Inverse optimal controller design based on multi-objective optimization criteria for discrete-time nonlinear systems

This paper proposes an inverse optimal controller design method for discrete-time affine nonlinear systems that relies on a multi-objective optimization criterion. Inverse optimal control approach circumvents the tedious task of solving the Hamilton-Jacobi-Bellman equation (HJB) that results from the classical solution of the nonlinear optimal control problem. Here, the inverse optimal controller is based on defining an appropriate quadratic control Lyapunov function (CLF) where the parameters of this candidate CLF were optimized in an off-line manner by using Big Bang-Big Crunch algorithm. The root-mean-square-error (RMSE) of system states with respect to a reference trajectory and the sum-of-squares of control effort are utilized as the multi-objective optimization criterion in the Big Bang-Big Crunch optimizing algorithm. In order to test the performance of the proposed method, a nonlinear example from the literature of inverse optimal control is taken into consideration. The simulation results enlighten the designer in making a choice between the classical inverse optimal control solution and the multi-objective function included case.