Optimal control and non-zero-sum differential game for Hurwicz model considering uncertain dynamic systems with multiple input delays

Uncertainty theory is a field in axiomatic mathematics committed to disposing of belief degrees. By dint of uncertain theory and Hurwicz criterion, this article mainly addresses optimal control and non-zero-sum differential game of uncertain delay dynamic systems, which are depicted as a sort of uncertain differential equation with multiple input delays. Employing the technology of dynamic programming, the optimality principle is put forward and the optimality equation is formulated simultaneously to deal with the optimal control problem. In addition, an equilibrium equation is derived to solve the Nash equilibrium for the multi-player non-zero-sum uncertain differential game on the strength of the proposed optimality equation. An example is devised to illustrate the availability of the results in the end.

Automated summary

Uncertainty theory in axiomatic mathematics aims to eliminate degrees of belief. This article focuses on the optimal control and non-zero-sum differential game of uncertain delay dynamic systems, using uncertainty theory and the Hurwicz criterion. By employing dynamic programming, the optimality principle is proposed and the optimality equation is formulated to solve the optimal control problem. Additionally, an equilibrium equation is derived to solve the Nash equilibrium in the multi-player non-zero-sum uncertain differential game based on the proposed optimality equation. An example is provided to illustrate the applicability of the results.