We generalise the optimisation technique of dynamic programming for discrete-time systems with an uncertain gain function. We assume that uncertainty about the gain function is described by an imprecise probability model, which generalises the well-known Bayesian, or precise, models. We compare various optimality criteria that can be associated with such a model, and which coincide in the precise case: maximality, robust optimality and maximinity. We show that (only) for the first two an optimal feedback can be constructed by solving a Bellman-like equation.
Keywords. optimal control, dynamic programming, uncertainty, imprecise probabilities
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Authors addresses:
Matthias Troffaes
Technologiepark Zwijnaarde 914
B-9052 Zwijnaarde
Belgium
Gert de Cooman
Universiteit Gent
Onderzoeksgroep SYSTeMS
Technologiepark - Zwijnaarde 9
9052 Zwijnaarde
Belgium
E-mail addresses:
| Matthias Troffaes | matthias.troffaes@rug.ac.be |
| Gert de Cooman | gert.decooman@rug.ac.be |