Adaptive Finite-time Tracking Control for Class of Uncertain Nonlinearly Parameterized Systems with Input Delay
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Adaptive Finite-time Tracking Control for Class of Uncertain Nonlinearly Parameterized Systems with Input Delay Dajie Yao, Xiaofei Liu, and Jian Wu* Abstract: In this paper, the tracking problem for a class of uncertain nonlinearly parameterized systems with input delay based the adaptive finite-time control scheme is investigated. The Pade approximation method is employed to handle the input delay problem. In combination with the variable separation technique and standard backstepping design process, a novel adaptive finite-time control strategy with a learning parameter is developed, and a simplified control law established. It can be proved that the system output signal follows the reference signal in finite time and all signals of the system are bounded under this control strategy. The experimental results demonstrate the feasibility and efficiency of the scheme. Keywords: Adaptive finite-time control, input-delay, nonlinear parameterization.
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INTRODUCTION
In the past two decades, nonlinearly parameterized systems have received increasingly more attention [1–4] since they exist in many engineering fields. A common characteristic of nonlinearly parameterized systems is that they contain unknown parameters without a linear structure. The adaptive technique has been proposed to study the stabilization problem of these systems (see, e.g., [5–9]). In [5], by using the adaptive control method, the control issue of the target dynamic instability system is solved. By establishing the variable separation technique and adding the integrator method, the global adaptive control problem has been solved for a class of nonlinearly parameterized systems [6]. Unknown nonlinearities in musculoskeletal dynamics have been compensated by adaptive control laws in [9], and tracking the human calf motion problem has been solved by designing two robust adaptive controllers. In recent years, numerous interesting results on the finite-time control problem have been reported. It is well known that for a practical engineering system, when considering the influence of the time factor, the study of the finite-time stability is very significant. Research on finitetime stability has been naturally added the study of non-
linear systems [10–17]. For a class of nonlinear uncertain systems with p normal form [13], the global finite-time stabilization problem has been addressed. In addition, for uncertain nonlinear systems in [16], the neural network approximator method has been used to solve the finitetime tracking control problem. To overcome the bounded virtual state tracking error problem for a class of nonlinear systems with strict-feedback form [17], the full state constraints in finite time have been guaranteed by using new tan-type barrier Lyapunov functions. However, time delay that usually has a negative impact on the systems exists in many control systems, such as transmission systems, chemical reactions, and rocket launch systems. In recent years, many control problems
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