The Picard’s Iteration Method for Finding Feedback Control of Linear Quadratic Optimal Control Problems

In this paper, the Picard’s iteration method is proposed to determine the optimal control law for time invariant and time varying linear systems with quadratic performance using the closed-loop configuration. The idea consists in deriving the nonlinear matrix Riccati differential equation to be transformed into an equivalent linear differential Hamiltonian system, and to be solved by the Picard’s iteration method to determine the feedback gain matrix that serves to deduce the optimal control law. To show the efficiency of the proposed method for handling these kind of optimal control problems, numerical examples, time invariant and time-varying problems, are treated and comparison with other methods and the exact solution is made.