Robust Disturbance Attenuation Problem Research Articles

Robust ℒ2 disturbance attenuation for a class of uncertain Lipschitz nonlinear systems with input delay

ABSTRACTIn this paper, we study a robust disturbance attenuation problem that arises when applying the Artstein–Kwon–Pearson reduction transformation for a class of uncertain Lipschitz nonlinear systems with input delay and external disturbances. A conventional predictor-based feedback controller is adopted with the control gain matrix carefully identified by solving a couple of sufficient conditions in terms of linear matrix inequalities . Lyapunov–Krasovskii functionals are constructed to guarantee that the robust disturbance attenuation problem can be solved by the proposed controller. A numerical example is included to validate the performance of the proposed controller.

Robust Disturbance Attenuation in Hamiltonian Systems Via Direct Digital Control

AbstractThe discrete‐time robust disturbance attenuation problem for the n‐degrees of freedom (dof) mechanical systems with uncertain energy function is considered in this paper. First, it is shown in the continuous time‐setting that the robust control problem of n‐dof mechanical systems can be reduced to a disturbance attenuation problem when a specific type of control rule is used. Afterwards, the robust disturbance attenuation problem is formulised as a special disturbance attenuation problem. Then, the discrete‐time counterpart of this problem characterised by means of L2 gain is given. Finally, a solution of the problem via direct‐discrete‐time design is presented as a sufficient condition. The proposed discrete‐time design utilizes discrete gradient of the energy function of considered system. Therefore, a new method is also proposed using the quadratic approximation lemma to construct discrete gradients for general energy functions. The proposed direct‐discrete‐time design method is used to solve the robust disturbance attenuation problem for the double pendulum system. Simulation results are given for the discrete gradient obtained with the method presented in this paper. Note that the solution presented here for the robust disturbance attenuation problem give an explicit algebraic condition on the design parameter, whereas solution of the same problem requires solving a Hamilton–Jacobi–Isaacs partial differential inequality in general nonlinear systems.

Robust disturbance attenuation for uncertain nonlinear networked control systems

This paper considers the problem of robust disturbance attenuation for a class of uncertain nonlinear networked control systems. Takagi-Sugeno fuzzy models are firstly employed to describe the nonlinear plant. Markov processes are used to model the random network-induced delays and data packet dropouts. The Lyapunov-Razumikhin method has been used to derive such a controller for this class of nonlinear systems such that it is stochastically stabilizable with a disturbance attenuation level. Sufficient conditions for the existence of such a controller are derived in terms of the solvability of bilinear matrix inequalities. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools. The effectiveness of the proposed design methodology is verified by a numerical example.

Robust disturbance attenuation for uncertain networked control systems with random time delays

The problem of robust stabilisation and disturbance attenuation for a class of uncertain networked control systems (NCSs) with random communication network-induced delays is studied. Both sensor-to-controller and controller-to-actuator random network-induced delays are considered. Furthermore, Markov processes are used to model these random network-induced delays. Based on the Lyapunov-Razumikhin method, a controller is designed such that both robust stability and a prescribed disturbance attenuation performance for the closed-loop NCS are achieved, irrespective of the uncertainties and network-induced delays. The controller design technique is given in terms of the solvability of bilinear matrix inequalities. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimisation problems, which can be solved effectively by the mathematical tools available. The effectiveness of the proposed design methodology is verified by a numerical example.

H∞ control of parameter-dependent state-delayed systems using polynomial parameter-dependent quadratic functions

This paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite-dimensional linear parameter-dependent state-delayed systems. The use of polynomial parameter-dependent quadratic Lyapunov functions and linear matrix inequalities (LMIs) formulations for robust H ∞ control are considered. It is shown that the state feedback control can be determined to guarantee the stability of the closed-loop system independently of the time-delay. We present an illustrative example to demonstrate the applicability of the proposed design approach.

MIMO Disturbance and Plant Uncertainty Attenuation by Feedback

This paper investigates the ability of feedback to reduce plant and disturbance uncertainties in the multiple-input-multiple-output (MIMO) case, by solving two fundamental problems posed by Zames in the late seventies. The first problem is termed the MIMO extension of the optimal robust disturbance attenuation problem, the second is a filtering of plant uncertainty two-degree of freedom feedback problem. The optimal solutions of these problems are characterized using Banach space duality theory and shown to satisfy an allpass condition and an extremal identity. Moreover, the duality description leads to a dual pair of optimizations and the introduction of two nonstandard matrix norms. In particular, the primal-dual optimization reduces naturally to approximate finite dimensional convex optimizations within desired tolerance. Whereas the computation of the nonstandard matrix norms are shown to be equivalent to specific semi-definite programming problems, and a numerical solution based on convex programming is provided. It is also shown using Douglas' range inclusion theorem that performance is a monotonic function of uncertainty, and some qualitative implications for feedback are derived.

Optimal robust disturbance attenuation for continuous time‐varying systems

AbstractIn this paper we consider the Optimal robust disturbance attenuation problem (ORDAP) for continuous time‐varying systems subject to time‐varying unstructured uncertainty. We show that for causal (possibly time‐varying) continuous systems, ORDAP is equivalent to finding the smallest fixed point of a ‘two‐disc’ type optimization problem under time‐varying feedback control laws. Duality is applied in the context of nest algebra of causal stable systems, to prove existence of optimal continuous time‐varying controllers. We also show that for time‐invariant nominal plants, time‐varying control laws offer no improvement over time‐invariant feedback control laws. Copyright © 2003 John Wiley & Sons, Ltd.

