Abstract
This paper presents a stochastic model predictive control problem for a class of discrete event systems, namely stochastic max-plus linear systems, which are of wide practical interest as they appear in many application domains for timing
and synchronization studies. The objective of the control problem is to minimize a cost function under constraints on states, inputs and outputs of such a system in a receding horizon fashion. In contrast to the pessimistic view of the robust approach on uncertainty, the stochastic approach interprets the constraints probabilistically, allowing for a sufficiently small violation probability level. In order to address the resulting nonconvex chance-constrained optimization problem, we present two ideas in this paper. First, we employ a scenario-based approach to approximate the problem solution, which optimizes the control inputs over a receding horizon, subject to the constraint satisfaction under a finite number of scenarios of the uncertain parameters. Second, we show that this approximate optimization problem is convex with respect to the decision variables and we provide a-priori probabilistic guarantees for the desired level of
constraint fulfillment. The proposed scheme improves the results in the literature in two distinct directions: we do not require any assumption on the underlying probability distribution of the system parameters; and the scheme is applicable to high dimensional problems, which makes it suitable for real industrial applications. The proposed framework is demonstrated on a twodimensional production system and it is also applied to a subset
of the Dutch railway network in order to show its scalability and study its limitations.
and synchronization studies. The objective of the control problem is to minimize a cost function under constraints on states, inputs and outputs of such a system in a receding horizon fashion. In contrast to the pessimistic view of the robust approach on uncertainty, the stochastic approach interprets the constraints probabilistically, allowing for a sufficiently small violation probability level. In order to address the resulting nonconvex chance-constrained optimization problem, we present two ideas in this paper. First, we employ a scenario-based approach to approximate the problem solution, which optimizes the control inputs over a receding horizon, subject to the constraint satisfaction under a finite number of scenarios of the uncertain parameters. Second, we show that this approximate optimization problem is convex with respect to the decision variables and we provide a-priori probabilistic guarantees for the desired level of
constraint fulfillment. The proposed scheme improves the results in the literature in two distinct directions: we do not require any assumption on the underlying probability distribution of the system parameters; and the scheme is applicable to high dimensional problems, which makes it suitable for real industrial applications. The proposed framework is demonstrated on a twodimensional production system and it is also applied to a subset
of the Dutch railway network in order to show its scalability and study its limitations.
Original language | English |
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Title of host publication | Proceedings of the 2016 IEEE International Conference on Systems, Man, and Cybernetics |
Place of Publication | Piscataway, NJ, USA |
Publisher | IEEE |
Pages | 3581-3588 |
ISBN (Electronic) | 9781509018970 |
DOIs | |
Publication status | Published - 2016 |
Event | 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016 - Budapest, Hungary Duration: 9 Oct 2016 → 12 Oct 2016 |
Conference
Conference | 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016 |
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Country/Territory | Hungary |
City | Budapest |
Period | 9/10/16 → 12/10/16 |
Keywords
- Multiprotocol label switching
- Stochastic processes
- Probabilistic logic
- Uncertainty
- Optimization
- Rail transportation
- Algebra