Adaptive Tracking Control for a Class of Nonaffine Nonminimum Phase Systems

A neural control synthesis method for output regulation based on backstepping combined with inverting design is considered for a class of single-input single-output nonaffine nonminimum phase nonlinear systems. Most previous backstepping approaches for nonminimum phase systems have been restricted to stabilization problems. By applying output regulation approach for nonminimum phase systems to a low dimensional auxiliary system, we show how the overall design procedure can be performed by recursive backstepping. At the final stage of backstepping, a controller is obtained by statically inverting a model and the modelling error is compensated by use of a neural network. The method does not need a fixed-point assumption nor a boundedness assumption on the time derivative of a control effectiveness term. Using Lyapunov´s direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the approach.