Optimal and robust controller synthesis using energy timed automata with uncertainty

Giovanni Bacci (1) , Patricia Bouyer (2, 3) , Uli Fahrenberg (4) , Kim Larsen (1) , Nicolas Markey (5) , Pierre-Alain Reynier (6)

1 AAU - Aalborg University [Denmark]
2 LSV - Laboratoire Spécification et Vérification
3 LMF - Laboratoire Méthodes Formelles
4 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
5 SUMO - SUpervision of large MOdular and distributed systems
6 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)

In this paper, we propose a novel framework for the synthesis of robust and optimal energy-aware controllers. The framework is based on energy timed automata, allowing for easy expression of timing constraints and variable energy rates. We prove decidability of the energy-constrained infinite-run problem in settings with both certainty and uncertainty of the energy rates. We also consider the optimization problem of identifying the minimal upper bound that will permit existence of energy-constrained infinite runs. Our algorithms are based on quantifier elimination for linear real arithmetic. Using Mathematica and Mjollnir, we illustrate our framework through a real industrial example of a hydraulic oil pump. Compared with previous approaches our method is completely automated and provides improved results.

Domains: Computer Science [cs]; Logic in Computer Science [cs.LO]; Computer Science and Game Theory [cs.GT]

Giovanni Bacci, Patricia Bouyer, Uli Fahrenberg, Kim Larsen, Nicolas Markey, et al.. Optimal and robust controller synthesis using energy timed automata with uncertainty. Formal Aspects of Computing, 2021, 33 (1), pp.3-25. ⟨10.1007/s00165-020-00521-4⟩. ⟨hal-03240104⟩