Dual performance Stackelberg game for unknown nonlinear system with saturating input constraint
Xiaohong Cui, Huaguang Zhang, Binrui Wang · 2023
In this paper, the dual performance $\mathrm{H}_{2} / \mathrm{H}_{\infty}$ optimization problem for the nonlinear system with constrained input is solved. The hierarchical multi-player control is described in the framework of the Stackelberg game. The control input and the external disturbance are deemed as the leader and follower, which makes the individual decisions in different levels. Thus the hierarchical control is considered as a two-stage optimization problem. The coupled hierarchical leader-follower Hamilton-Jacobi(HJ) equations with considering the saturating and costate constraints are derived. The existence of the Stackelberg equilibrium is supplied. To avoid the requirement of the internal drift dynamic, a hierarchical integral learning algorithm is proposed for solving the dual performance problem, where the constraints are considered in the iteration steps. A single critic Neural Network(NN) is built to accomplish the designed learning scheme and lessen the computation burden. A nonlinear simulation example with considering the saturating input bound is given to show the effectiveness of the addressed online learning algorithm.