A parameter set division and switching gain-scheduling controllers design method for time-varying plants

This paper presents a new technique to design switching gain-scheduling controllers for plants with measurable time-varying parameters. By dividing the parameter set into a sufficient number of subsets, and by designing a robust controller to each subset, the designed switching gain-scheduling controllers achieve a desired L₂-gain performance for each subset, while ensuring stability whenever a controller switching occurs due to the crossing of the time-varying parameters between any two adjacent subsets. Based on integral quadratic constraints theory and Lyapunov stability theory, a switching gain-scheduling controllers design problem amounts to solving optimization problems. Each optimization problem is to be solved by a combination of the bisection search and the numerical nonsmooth optimization method. The main advantage of the proposed technique is that the division of the parameter region is determined automatically, without any prespecified parameter set division which is required in most of previously developed switching gain-scheduling controllers design methods. A numerical example illustrates the validity of the proposed technique.     

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.     

Optimal H2 and H∞ fixed-order dynamic compensation using canonical forms

This paper presents a technique for designing fixed order dynamic compensators in controller canonical form which are robust to both structured and unstructured uncertainty. The formulation uses an approach which combines an H₂ and H_∞ optimization process. Specifically, a quadratic performance index is minimized subject to a constraint on the H_∞ norm of the closed loop transfer function from disturbances to controlled outputs. This provides robustness to unstructured uncertainty. To provide robustness to structured uncertainty, an upper bound is computed for the worst case parameter variations, and it is then included in the derivation of the optimality conditions. A robust controller for a jetfoil boat is used to demonstrate this design technique. For the specific case of no structured uncertainty, the results of this approach using the canonical form compensator are analytically related to the previously published results for a fixed-order dynamic compensator. It is demonstrated that the use of the canonical form greatly simplifies the system of necessary conditions.     

Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

Identification and robust control for systems with ellipsoidal parametric uncertainty by convex optimization

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities (LMIs) Performance specifications are in terms of combined pole placement with sensitivity function shaping in the H₂ or H_∞ norm. Furthermore, an optimal input design technique for parameter estimation that is integrated into the robust control design is employed in this paper. This means that performance specifications on the closed‐loop transfer functions are translated into the requirements on the input signal spectrum. The simulation results show the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Fixed‐order robust H∞ control and control‐oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty

In this paper, sufficient conditions for robust output feedback controller design for systems with ellipsoidal parametric uncertainty are given in terms of solutions to a set of linear matrix inequalities. A polynomial method is employed to design a fixed‐order controller that assigns closed‐loop poles within a given region of the complex plane and that satisfies an H_∞ performance specification. The main feature of the proposed method is that it can be extended easily for control‐oriented uncertainty set shaping using a standard input design approach. Consequently, the results can be extended to joint robust control/input design procedure whose controller structure and performance specifications are translated into the requirements on the input signal spectrum used in system identification. This way, model uncertainty set can be tuned for the robust control design procedure. The simulation results show the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.     

Nonlinear robust H∞ control via dynamic output feedback

The problem on robust H_∞ control for a class of nonlinear systems with parameter uncertainty is studied. Sufficient conditions for the existence of the dynamic output feedback controller are obtained. Under these conditions, the closed-loop systems have robust H_∞-performance. A numerical example is given to illustrate the design of a robust controller using the proposed approach.     

Robust H2/H∞ control for time‐delay systems with polytopic uncertainty

In this paper, new separated H_∞ and H₂ performance criteria are derived for a class of time‐delay systems. When used in robust performance analysis and synthesis for real polytopic uncertainty and in multiobjective controller synthesis, they can partially rule out the technical restriction of using a single Lyapunov function, and therefore, lead to potentially less conservative linear matrix inequality (LMI) characterizations. Based on the criteria, robust multiobjective H₂/H_∞ controller is designed for time‐delay systems with polytopic uncertainty. All the conditions are given in terms of LMIs. Numerical examples are given to illustrate the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Passivity-based robust feedback control for non-linear systems with input dynamical uncertainty

This paper addresses the robust feedback control problem for a class of non-linear systems with uncertain input dynamics. The main objective is to develop a passivity-based systematic design approach for this kind of uncertain system. First, a passivity condition is presented for a non-linear system in feedback interconnection form, and then it is shown that with the help of this condition, a state feedback control law can be designed to render the uncertain system passive. Moreover, the extensions of the passivation controller are investigated in two cases where the uncertainty allows unknown control direction and there exists the external disturbance, respectively. It will be shown that an adaptive controller with a Nussbaum-type function can be incorporated into the passivation controller to deal with the unknown control direction and the L ₂-gain performance can be achieved by gain re-assignment of the passivation controller. Finally, a numerical example is given to demonstrate the proposed approach.     

