Adaptively Controlling Nonlinear Continuous-Time Systems Using Neural Networks

Layered neural networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable continuous-time system, represented in a state space form. A transformation is made on the plant to decompose the plant into two parts: The first part is modeled and controlled by multilayer neural networks. The second part is unobservable and can not be directly influenced by the control; this part is assumed to be stable. The control law is defined in terms of the neural network model to control the plant to track a reference command. The network parameters are updated on-line according to the tracking error. A theorem is given on the convergence of i) the tracking error and ii) the weight updating. The simulation is performed using Advanced Continuous Simulation Language (ACSL).