Qualitative analysis of an infinite horizon optimal control problem of a shallow lake. (English) Zbl 1521.49018
Olenev, Nicholas (ed.) et al., Optimization and applications. 13th international conference, OPTIMA 2022, Petrovac, Montenegro, September 26–30, 2022. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 13781, 121-132 (2023).
Summary: This paper studies a classical infinite horizon optimal control problem for a shallow lake model and a variation thereof. We carry out a qualitative analysis of solutions to the canonical system and identify possible scenarios. Specifically, we describe a particular case that has not been addressed in the previous works. This case corresponds to the situation, when the canonical system has only two saddle equilibrium points without a source between them. Furthermore, the set of parameters, for which this situation occurs remains unchanged for two alternative formulations of the optimal control problem, which indicates a possibility for a hidden invariant structure. Both formulations of the optimal control problem are studied in detail, both analytically and numerically. The appearance of the Skiba point is discussed.
For the entire collection see [Zbl 1516.90004].
For the entire collection see [Zbl 1516.90004].
MSC:
| 49K10 | Optimality conditions for free problems in two or more independent variables |
| 90C26 | Nonconvex programming, global optimization |
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