The use of adaptive multiple models for predefined exponential stability of control systems of uncertain discrete-time nonlinear objects

In this work, an adaptive multiple model pre-assigned exponential convergence control scheme based on the time varying exponential function is demonstrated for a class of discrete-time nonlinear systems. For coping with the noncausality problem from previous adaptive backstepping design method of nonlinear discrete-time systems, a first-order recursive filter is used in controller design procedures and the n-step prediction model is not needed, thereby reducing the computational burden effectively. The time varying function is employed to force all states variables to convergence to zero with a pre-defined rate which does not rely on the initial conditions of systems. In addition, the multiple model set is constructed to address unknown parameters problem and further the second level adaptive algorithm of unknown parameters is developed. A characteristic feature of the second-level multi-model adaptation algorithm is that it dynamically adapts to time changes in the identified model (it uses identification information better than the switching multiple model control). In a unified framework of second level adaption, a first-order recursive filter and backstepping technique, a pre-assigned exponential convergence controller is presented. Finally, the results about discrete-time pre-assigned exponential convergence method are compared with other methods using two case studies.