Integrated optimal control and parameter estimation algorithms for discrete-time nonlinear stochastic dynamical systems

This thesis describes the development of an efficient algorithm for solving nonlinear stochastic optimal control problems in discrete-time based on the principle of model-reality differences. The main idea is the integration of optimal control and parameter estimation. In this work, a simplified model-based optimal control model with adjustable parameters is constructed. As such, the optimal state estimate is applied to design the optimal control law. The output is measured from the model and used to adapt the adjustable parameters. During the iterative procedure, the differences between the real plant and the model used are captured by the adjustable parameters. The values of these adjustable parameters are updated repeatedly. In this way, the optimal solution of the model will approach to the true optimum of the original optimal control problem. Instead of solving the original optimal control problem, the model-based optimal control problem is solved. The algorithm developed in this thesis contains three sub-algorithms. In the first sub-algorithm, the state mean propagation removes the Gaussian white noise to obtain the expected solution. Furthermore, the accuracy of the state estimate with the smallest state error covariance is enhanced by using the Kalman filtering theory. This enhancement produces the filtering solution by using the second sub-algorithm. In addition, an improvement is made in the third sub-algorithm where the minimum output residual is combined with the cost function. In this way, the real solution is closely approximated. Through the practical examples, the applicability, efficiency and effectiveness of these integrated sub-algorithms have been demonstrated through solving several practical real world examples. In conclusion, the principle of modelreality differences has been generalized to cover a range of discrete-time nonlinear optimal control problems, both for deterministic and stochastic cases, based on the proposed modified linear optimal control theory