ADAPTIVELY CONTROLLING NONLINEAR-SYSTEMS, USING TRAJECTORY APPROXIMATIONS

The structure underlying most adaptive algorithms is a linear parametrized set. This set either represents the universe of controllers the adaptive algorithm can choose from in order to achieve the control task or it may represent a class of models the adaptive algorithm may exploit to approximate the open-loop plant behaviour. In the latter approach the controller used to close the loop is selected via some non-linear map of the identified model parameters. The emphasis is on approximating the vector field that generates the trajectories of the system. Alternatively we propose to predict the trajectories over a short period of time directly, not indirectly involving a representation of the underlying vector fields. The feasibility of such an approach using a one-step-ahead-type algorithm for both prediction and control is analysed. The scheme is hybrid in that the plant is continuous-time, whilst the control action is implemented in discrete time. The control action is of the model reference type. The algorithm is applied to a class of (non)-linear time-varying systems of a given structure (known relative degree) and possessing a stable inverse. Given input/output measurements only, the algorithm can enforce a desired response within guaranteed error bounds. Robustness properties with respect to partial state measurement (e.g. neglecting parasitic dynamics) and violation of the stable inverse assumption are investigated.