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Adaptive control of a class of multivariable nonaffine systems

A neural synthesis method is considered for a class of multivariable nonaffine uncertain systems. The method extends the previous approach developed in a single-input single-output system to a multi-input multi-output system without resorting to a fixed-point assumption or boundedness assumption on the time derivative of a control effectiveness term. By assuming that the uncertain input matrix term is dominated by the known part of the input matrix, we show that a new inverting method can be developed taking nonaffineness into account for its synthesis procedure. Using Lyapunov's direct method, it is shown that all the signals of the closed- loop system are uniformly ultimately bounded, and that the tracking error converges to an adjustable neighborhood of the origin. Simulation with a double Van Der Pol system having nonaffine control terms illustrates the approach.