Multicriteria optimization problems of finite horizon stochastic cooperative linear-quadratic difference games
Multicriteria optimization problems of finite horizon stochastic cooperative linear-quadratic difference games
复制标题
DOI：
10.1007/s11432-020-3177-8
复制
发表时间：
2022-06
期刊：
影响因子：
--
通讯作者：
Chenchen Peng;Weihai Zhang
中科院分区：
文献类型：
--
作者：
Chenchen Peng;Weihai Zhang
本文研究了有限时间内正则和不定随机合作线性二次差分对策的Pareto最优性。通过定义几个有界线性算子序列，得到了线性随机差分系统解的一般形式和线性性质。在加权矩阵的约束下，正则合作对策的性能指标的凸性可以自然地得到保证，加权技术可以很好地刻画Pareto最优性。我们还建立了一个新的凸性准则的不确定合作对策的成本泛函，其中我们发现，性能指标的加权和的最小化是等价的帕累托最优策略。为了得到所有的Pareto最优策略和解，我们给出了一个计算算法，使用加权差分Riccati方程和加权差分李雅普诺夫方程的规则和不确定的情况下。我们提出了一个实际的例子，在经济上验证的结果。
This paper investigates the Pareto optimality of the regular and the indefinite stochastic cooperative linear-quadratic difference games in a finite time horizon. We derive a general form and a linear property of the solution to the linear stochastic difference system by defining several sequences of bounded and linear operators. The performance criteria’s convexity can be guaranteed naturally under the weighted matrices’ constraints for the regular cooperative game, and the weighting technique can well characterize the Pareto optimality. We also establish a novel convexity criterion for the cost functionals of the indefinite cooperative game, in which we find that the minimization of the performance criteria’s weighted sum is equivalent to the Pareto optimal strategies. To derive all the Pareto optimal strategies and solutions, we present a computing algorithm using the weighted difference Riccati equation and the weighted difference Lyapunov equation for the regular and the indefinite cases. We present a practical example in the economy to validate the results.