Robust/optimal temperature profile control using neural networks

An approximate dynamic programming (ADP) based neurocontroller is developed for a heat transfer application. Heat transfer problem for a fin in a car's electronic module is modeled as a nonlinear distributed parameter (infinite-dimensional) system by taking into account heat loss and generation due to conduction, convection and radiation. A low-order, finite-dimensional lumped parameter model for this problem is obtained by using Galerkin projection and basis functions designed through the 'Proper Orthogonal Decomposition' technique (POD) and the 'snap-shot' solutions. A suboptimal neurocontroller is obtained with a single-network-adaptive-critic (SNAC). Further contribution of this paper is to develop an online robust controller to account for unmodeled dynamics and parametric uncertainties. A weight update rule is presented that guarantees boundedness of the weights and eliminates the need for persistence of excitation (PE) condition to be satisfied. Since, the ADP and neural network based controllers are of fairly general structure, they appear to have the potential to be controller synthesis tools for nonlinear distributed parameter systems especially where it is difficult to obtain an accurate model.