Linear Full-Information Feedback Approach to Closed-Loop Stackelberg Strategy

Stackelberg strategy has received great attention since the 1970s. The closed-loop solution still faces many difficulties though the open-loop problems have been well studied. An obvious fact for the difficulty is that the optimal closed-loop solution to the Stackelberg strategy is implicit nonlinear. By presenting a novel approach of full-information linear feedback strategy, substantial progress for the problem is made in this paper. We are the first to present explicit linear closed-loop Stackelberg controllers in terms of the current state and Riccatilike equations. Due to the elegance and simplicity of the solution, the proposed results will be extended to other game control problems with asymmetry status players. More importantly, the Q-Iearning algorithm for the Stackelberg strategy will become possible with the proposed optimal solution.