Multidimensional uncertain optimal control with jump

Deng, Liubao; Zhu, Yuanguo

doi:10.1109/icsai.2012.6223502

Cited by 9 publications

(13 citation statements)

References 22 publications

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“…Definition 2.2. (Deng and Zhu 17 ). An uncertain process V t is said to be a V-jump process with parameters r 1 and r…”

Section: Theorem 22 (Sheng and Zhumentioning

confidence: 99%

“…Yang and Gao 16 studied an uncertain differential game. Taking the influence of some external extreme events or noises on uncertain dynamic systems into account, Deng and Zhu [17][18][19] and Deng 20 further studied some expected value models of optimal control problem for uncertain dynamic systems with jump and the equations of optimality were derived.…”

Section: Introductionmentioning

confidence: 99%

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Hurwicz model of uncertain optimal control with jump

Deng

Shen

Chen

2020

Math Methods in App Sciences

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How to choose the optimization criterion of the objective function is an important issue for uncertain optimal control. The Hurwicz criterion is a flexible optimization criterion attempting to find the intermediate area between the extremes posed by the optimistic and pessimistic criteria. Based on uncertainty theory, in this paper, we establish a new uncertain optimal control model with jump by making use of Hurwicz criterion to optimize an uncertain objective function. By applying Bellman's principle of optimality, the principle of optimality for the proposed model is presented and then the equation of optimality is derived. Finally, an example is given to show the the effectiveness of the results obtained.

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“…Definition 2.2. (Deng and Zhu 17 ). An uncertain process V t is said to be a V-jump process with parameters r 1 and r…”

Section: Theorem 22 (Sheng and Zhumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hurwicz model of uncertain optimal control with jump

Deng

Shen

Chen

2020

Math Methods in App Sciences

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“…V -jump uncertain processes proposed by Deng et al [26] were often used to describe the evolution of an uncertain phenomenon with jumps, in which the uncertain process may undergo a sudden change because of emergency such as economic crisis, outbreaks of infectious diseases, earthquake, war, etc. The definition of V -jump uncertain process is as follows.…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness, and stability of uncertain delay differential equations with V-jump

Jia

Liu

2020

Adv Differ Equ

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No previous study has involved uncertain delay differential equations with jump. In this paper, we consider the uncertain delay differential equations with V-jump, which is driven by both an uncertain V-jump process and an uncertain canonical process. First of all, we give the equivalent integral equation. Next, we establish an existence and uniqueness theorem of solution to the differential equations we proposed in the finite domain and the infinite domain, respectively. Once more, the concept of stability for uncertain delay differential equations with V-jump is proposed. In addition, the sufficient condition for stability theorem is derived. To judge existence, uniqueness, and stability briefly, we provide some examples in the end.

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“…Especially, uncertain bang‐bang optimal control problems were discussed in . Deng and Zhu investigated a kind of optimal control problems for an uncertain dynamic system with jump. Chen and Zhu discussed an uncertain control model with time‐delay.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Optimal Control Approach for CO₂ Mitigation Problem

Sheng

Zhu

Yan

et al. 2017

Asian Journal of Control

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The new types of uncertain control approaches based on the critical value criterion and chance criterion are respectively introduced to deal with multi-stage dynamic optimization problems in the presence of target constraints. Integrating the method of dynamic programming with the viability approach, the solving procedure of the optimal control sequence is provided. As a case study, a cost-effectiveness problem of mitigation policies for uncertain carbon dioxide emissions is analyzed and numerically computed to illustrate the proposed approaches.

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Multidimensional uncertain optimal control with jump

Cited by 9 publications

References 22 publications

Hurwicz model of uncertain optimal control with jump

Hurwicz model of uncertain optimal control with jump

Existence, uniqueness, and stability of uncertain delay differential equations with V-jump

Uncertain Optimal Control Approach for CO₂ Mitigation Problem

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Multidimensional uncertain optimal control with jump

Cited by 9 publications

References 22 publications

Hurwicz model of uncertain optimal control with jump

Hurwicz model of uncertain optimal control with jump

Existence, uniqueness, and stability of uncertain delay differential equations with V-jump

Uncertain Optimal Control Approach for CO2 Mitigation Problem

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Uncertain Optimal Control Approach for CO₂ Mitigation Problem