Reduced order optimal control synthesis of a class of nonlinear distributed parameter systems using single network adaptive critic design

A computational tool is presented in this paper for the optimal control synthesis of a class of nonlinear distributed parameter systems. This systematic methodology incorporates proper orthogonal decomposition based basis function design followed by Galerkin projection, which results in a low-dimensional lumped parameter model. The optimal control problem in the reduced lumped parameter framework is then solved following the philosophy of recently developed 'single network adaptive critic (SNAC)' neural networks. This time domain solution is then mapped back to the distributed domain, which essentially leads to a closed form solution for the control variable in a state feedback form. Finite-element based numerical simulation results are presented for a one-dimensional benchmark nonlinear heat conduction problem.