Optimality conditions for optimal impulsive control problems with multipoint state constraints

• Published in: Journal of global optimization Vol. 76; no. 3; pp. 625 - 644
• Main Author: Samsonyuk, Olga N.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-03-2020; Springer; Springer Nature B.V
• Subjects: Advertising expenditures; Analysis; Computer Science; Control systems; Mathematics; Mathematics and Statistics; Nonlinear programming; Operations Research/Decision Theory; Optimization; Real Functions; Trajectory control; Well posed problems; 49K21; 34A37; Global optimality conditions; Measure-driven differential equations; Impulsive control; 34H05; Trajectories of bounded variation
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-019-00868-w

This paper addresses an optimal impulsive control problem whose trajectories are functions of bounded variation and impulsive controls are regular vector measures. This problem is characterized by two main features. First, the dynamical control system to be considered may not possess the so-called well-posedness property. Second, the constraints on the one-sided limits of states are presented. Such constraints are interpreted as multipoint state constraints. For this problem, we derive global optimality conditions based on using of compound Lyapunov type functions which possess strongly monotone properties with respect to the control system. As a motivating case, a model of advertising expenses optimization for mutually complementary products is considered. For this model, we propose four variants of resolving sets of Lyapunov type functions and explain the technique of applying the optimality conditions.