Uncertain random linear quadratic control with multiplicative and additive noises

Abstract

This paper studies two types of linear quadratic (LQ) optimal control models for multistage uncertain random systems. The first model is an LQ model with additive noises, while the second model is an LQ model with both multiplicative noises and additive noises. Chance theory is a useful tool to deal with the analysis of indeterminacy including both uncertainty and randomness. Based on Bellman's principle and chance theory, the recurrence equations are presented for settling such optimal control problems. Then, by applying recurrence equations, the analytical expressions are derived for solving both the optimal objective function and optimal control strategies of the LQ models. Meanwhile, an application and a numerical example are provided to show the effectiveness of our results.

Linear quadratic control for multiple time‐delayed uncertain random systems

“…These systems can be found in a number of contexts, including game problems [24], portfolio selection [25], and reliability analysis [26]. Chance theory is a useful technique for dealing with uncertain random control problems [27][28][29][30].…”

“…Based on the chance theory and dynamic programming method, this paper proposes the recurrence equations in uncertain random environments to solve the optimization problem. Compared with Chen and Zhu [28,29], we all discussed the uncertain random LQCPs according to the dynamic programming method. Chen and Zhu [28,29] discussed the LQCPs with positive definite control weighting matrices.…”

“…Compared with Chen and Zhu [28,29], we all discussed the uncertain random LQCPs according to the dynamic programming method. Chen and Zhu [28,29] discussed the LQCPs with positive definite control weighting matrices. And the time delay does not take into account in Chen and Zhu [28,29].…”

“…Chen and Zhu [28,29] discussed the LQCPs with positive definite control weighting matrices. And the time delay does not take into account in Chen and Zhu [28,29]. Here, we consider time-delayed LQCPs with positive definite and indefinite control weighting matrices.…”

Two‐person games for uncertain random singular dynamic systems

“…Meanwhile, Qin [35] showed that uncertainty as well as randomness could coexist in a portfolio optimization problem, and addressed this problem via chance theory. Subsequently, uncertain random optimal control problems [36,37] were constructed exerting chance theory. Game problem is essentially a multi-person multi-objective optimal control problem.…”