State-dependent indirect pseudospectral method for nonlinear optimal control problems.

The state-dependent Riccati equation (SDRE) method is an efficient approach to solve nonlinear optimal control problems (OCPs), but nonlinear necessary conditions for the first-order optimality are seldom met in the SDRE approach. In this paper, a state-dependent indirect pseudospectral (SDIP) technique is developed to design nonlinear optimal controllers. To preserve the nonlinearity of the system and reduce the computational cost as well, the state-dependent coefficient (SDC) parameterization technique is employed. Then the optimality conditions are derived under input and state constraints, and spectral methods are used to discretize the optimality conditions into a series of mixed linear complementarity problems (MLCPs). The developed SDIP method is able to handle the finite and infinite-horizon nonlinear OCPs in a unified framework. Numerical comparisons also verify the performance of the developed SDIP method.