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 appr oximator is developed and its universal approximation capability is proved. The controller architecture is based on adaptive feedback linearization pl us sliding mode control. A time varying activation region is introduced for efficient self-organization of the approximator during operation. We modif y the adaptive control approach for piecewise linens approximation and self -organizing structures. In addition, we provide analyses of asymptotic stab ility of the tracking error and parameter convergence for the proposed adap tive control scheme with the on-line self-organizing structure, The method with a deadzone is also discussed to prevent a high-frequency input which m ight excite the unmodeled dynamics in practical applications. The applicati on of the piecewise linear adaptive control method is demonstrated by a com putational simulation.