Motivated by the converse Lyapunov technique for investigating converse results of semistable switched systems in control theory, this paper utilizes a constructive induction method to identify a cost function for performance gauge of an average, multi-cue multi-choice ( MCMC ) , cognitive decision making model over a switching time interval. It shows that such a constructive cost function can be evaluated through an abstract energy called Lyapunov function at initial conditions. Hence, the performance gauge problem for the average MCMC model becomes the issue of finding such a Lyapunov function, leading to a possible way for designing corresponding computational algorithms via iterative methods such as adaptive dynamic programming. In order to reach this goal, a series of technical results are presented for the construction of such a Lyapunov function and its mathematical properties are discussed in details. Finally, a major result of guaranteeing the existence of such a Lyapunov function is rigorously proved.

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关于平均多线索多选决策的绩效评估：逆Lyapunov方法

基于逆Lyapunov技术研究控制理论中的半稳定切换系统的逆结果，本文采用一种构造性归纳方法来确定成本函数，用于平均，多线索多选（MCMC），认知决策的性能指标在切换时间间隔内建立模型。它表明，可以在初始条件下通过称为Lyapunov函数的抽象能量来评估这种建设性的成本函数。因此，平均MCMC模型的性能指标问题变成了找到这种Lyapunov函数的问题，从而导致了通过诸如自适应动态规划之类的迭代方法设计相应的计算算法的可能方式。为了达到这个目标，提出了一系列构造这种Lyapunov函数的技术结果，并详细讨论了其数学性质。最后，严格证明了保证这种Lyapunov函数存在的主要结果。