Infinite horizon multiobjective optimal control of stochastic cooperative linear-quadratic dynamic difference games
Infinite horizon multiobjective optimal control of stochastic cooperative linear-quadratic dynamic difference games
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DOI：
10.1016/j.jfranklin.2021.08.022
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Chenchen Peng;Weihai Zhang;Limin Ma
中科院分区：
文献类型：
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作者：
Chenchen Peng;Weihai Zhang;Limin Ma
本文研究了无限时域随机合作线性二次动态差分对策的正则和不定情形。首先，由于加权矩阵的约束和动态系统的线性性，证明了正则随机合作LQ差分对策的代价是自发凸的，从而得到了代价加权和最小化与Pareto最优控制的等价性.其次，在精确能观条件下，基于加权代数Riccati方程（WARE）的解导出了正则对策的Pareto最优控制，然后通过最优反馈增益矩阵和加权代数李雅普诺夫方程（WALE）的解确定了Pareto解。在此基础上，提出了一个新的不确定情形下保证费用凸的充分必要条件，并结合半定规划（SDP），研究了加权广义代数Riccati方程（WGARE）和加权广义代数李雅普诺夫方程（WGALE）的解的Pareto最优性.最后，以经济中的渔业管理博弈为例说明了所得结果.
This article is concerned with the infinite horizon stochastic cooperative linear-quadratic (LQ) dynamic difference game in both the regular and the indefinite cases. Firstly, due to the constraints imposed on the weighting matrices and the linearity of the dynamic system, the costs are shown to be convex spontaneously for the regular stochastic cooperative LQ difference game, which yields the equivalence between the minimization of the weighted sum of costs and the Pareto optimal control. Secondly, the Pareto optimal control is derived for the regular game on the ground of the solution to the weighted algebraic Riccati equation (WARE) under exact observability, and then Pareto solutions are identified via the optimal feedback gain matrices and the solution to the weighted algebraic Lyapunov equation (WALE). Moreover, a new criterion which is also necessary and sufficient is developed to guarantee the costs to be convex for the indefinite case, and the Pareto optimality is investigated based on the solutions to the weighted generalized algebraic Riccati equation (WGARE) and the weighted generalized algebraic Lyapunov equation (WGALE) combining with the semidefinite programming (SDP). Finally, the fishery management game in the economy is presented to illustrate the obtained results.