Adaptive Backstepping Learning Control for a Class of Nonlinear Time-Varying Systems

Abstract

Combining the backstepping approach with the Nussbaum-type function and backstepping technique, can pointwise integral mechanism, a novel adaptive repetitive guarantee uniform ultimate boundedness of the states. learning control for high-order nonlinear systems with In this paper, utilizing the backstepping approach, time-varying and time-invariant parameters is proposed. It can introducing a differential-difference parametric periodic be applied to the time-varying parametric uncertainty systems with unknown compact set, non-vanishing, rapid time-varying, adaptive law, we design a class of periodic adaptive control periodic and where the prior knowledge is the periodicity only. A mechanism for high-order nonlinear systems with mixed differential-difference adaptive law and an adaptive repetitive parameters. Constructing Lyapunov fuction, we guarantee that learning control one are constructed to ensure the asymptotic the tracking error converges to zero asymptotically convergence of the tracking error in the sense of square error in L 2 -norm sense. norm. Also, a sufficient condition of the convergence of the T method is given. A simulation example illustrates the In this paper, the L 2 T -norm of the function is effectiveness of the proposed method. f ( ) s t 2 Keywords-mixed parametric; nonlinear system; adaptive control; defined as f ( ) τ τ d , where, T is a known finite repetitive learning control; Lyapunov functional ∫ t T − positive constant. Ⅰ. IntroductionⅡ. Problem Description In many Industrial applications, the system power of the Consider a class of high-order nonlinear systems control object is completely unknown or partially unknown, then, the design problem of the controller of the uncertain nonlinear system becomes a challenging topic. Generally, if the configuration of the system power is known, i.e., the uncertainty of the system satisfies the condition of linear parameters, then, utilizing adaptive control law, the asymptotical tracking result is obtained[1],however, implementing adaptive control is still open difficult problem[2] [3].The concept of the repetitive control is firstly proposed in [4].In [4], convergence analysis is done in frequency domain by using small gain theorem. the repetitive control can effectively deal with the repetitive tracking control problem [6] or restrain periodic disturbance problem [7],and the repetitive control is extensively applied in the robot system [5] and the electromotion hydraulic pressure material checking system [8].When the period of uncertain parameters of the system is known in advance, in [9], by the pointwise integral mechanism, a new adaptive control approach characterized by periodic parameter adaptation is proposed, which complements periodic parameter adaptation control of the one-order uncertain system with mixed linear parameters, such that the tracking error converges to zero asymptotically in L 2 T -norm sense. In [10], a new method approach of designing a repetitive learning controller for a class of unmatched nonlinear systems with bot...

Adaptive iterative learning control of non-uniform trajectory tracking for strict feedback nonlinear time-varying systems with unknown control direction

“…In [7], a new method of designing a repetitive learning controller for a class of unmatched nonlinear systems with both completely unknown virtual control coefficients and unknown time-varying parameters was proposed, which by incorporating a Nussbaum-type function and backstepping technique, can guarantee uniform ultimate boundedness of the states. In [8], combining the backstepping approach with the pointwise integral mechanism, a novel adaptive repetitive learning control for high-order nonlinear systems with timevarying and time-invariant parameters was proposed. An iterative learning controller was presented for a class of strict-feedback nonlinear systems with time-varying uncertainties in [9].…”

Adaptive Iterative Learning Control of Non-uniform Trajectory Tracking for Strict Feedback Nonlinear Time-varying Systems

“…In [13], a new approach of designing a repetitive learning controller for a class of unmatched nonlinear systems with both completely unknown virtual control coefficients and unknown time-varying parameters was proposed, which by incorporating a Nussbaum-type function and backstepping technique, can guarantee uniform ultimate boundedness of the states. In [14], combining the backstepping approach with the pointwise integral mechanism, a novel adaptive repeti-tive learning control for high-order nonlinear systems with time-varying and time-invariant parameters was proposed. An iterative learning controller was presented for a class of strict-feedback nonlinear systems with time-varying uncertainties in [15].…”