Adaptive Iterative Learning Control of Nonlinearly Parameterized Pure Feedback Nonlinear Systems
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Adaptive Iterative Learning Control of Nonlinearly Parameterized Pure Feedback Nonlinear Systems Hocine Benslimane1,2 · Abdesselem Boulkroune2 · Hachemi Chekireb1
Received: 7 June 2016 / Revised: 19 March 2017 / Accepted: 25 March 2017 © Brazilian Society for Automatics–SBA 2017
Abstract In this work, an adaptive iterative learning control scheme is proposed to deal with nonlinearly parameterized and completely non-affine pure feedback nonlinear systems. The considered systems are assumed to perform the same operation repeatedly under alignment condition. To overcome the design difficulty from non-affine structure of pure feedback system, mean value theorem is exploited to deduce affine appearance of state variables to be used as virtual controls and actual control. The nonlinearly connected parameters are separated from the local Lipschitz continuous nonlinear functions, and then iterative learning laws and adaptive iterative learning laws are designed. Lyapunov functional stability analysis method has been used to prove the stability of the closed-loop control system and the convergence of tracking error to zero as iteration goes to infinity. Simulation results are provided to illustrate the performance of the proposed scheme. Keywords Adaptive iterative learning control · Alignment condition · Backstepping method · Lyapunov functional theory · Nonlinear parametric functions · Pure feedback nonlinear systems
1 Introduction Various control approaches have been developed to satisfy increasing demands on the performance of control systems.
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Hocine Benslimane [email protected]
1
LCP, Department of Automatic Control, ENP, BP 182, 10 Avenue Hassan Badi, El-Harrach, Algiers, Algeria
2
LAJ, Department of Automatic Control, University of Jijel, BP 98, Ouled-Aissa, Jijel, Algeria
These approaches can be classified essentially into two main categories. The first category consists of those analytical design approaches based on an exact analytical model of the system under consideration. Many such control theories have been developed and have been successfully applied to a large class of control systems. However, analytical techniques do not find it easy to solve control problems concerning complex systems. The other category consists of intelligent control techniques based on an approximate numerical model of the system under consideration. Many such control theories have been developed to deal with complex systems using universal approximators. Although intelligent control can provide an alternative way to deal with poorly modeled systems, we usually need to have a detailed understanding of the system under consideration for this approach to be successful. For dynamical systems with repetitive operation over a fixed time interval, the designed control, whether derived from analytical or numerical approaches, will result in the same level of tracking error being repeated in every tracking interval. Iterative learning control (ILC) is an effective approach that can be used to overcome the shortcomings of such
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