Deterministic learning and neural control of a class of nonlinear systems toward improved performance
A deterministic learning theory was recently presented which states that an appropriately designed adaptive neural controller can learn the system internal dynamics while attempting to control a class of nonlinear systems in normal form. In this paper, we further investigate deterministic learning of the class of nonlinear systems with relaxed conditions, and neural control of the class of system toward improved performance. Firstly, without the assumption on the upper bound of the derivative of the unknown affine term, an adaptive neural controller is proposed to achieve stability and tracking of the plant states to that of the reference model. When output tracking is achieved, a partial PE condition is satisfied, and deterministic learning from adaptive neural control of the class of nonlinear systems is implemented without the priori knowledge on the upper bound of the derivative of the affine term. Secondly, by utilizing the obtained knowledge of system dynamics, a neural controller with constant RBF networks embedded is presented, in which the learned knowledge can be effectively exploited to achieve stability and improved control performance. Simulation studies are included to demonstrate the effectiveness of the results.
KeywordsDeterministic learning Input-to-state stability Small-gain theorem Adaptive neural control Learning control
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