂-gain property is analysed over the set of tolerable disturbances. An upper bound on the restricted L ₂-gain is estimated by solving a constrained optimisation problem. Furthermore, when controller gain matrices are design variables, these optimisation problems can be adapted for controller design. All the results are achieved by utilising the multiple Lyapunov functions method and presented in terms of an LMI optimisation-based approach. A numerical example is given to show the effectiveness of the proposed method.     

Robust H∞ control for uncertain discrete-time systems with circular pole constraints

This paper investigates the problem of robust H_∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H_∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H_∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H_∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H_∞ control and robust pole assignment of uncertain systems.     

Robust H ∞ control via a stable decentralized nonlinear output feedback controller

This paper presents a new method to construct a decentralized nonlinear robust H ^∞ controller for a class of large‐scale nonlinear uncertain systems. The admissible uncertainties and nonlinearities in the system satisfy integral quadratic constraints and global Lipschitz conditions, respectively. The decentralized controller, which is required to be stable, is capable of exploiting known nonlinearities and interconnections between subsystems without treating them as uncertainties. Instead, additional uncertainties are introduced because of the discrepancies between nondecentralized and decentralized nonlinear output feedback controllers. The H ^∞ control objective is to achieve an absolutely stable closed‐loop system with a specified disturbance attenuation level. A solution to this control problem involves stabilizing solutions to algebraic Riccati equations parametrized by scaling constants corresponding to the uncertainties and nonlinearities. This formulation is nonconvex; hence, an evolutionary optimization method is applied to solve the control problem considered. Copyright © 2012 John Wiley & Sons, Ltd.     

On convex parameterization of robust control design for minimizing (conditional) performance at risk

This paper introduces performance at risk and conditional performance at risk as design metrics for the formulation of robust control design. These two metrics are used to characterize the high percentile or tail distribution of a performance specification when system uncertain parameters are random variables described by statistical distributions. The probabilistic robust control design is then formulated as a minimization problem with respect to the (conditional) performance at risk or as a constrained problem in terms of them. Performance specifications in terms of the high percentile or tail distribution are more stringent than that are defined in terms of the average (mean) value, which are often used in current literature for probabilistic robust control. Furthermore, the convexity of the conditional performance at risk does not have particular requirements on the underlying distribution of uncertain parameters; thus, convex optimization can be applied to the probabilistic robust control with respect to uncertain parameters with general distributions. The proposed probabilistic robust approach is applied to search solutions to linear matrix inequality containing random parametric uncertainties as well as to design a stabilizing controller for polynomial vector fields subject to random parametric uncertainties. Copyright © 2007 John Wiley & Sons, Ltd.     

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.