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In this paper a special case of the Regulator Problem with Internal Stability (RPIS) [1] is studied from the standpoint of obtaining solutions that are insensitive to perturbations in both the system parameters and the controller gains. The ability to include "robustness" into the problem yields new insight into the role played by dynamic compensation in linear control system synthesis.

Robust control for nonlinear uncertain systems has been solved for matched uncertainty but has not been completely solved yet for unmatched uncertainty. This paper developed a new method in which an adaptive radial basis function neural network is used to compensate for the effects of unmatched uncertainty in the framework of integral sliding mode control. The stability of the whole system is guaranteed by the Lyapunov method. The adaptation algorithm of the network is also derived by the Lyapunov function so that its convergence is also guaranteed. A numerical example is used to show the effectiveness of the proposed method. Improvement against existing methods is also demonstrated.

Sufficient conditions for the stability of self-organizing control algorithms based on a subgoal approach are given. A method is presented which aids in the a-priori choice of the structure of the feedback control law under the assumption that on-line or off-line identification of the structure of the plant has been accomplished. Subsequent to closing the loop, bounds, which depend on the control law chosen on the performance index say be estimated. Illustrative examples are presented.