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Optimality conditions for optimal impulsive control problems with multipoint state constraints

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Abstract

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.

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  1. Matrosov Institute for System Dynamics and Control Theory of SB RAS, Irkutsk, Russia

    Olga N. Samsonyuk

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  1. Olga N. Samsonyuk
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Correspondence to Olga N. Samsonyuk.

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The work is partially supported by the Russian Foundation for Basic Research, Projects Nos. 17-01-00733 and 18-01-00026.

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Samsonyuk, O.N. Optimality conditions for optimal impulsive control problems with multipoint state constraints. J Glob Optim 76, 625–644 (2020). https://doi.org/10.1007/s10898-019-00868-w

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