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Lipschitz Condition (lipschitz + condition)

Distribution by Scientific Domains
Engineering66%

Selected Abstracts

Predictor-based repetitive learning control for a class of remote control nonlinear systems

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2007
Ya-Jun Pan
Abstract In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. The proposed approach is to deal with the remote tracking control problem when the environment is periodic or repeatable over infinite time domain. Since there exist time delays in the two transmission channels: from the controller to the actuator and from the sensor to the controller, tracking a desired trajectory through a remote controller is not an easy task. In order to solve the problem caused by time delays, a predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality (LMI) techniques developed by Lyapunov Kravoskii method for time delay systems. The RLC law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. The proof of the stability is based on a constructed Lyapunov function related to the Lyapunov Kravoskii functional used for the proof of the predictor's convergence. By well incorporating the predictor and the RLC controller, the system state tracks the desired trajectory independent of the influence of time delays. A numerical simulation example is shown to verify the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Pseudodifferential operators with compound non-regular symbols

MATHEMATISCHE NACHRICHTEN, Issue 9-10 2007
Yu. I. Karlovich
Abstract Let V (,) denote the Banach algebra of absolutely continuous functions of bounded total variation on ,. We study an algebra ,, of pseudodifferential operators of zero order with compound slowly oscillating V (,)-valued symbols (x, y) , a (x, y, ·) that satisfy a Lipschitz condition with respect to the spatial variables x, y , ,. Sufficient conditions for the boundedness and compactness of pseudodifferential operators with compound symbols on the Lebesgue spaces Lp(,), for p = 2 and 1 < p < ,, are obtained. A Fredholm criterion and an index formula for pseudodifferential operators A , ,, are presented. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Singular operators in variable spaces Lp (·)(,, ,) with oscillating weights

MATHEMATISCHE NACHRICHTEN, Issue 9-10 2007
Vakhtang Kokilashvili
Abstract We study the boundedness of singular Calderón,Zygmund type operators in the spaces Lp (·)(,, ,) over a bounded open set in ,n with the weight , (x) = wk(|x , xk|), xk , , where wk has the property that wk(r) , , where is a certain Zygmund-type class. The boundedness of the singular Cauchy integral operator S, along a Carleson curve , is also considered in the spaces Lp (·)(,, ,) with similar weights. The weight functions wk may oscillate between two power functions with different exponents. It is assumed that the exponent p (·) satisfies the Dini,Lipschitz condition. The final statement on the boundedness is given in terms of the index numbers of the functions wk (similar in a sense to the Boyd indices for the Young functions defining Orlicz spaces). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

ADAPTIVE CONTROL DESIGN FOR NONLINEARLY PARAMETERIZED SYSTEMS WITH A TRIANGULAR STRUCTURE

ASIAN JOURNAL OF CONTROL, Issue 2 2007
Kiyoshi Yokoi
ABSTRACT A novel adaptive backstepping design for a class of nonlinearly parameterized systems with a triangular structure is proposed. Under the Lipschitz condition with respect to unknown parameters of the system, an effective adaptive controller is designed without the requirement on the compactness of the unknown parametric set. Especially, the proposed adaptive control enables the advantage of "tuning function concept", which results in only one estimation law for the unknown parameters. Our simulation with induction motor model particularly shows the viability of the obtained results. [source]

GENERALIZED QUADRATIC STABILIZATION FOR DISCRETE-TIME SINGULAR SYSTEMS WITH TIME-DELAY AND NONLINEAR PERTURBATION

ASIAN JOURNAL OF CONTROL, Issue 3 2005
Guoping Lu
ABSTRACT This paper discusses a generalized quadratic stabilization problem for a class of discrete-time singular systems with time-delay and nonlinear perturbation (DSSDP), which the satisfies Lipschitz condition. By means of the S-procedure approach, necessary and sufficient conditions are presented via a matrix inequality such that the control system is generalized quadratically stabilizable. An explicit expression of the static state feedback controllers is obtained via some free choices of parameters. It is shown in this paper that generalized quadratic stability also implies exponential stability for linear discrete-time singular systems or more generally, DSSDP. In addition, this new approach for discrete singular systems (DSS) is developed in order to cast the problem as a convex optimization involving linear matrix inequalities (LMIs), such that the controller can stabilize the overall system. This approach provides generalized quadratic stabilization for uncertain DSS and also extends the existing robust stabilization results for non-singular discrete systems with perturbation. The approach is illustrated here by means of numerical examples. [source]

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

ASIAN JOURNAL OF CONTROL, Issue 2 2005
Huijun Gao
ABSTRACT This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete-time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H, or l2 - l, sense with respect to all energy-bounded noise disturbances for all admissible uncertainties and time delays. Both delay-dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays. [source]