| In this dissertation, two systematic optimal control synthesis techniques are presented for distributed parameter systems based on the adaptive critic neural networks. Following the philosophy of dynamic programming, this adaptive critic optimal control synthesis approach has many desirable features, viz. having a feedback form of the control, ability for on-line implementation, no need for approximating the nonlinear system dynamics, etc. More important, unlike the dynamic programming, it can accomplish these objectives without getting overwhelmed by the computational and storage requirements. First, an approximate dynamic programming based adaptive critic control synthesis formulation was carried out assuming an approximation of the system dynamics in a discrete form. A variety of example problems were solved using this proposed general approach. Next a different formulation is presented, which is capable of directly addressing the continuous form of system dynamics for control design. This was obtained following the methodology of Galerkin projection based weighted residual approximation using a set of orthogonal basis functions. The basis functions were designed by with the help of proper orthogonal decomposition, which leads to a very low-dimensional lumped parameter representation. The regulator problems of linear and nonlinear heat equations were revisited. Optimal controllers were synthesized first assuming a continuous controller and then a set of discrete controllers in the spatial domain. Another contribution of this study is the formulation of simplified adaptive critics for a large class of problems, which can be interpreted as a significant improvement of the existing adaptive critic technique. |
