On-line modeling and inverse optimal control of a class of unknown nonlinear systems using dynamic neural networks

This dissertation presents a Dynamic Neural Network (DNN) modeling and inverse optimal control for a class of unknown nonlinear systems which are observable, controllable and feedback linearizable.; First, a DNN is considered for modeling of a class of unknown nonlinear systems that are controllable and feedback linearizable. At this stage, it is assumed that we have access to the states of the system. Using Lyapunov technique the stability of the controlled system is proven.; In the next section, it is assumed that the states of the system are unknown and that the input and output of the unknown system are the only available data. A nonlinear observer is designed to estimate the states of the equivalent DNN model of the system. The DNN model and its estimated states are then used for the design of an adaptive observer-based stabilizing controller.; Next, the results of stabilization problem are extended to tracking problem where the output of the system follows a given reference output. A second DNN model is introduced to generate a set of reference states such that when the estimated states of the DNN model follow the reference states then the actual output of the system follows the reference output. Using the state error equation, an observer-based adaptive control design is proposed to force the output tracking error to zero.; Finally, a control strategy is proposed to design an inverse optimal control for an unknown nonlinear system that is observable, controllable and feedback linearizable, using only input-output data of the system. First, a stabilizing control is designed and, then, an inverse optimal control is proposed along with a control Lyapunov function (CLF), which satisfies the Hamilton-Jacobi-Bellman equation for a meaningful cost function.; Numerical examples are given for each section and simulation results are shown to illustrate the effectiveness of the proposed methods.