Optimistic value based optimal control for uncertain linear singular systems and application to a dynamic input-output model

• Published in: ISA transactions Vol. 71; no. Pt 2; pp. 235 - 251
• Main Authors: Shu, Yadong, Zhu, Yuanguo
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.11.2017
• Subjects: Equation of optimality; Optimal control; Optimistic value; Recurrence equation; Uncertain singular system; Equation of optimality; Recurrence equation; Optimistic value; Optimal control; Uncertain singular system
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2017.08.007

In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained. •Optimal control problems subject to uncertain discrete-time (and continuous-time) singular systems are considered under optimistic value criterion.•Employing Bellman’s principle of optimality, a recurrence equation is presented to study uncertain discrete-time optimal control models.•The corresponding optimal controls are bang-bang provided that the objective function is linear in an uncertain discrete-time optimal control problem.•An equation of optimality is derived to solve optimal control problems for uncertain continuous-time singular systems if the input vector is derivable.•A dynamic input-output model is investigated as an application to illustrate the results obtained.