Optimal robust disturbance attenuation for linear time-varying systems

The time-varying optimal robust disturbance attenuation problem is considered first as two-block problem and then as a two-disk problem.

On optimal robust disturbance attenuation

In this article, we give an explicit solution to the nonstandard H ∞ problem which includes the optimal robust disturbance attenuation problem and the two-disc problem. The solution depends on an operator which is analogous to the Sarason operator for the standard H ∞ problem, it allows to quantify the optimal performance of feedback systems and provides an explicit formula for the optimal controller. The nonstandard H ∞ problem is perhaps the simplest control problem which deals with significant plant uncertainty. Surprisingly, relatively little work has been done on it despite the large number of papers in the H ∞ control literature.

Decentralized global disturbance attenuation for a class of large-scale uncertain nonlinear systems

This paper studies the problem of global robust disturbance attenuation via decentralized state feedback for a class of large-scale nonlinear systems with parameter and interconnection uncertainties. The parameter uncertainty is from a compact set and the uncertain interconnections are bounded by higher-order polynomials of state variables. The problem that we address is to design a robust decentralized controller such that the closed-loop large-scale nonlinear system is input-to-state stable and the L2 gain from the disturbance input to the controlled output is below a prescribed value for all admissible uncertain parameters and interconnections. A Lyapunov-based recursive design approach is developed to construct the decentralized controller explicitly. As a special case, the problem of almost disturbance decoupling via decentralized state feedback is also solved.

Robust feedback design of a class of nonlinear cascaded systems with structural uncertainty

This paper is concerned with the robust stabilization and robust L 2 disturbance attenuation of a class of cascaded nonlinear systems with structural uncertainties. The design tools are construction of a Lyapunov function for robust stabilization and a storage function for robust L 2 gain performance. It is shown that, if for each subsystem there exist Lyapunov functions satisfying Hamilton-Jacobi inequalities related with nominal subsystems, then a robust stabilizing controller can be constructed such that the sum of the functions becomes a Lyapunov function for the cascaded system with uncertainties. This concept, is extended do the construction of the storage function and the controller for the robust L 2 disturbance attenuation problem by introducing an appropriate weight into the sum of the subsystem's Lyapunov functions.

Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems

In this paper, the problem of robust stability and robust disturbance attenuation is investigated for a class of singularly perturbed linear systems with norm-bounded parameter uncertainties in both state and output equations. Based on the slow and fast subsystems, a composite linear controller is designed such that both robust stability and a prescribed H infinity performance for the full-order system are achieved, irrespective of the uncertainties. Our results show that the above problem can be converted to an H infinity control problem for a related singularly perturbed linear system without parameter uncertainty. Thus, the existing results on H infinity control of singularly perturbed systems can be applied to obtain solutions to the problem of robust H infinity control for the uncertain systems, which is independent of the singular perturbation epsilon when epsilon is sufficiently small. An example is given to show the potential of the proposed technique.

Disturbance attenuation for a class of distributed parameter systems

This paper deals with the problem of robust stabilization and disturbance attenuation via measured feedback, for a class of dissipative collocated distributed systems with disturbances affecting both the input and the measured output. The proposed solution is based on a direct ℒ2-gain characterization which avoids the usual Riccati equation argument. For this purpose only strong stabilizability of the semigroup is required. A flexible slewing link is chosen as an application example. © 1997 John Wiley & Sons, Ltd.

GLOBAL ROBUSTH∞ CONTROL OF A CLASS OF NONLINEAR SYSTEMS

AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract This paper considers the problem of robust disturbance attenuation for a class of systems with both Lipschitz bounded and nonlinear uncertainties. The nonlinear uncertainty is assumed to satisfy a ‘matching condition’ and bounded by a known nonlinear function. The Lipschitz bounded one could be with any mismatched uncertainties. We develop a Riccati equation approach for designing a state feedback controller such that the so-called ℒ︁2-gain from the exogenous input noise to the state is minimized or guaranteed to be no larger than a prescribed value. © 1997 by John Wiley & Sons, Ltd. Citing Literature Volume7, Issue1January 1997Pages 75-84 RelatedInformation

Robust disturbance attenuation with stability for linear systems with norm-bounded nonlinear uncertainties

In this paper, the problem of robust stabilization and robust disturbance attenuation is investigated for systems with linear nominal parts and norm-bounded nonlinear uncertainties on both states and control inputs. It is shown that the type of nonlinear uncertainty sets considered in this paper has an equivalent representation by linear uncertainty sets. Based on this key result and some standard Riccati inequality approaches for robust control of linear uncertain systems, a constructive design procedure is developed.

Duality theory for MIMO robust disturbance rejection

Banach space duality theory is used to characterize the solutions of a nonstandard H/sup infinity / optimization problem which is shown to be allpass in general and unique in the single-input single-output (SISO) ease. The theory leads to a numerical solution of duality and convex optimization, which is applied to an example. For a limiting case of sharp cutoff filters, an explicit solution of the optimal robust disturbance attenuation problem (ORDAP) resembling the two arc theorem of complex analysis is derived. >