Neural Network Control of Nonlinear Time-Delay System with Unknown Dead-Zone and Its Application to a Robotic Servo Syst
An adaptive controller is proposed for a class of nonlinear systems with unknown time-varying delays and a dead-zone input. Taking the dead-zone as a part of the system dynamics, the construction of the dead-zone inverse model is not needed and thus the c
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School of Automation, Beijing Institute of Technology, Beijing, 100081, P.R. China Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR UK {najing2120002,xmren}@bit.edu.cn, [email protected]
Abstract. An adaptive controller is proposed for a class of nonlinear systems with unknown time-varying delays and a dead-zone input. Taking the dead-zone as a part of the system dynamics, the construction of the dead-zone inverse model is not needed and thus the characteristic parameters of the dead-zone are not necessarily known. Unknown time delays are handled by introducing improved Lyapunov-Krasovskii functions, where the requirements on the delayed functions/control coefficients are further relaxed without the singularity problem. A novel high-order neural network with only a scalar weight parameter is developed to approximate unknown nonlinearities. The closed-loop system is proved to be semi-globally uniformly ultimately bounded (SGUUB). Experiments on a robotic servo system are provided to verify the reliability of the presented method. Keywords: Adaptive control, Dead-zone, Time-delay systems, Neural Networks, Servo systems.
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Introduction
The existence of an unknown dead-zone in the control input may severely limit the system performances, which has created significant attention in recent years in this field, such as [1]-[6]. Similarly, the existence of time-delays in the system also renders the control design much more difficult and challenging. Neural-based local linearization controls are proposed for uncertain nonlinear systems with input delay [7]-[8]. To deal with delays in system states, Lyapunov-Krasovskii functions have been widely utilized [9]-[12]. Novel integral Lyapunov functions and discontinuous functions can avoid the control singularity [9]-[11]. Inspired by previous work, this paper focuses on the adaptive tracking control design for a class of strict-feedback nonlinear time-delay systems with an
The work was supported by National Natural Science Foundation of China (No.60974046), Royal Society (Research Grant/Round 2007/R2), and a joint grant between the National Natural Science Foundation of China and Royal Society UK under grant No.61011130163/JP090823. Jing Na was also supported by Chinese Scholarship Council (No.2008603002).
P. Vadakkepat et al. (Eds.): FIRA 2010, CCIS 103, pp. 338–345, 2010. c Springer-Verlag Berlin Heidelberg 2010
NN Control of System with Dead-Zone and Application to Robotic System
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unknown dead-zone input and time-varying delays. The control singularity problem and the unknown time-delays are all handled by introducing an improved Lyapunov-Krasovskii function. Compared with some existing results on the adaptive control for time-delay systems [9], [10], the slightly restrictive information on the bounds of the delayed functions or control coefficients is not required [13], [15]. The unknown dead-zone is taken as a part of the system dynamics, and then handled without using any characteristic parameter and inverse dead-zone model. More
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