A Stackelberg strategy for continuous-time mixed H2/H∞ control problem with time delay

This paper is concerned with the mixed H2/H∞ control with linear continuous time system and time delay. To deal with this, we presents a Stackelberg strategy by treating the control input and the disturbance as leader and follower, respectively. The leader＇s control strategy minimizes the cost function which is in H2 norm and the follower＇s control strategy maximizes the cost function which is in H∞ norm. The main technique of this paper is deal with the noncausal relationship of the variables caused by time delay in the control input by introducing two costates to capture the future information and one state to capture the past information. Through theory analyzing, the Stackelberg strategy exists uniquely. Moreover, with the assistance of the extended state space expression, the explicit expression of the strategy is obtained.

Equalizer Zero-Determinant Strategy in Discounted Repeated Stackelberg Asymmetric Game

This paper focuses on the performance of equalizer zero-determinant(ZD)strategies in discounted repeated Stackelberg asymmetric games.In the leader-follower adversarial scenario,the strong Stackelberg equilibrium(SSE)deriving from the opponents’best response(BR),is technically the optimal strategy for the leader.However,computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states.To this end,the authors propose an equalizer ZD strategy,which can unilaterally restrict the opponent’s expected utility.The authors first study the existence of an equalizer ZD strategy with one-to-one situations,and analyze an upper bound of its performance with the baseline SSE strategy.Then the authors turn to multi-player models,where there exists one player adopting an equalizer ZD strategy.The authors give bounds of the weighted sum of opponents’s utilities,and compare it with the SSE strategy.Finally,the authors give simulations on unmanned aerial vehicles(UAVs)and the moving target defense(MTD)to verify the effectiveness of the proposed approach.

Feedback Stackelberg Solution for Mean-Field Type Stochastic Systems with Multiple Followers

This paper discusses feedback Stackelberg strategies for the continuous-time mean-field type stochastic systems with multiple followers in infinite horizon.First,optimal control problems of the followers are studied in the sense of Nash equilibrium.With the help of a set of generalized algebraic Riccati equations(GAREs),sufficient conditions for the solvability are put forward.Then,the leader faces a constrained optimal control problem by transforming the cost functional into a trace criterion.Employing the Karush-Kuhn-Tucker(KKT)conditions,necessary conditions are presented in term of the solvability of the cross-coupled stochastic algebraic equations(CSAEs).Moreover,feedback Stackelberg strategies are obtained based on the solutions of the CSAEs.In addition,an iterative scheme is introduced to obtain efficiently the solutions of the CSAEs.Finally,an example is given to shed light on the effectiveness of the proposed results.

Revenue-sharing contract to coordinate independent participants within the supply chain

To improve the performance of the supply chain with one supplier and multiple retailers under deterministic price-sensitive customer demand, an optimal strategy is proposed based on knowledge discovery. First the decentralized system in which the supplier and the retailers are independent, profit-maximizing participants with the supplier acting as a Stackelberg game leader is studied. Numerical examples illustrate the importance of the coordination. The conventional quantity discount mechanism needs to be modified to coordinate the supply chain, so a revenue-sharing contract is proposed to coordinate such supply chain. Lastly, a special decision under certain demand rates is studied. The pricing and replenishment policies can be decided sequentially, which yields much less loss comparing with optimal decision when the demand rates are sufficiently large.