Showing papers by "Petar V. Kokotovic published in 1990"

Global stabilization of partially linear composite systems

Abstract: A linear stabilizable, nonlinear asymptotically stable, cascade system is globally stabilizable by smooth dynamic state feedback if (a) the linear subsystem is right invertible and weakly minimum phase, and, (b) the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output. Both of these conditions are coordinate-free and there is freedom of choice for the linear output variable. This result generalizes several earlier sufficient conditions for stabilizability. Moreover, the weak minimum-phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem.

Observer-based Adaptive Control of Nonlinear Systems Under Matching Conditions

Abstract: A new adaptive scheme that requires only output (instead of full-state) measurement is developed for a class of linearizable systems. This class is restricted by an output-matching condition and by sector-type conditions on the nonlinearities multiplying unknown parameters. The adaptive scheme consists of a certainty-equivalence control utilizing state estimates generated by an adaptive observer and parameter estimates generated by a prediction-error-type estimator.

Indirect adaptive output-feedback control of a class on nonlinear systems

Abstract: The authors present an indirect model-reference adaptive control scheme, which requires only output measurement, for SISO full-linearizable minimum-phase nonlinear systems. The nonlinearities are assumed to satisfy an output-matching condition, and only sector-type nonlinearities are allowed to multiply unknown parameters. The adaptive scheme consists of a certainty-equivalence control law and a prediction-error-type parameter estimator. >

Robustness of adaptive nonlinear control under an extended matching condition1

Abstract: A new direct adaptive regulation scheme is proposed for nonlinear systems satisfying an extended matching condition. For this class of systems, the usual overparametrization in parameter estimates is avoided. Conditions are given, under which some of the obtained local results become global. It is also shown that the new scheme is robust with respect to unmodeled dynamics.

Adaptive Control Design for a Class of Nonlinear Systems

Abstract: The proposed adaptive scheme achieves regulation without restricting the nonlinearities by any growth conditions. Motivated by many systems of practical importance, such as most types of electric motors, the dependence on the unknown parameters is restricted by an extended matching condition.

Boundedness conjecture for an output error adaptive algorithm

Abstract: This paper compares conditions for instability with conditions for global asymptotic stability of a discretetime output error adaptive estimation algorithm. This comparison leads to a boundedness conjecture which states that all signals within this adaptive system as well as the output error and parameter estimates remain globally bounded for all time despite any unstable behaviour. The investigation into the stability properties of this algorithm begins with a global stability criterion applied to a transfer function which is not strictly positive real. This criterion states that for large enough adaptation gain and/or input signal magnitude the system will be asymptotically stable. Then a local result is applied which states that for small enough adaptation gain and/or input signal magnitude the same system is unstable. The result is a bifurcation due to the decrease of the adaptation gain and/or input signal magnitude as the system goes from asymptotic stability to instability which remains bounded. The results suggested by the computer simulations are verified by an exact analysis of a linearized periodic version of the adaptive system.

Robust Adaptive Nonlinear Control Under Extended Matching Conditions

Abstract: : A new direct adaptive regulation scheme is proposed for nonlinear systems satisfying extended matching conditions. Two sets of additional conditions are given: first, for the regulation to be global, and second, for asymptotic parameter convergence. It is also shown that the new scheme is robust with respect to unmodeled dynamics. Keywords: Robust adaptive nonlinear control, Nonlinear systems, Matching.