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Abstract: In this paper, adaptive control is studied for a class of single-input–single-output (SISO) nonlinear discrete-time systems in strict-feedback form with nonparametric nonlinear uncertainties of the Lipschitz type. To eliminate the effect of the nonparametric uncertainties in an unmatched manner, a novel future states prediction is designed using states information at previous steps to compensate for the effect of uncertainties at the current step. Utilizing the predicted future states, constructive adaptive control is developed to compensate for the effects of both parametric and nonparametric uncertainties such that global stability and asymptotical output tracking is achieved. The effectiveness of the proposed control law is demonstrated in the simulation. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the robustness of adaptive controllers designed using the standard backstepping technique with respect to unmodeled dynamics involving unknown input time delay. While noting that some results on robust stabilization of non-minimum phase systems using the backstepping technique are available, we realize that the standard adaptive backstepping technique has only been shown applicable to unknown minimum phase systems. Another significance of our result is to enable the class of systems stablizable by adaptive backstepping controllers to cross the boundary of minimum phase systems, since systems with input time delay belong to non-minimum phase systems. Moreover, the and norms of the system output are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. [Copyright &y& Elsevier]

We develop a new adaptive gain-scheduling control scheme for continuous-time linear systems with polytopic uncertainties. The gain-scheduled control law is proposed as a convex sum of a fixed set of controller gains, exploiting the polytopic representation of the system uncertainty, which is not possible with classical robust control results in the literature. To realize this scheme, an adaptation law is proposed to adaptively provide the tuning parameter for the gain-scheduling implementation. The admissible domain of the stabilizing control feedback gains, defined by the fixed set of controller gains, can be determined offline by solving a set of linear matrix inequality constraints over a scalar line search. Using Lyapunov-based arguments, the proposed design conditions and the adaptation law ensure that all closed-loop signals are bounded. In particular, if the uncertain parameters are not time-varying, then the system states asymptotically converge to the origin. Theoretical arguments and appropriate numerical illustrations are provided to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]