Solutions of nonlinear constrained optimal control problems using quasilinearization and variational pseudospectral methods

Abstract

An alternative method for nonlinear constrained optimal control problems is developed in this paper. The proposed method converts the nonlinear optimal control problem into a sequence of constrained linear quadratic (LQ) optimal control problems using quasilinearization methods. And then we present a variational pseudospectral method based on dual variational principles and pseudospectral approximations in order to transform the constrained LQ problem into standard linear complementary problems (LCPs) which can be solved easily. The proposed method is highly efficient due to the benefits of qualsilineaization techniques and the sparse and symmetric properties of coefficient matrixes obtained by variational principles. And solutions of high precisions can be obtained with few time nodes and boundary conditions can be prescribed because of pseudospectral approximations. Besides, extra costate estimations are not required simply because this method is constructed by dual variational principles. Several numerical examples are simulated and comparisons between different methods are offered to demonstrate effectiveness and advantages of the proposed method.