Robust adaptive control of uncertain nonlinear systems

The purpose of this research is to examine adaptive control strategies for certain classes of uncertain nonlinear systems. The problem can be formulated as a stochastic control problem as well as a deterministic disturbance attenuation problem which may be solved as a differential game problem using dynamic programming to determine an optimal feedback solution. Solutions for the class of uncertain linear systems with unknown control coefficients are developed and extended to more general classes of linear systems having uncertain state and measurement coefficients. A more general class of nonlinear systems having nominal linear dynamics perturbed by small polynomial functions of the state which multiply the state, control and measurements is considered. Using a perturbation approach, an approximate worst case adaptive compensator obtained from the resulting differential game problem is found. For polynomial nonlinearities, the elements which compose the approximate accumulation function associated with the estimation process are propagated forward in time by first order ordinary differential equations. This allows the approximate worst case state, and thereby the controller, to be determined explicitly without the state history smoothing that is required for general nonlinearities. Numerical examples including application to flight control are presented to illustrate the behavior of the resulting compensator structures.