AbWac-We propose a modification of the traditional adaptive backstepping method which leads to substantially less control effort in the problem of adaptive chaos control. Our technique, which is applicable to all system that exhibit chaotic behaviour and can be rendered into parametric strict feedback form, is based on a recently introduced Invariance Principle Extension and employs genetic algorithms to optimise the controller parameten. Simulations with the Chua's system are conducted to show the effectiveness of the approach.
Zndex Terms-Modified adaptive backstepping, optimised chaos control, genetic algorithms, uncertain Chua's system.
I. INlRODUCTlONANY electronic mechanical and chemical systems exhibit chaotlc dynarmcs. Because these irregular and unpredictable phenomena are usually undesirable in practice, as they restrict the operating range of many devices, the issue of controlling chaos has been an important research topic in recent years (see, e.g. 111).In real life applications, a complete knowledge of the chaotic system model is not always possible. If that is the case, special techniques are required to control the chaotic system. Basically there are two approaches to the control of an unknown chaotic system as far as feedback control is concemed: data-based control and model-based control. The daw-based approach usually follows the traditional OnGrebogy-Yorke (OGY) technique [ll], which consists in readjusting a control parameter each time the trajectory crosses the Poincark section. It converts a chaotic response into one of a large number of unstable periodic orbits embedded within the strange attractor. With delay coordinate embedding, the OGY method is applicable to situations in which a priori analytical knowledge of the system dynamics is not available. The application of the OGY method, however, is limited due to measurement errors [6]. Moreover, generally steady state solutions The authocs ace with the Machines, Components and intelligent Systems Depanment at the Faculty of Electrical and Computational Engineering, State Universily of Campinns, Campinas, SP, Brazil (phone: egrinits @dmcsi.fee.unicamp.br, bormru@dmcsi.fee.unicampbr).
Considera-se, neste trabalho, a sincronização otimizada de dois sistemas caóticos de Chua. Propõe-se um procedimento baseado em modificação da técnica de backstepping aliado a um algoritmo genético de forma a se conseguir um melhor desempenho na sincronização de dois sistemas de Chua em termos de esforço de controle em comparação ao método de backstepping tradicional. A modificação no backstepping clássico fundamenta-se em recente Extensão ao Princípio de Invariância de La Salle. Como ilustração da eficácia do método proposto, são apresentadas simulações em Matlab.
A-d-It is proposed an approach for adaptive neuralbased backstepping control for uncertain MIMO nonlinear systems that uses hvo neural networks in each backstepping design step. This leads to a more straightforward implementation when compared to methodologies that employ just o m NN in each design step, as the neural networks inputs here do not depend on derivatives of the virtual control laws. Furthermore, it is verified that the total number of NN's necessary to obtain an adequate tracking response is si@icantly reduced. Semiglobal uniform ultimate boundedeness of all the signals in the closed loop of the MIMO nonlinear system is achieved and all the outputs converge to small neighborhoods of the desired reference trajectories.
IEldax TI-Adaptive nonlinear control, neural-based backstepping, uncertain MIMO nonlinear systems.
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