An optimization algorithm for checking feasibility of robust H ∞-control problem for linear time-varying uncertain systems

An algorithm for checking feasibility of the robust H _∞-control problem for systems with time-varying norm bounded uncertainty is suggested. This algorithm is an iterative procedure on each step of which an optimization problem for a linear function under convex constraints determined by LMIs is solved. The effectiveness of the proposed algorithm is demonstrated on the numerical example of a parametrically disturbed pendulum.     

Output‐Feedback Control for Continuous‐time Interval Positive Systems under L1 Performance

This paper is concerned with the design of an L₁‐induced output‐feedback controller for continuous‐time positive systems with interval uncertainties. A necessary and sufficient condition for stability and an L₁‐induced performance of interval positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust static output‐feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions. For special single‐input‐multiple‐output (SIMO) positive systems, the problem of controller synthesis is completely solved with the help of an analytical formula for the L₁‐induced norm. An illustrative example is provided to show the effectiveness and applicability of the theoretical results.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic output feedback robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control of uncertain switched nonlinear systems

The problem of robust H _∞ control problem for a class of switched nonlinear systems with parameter uncertainty is studied by using single Lyapunov function method. The problem under switch-dependent and switch-independent dynamic output feedbacks is solved respectively. Sufficient conditions for solvability of the problem are obtained. The Lyapunov function and the corresponding switching law are explicitly constructed. A numerical example is given to demonstrate the validity of the proposed approach.     

Controller design for nonlinear systems using the Contoured Robust Controller Bode plot

In this paper, we develop the Contoured Robust Controller Bode (CRCBode) plot and demonstrate its use in the design of robust controllers for nonlinear single‐input single‐output (SISO) systems. The CRCBode plot shows contours (level sets) of a robust performance quantity on the Bode magnitude and phase plots of the controller. An iterative frequency domain loop‐shaping design approach is employed to eliminate all intersections of the controller frequency response with certain ‘forbidden regions,’ indicating that a standard SISO robust stability and performance criterion is satisfied. Nonlinearities are accounted for by avoiding the maximum forbidden regions over a structured uncertainty set consisting of linearizations of the system dynamics about several operating points. We demonstrate this technique by designing and experimentally verifying a flow‐rate controller for a butterfly‐valve based liquid cooling system, which is robust to valve nonlinearities and flow disturbances. Finally, we compare this compensator with one generated using an automated H _∞ synthesis algorithm and discuss the advantages of the CRCBode approach. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Fixed‐Structure ℋ∞ Controller Design for Systems with Polytopic Uncertainty: An LMI Solution

This note provides a new method for fixed‐structure H_∞ controller design for discrete‐time single input single output (SISO) systems with polytopic uncertainty. New conditions are derived based on the concept of robust strict positive realness (SPRness) of an uncertain polynomial with respect to a parameter‐dependent polynomial. The quality of this approximation depends on this SPR‐maker. A procedure is proposed for choosing the parameter‐dependent SPR‐maker that guarantees the improvement of the performance for the designed controller in comparison with the traditional approaches employed fixed SPR‐makers. The proposed conditions are given in terms of solutions to a set of linear matrix inequalities. The effectiveness of the proposed approach is demonstrated by comparing with the existing results.     

Robust neural network control system design for linear ultrasonic motor

Linear ultrasonic motor (LUSM) has much merit, such as high precision, fast control dynamics and large driving force, etc.; however, the dynamic characteristic of LUSM is nonlinear and the precise dynamic model of LUSM is difficult to obtain. To tackle this problem, this study presents a robust neural network control (RNNC) system for LUSM to track a reference trajectory with L ₂ robust tracking performance. The developed RNNC system is composed of a neural network controller and a robust controller. The neural network controller is the principal controller used to mimic an ideal controller and the robust controller is adopted to achieve L ₂ robust tracking performance. The developed RNNC system is then applied to control an LUSM. Experimental results show that the developed RNNC system can achieve favorable tracking performance with unknown of LUSM model.