Simple robust adaptive control for a class of non-linear systems: An adaptive signal synthesis approach

A simple robust adaptive control is presented for a class of non-linear systems with parameter uncertainty and under bounded disturbances. In the proposed scheme, assuming that a nominal control law, designed with the knowledge of the plant parameters ensures the uniform asymptotic stability of the closed loop system in the absence of the parameter uncertainty and free of disturbances, an adaptive compensation signal is synthesized to guarantee the uniform ultimate stability (Corless, M., and G. Leitmann, IEEE Trans. Automatic Control, AC-26, 1139-1144 (1981)) in the presence of the uncertainty and disturbances. Unlike in traditional parameter adaptive control, in this adaptive signal synthesis approach only the upper bounds on the parameter uncertainty and disturbances are updated. This gives a simple control law for its implementation, since the difficulty of tuning numerous adaptation gains is avoided, and robustness with respect to disturbances, since the parameter drift due to disturbances is overcome. A simulation example is included to illustrate the main features of this approach.