Nonlinear adaptive control using networks of piecewise linear approximators

This paper presents a stable nonparametric adaptive control approach using a piecewise local linear approximator. The continuous piecewise linear approximator is developed and its universal approximation capability is proved. The controller architecture is based on adaptive feedback linearization plus sliding mode control. A time varying activation region is introduced for efficient self-organization of the approximator during operation. We modify the adaptive control approach for piecewise linens approximation and self-organizing structures. In addition, we provide analyses of asymptotic stability of the tracking error and parameter convergence for the proposed adaptive control scheme with the on-line self-organizing structure, The method with a deadzone is also discussed to prevent a high-frequency input which might excite the unmodeled dynamics in practical applications. The application of the piecewise linear adaptive control method is demonstrated by a computational simulation.