On Nonlinear Prices in Timed Automata

Bhave, Devendra; Krishna, Shankara Narayanan; Trivedi, Ashutosh

doi:10.4204/eptcs.232.9

Cited by 6 publications

(6 citation statements)

References 17 publications

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“…A number of works have encoded dynamical systems with propositional logic and have used model checking software to obtain feasible and optimal solutions to their problems [10]- [12], [19]- [21]. Several works have developed frameworks that use SMT solvers to solve an optimization problem over a PTA [11], [12]. To solve the MPC problem posed in (3), we leverage these works to reformulate the optimal control problem in FOL and analyze the recursive feasibility of the MPC problem.…”

Section: Solving the Mpc Problem For Ptamentioning

confidence: 99%

“…To encode the underlying timed automata of the PTA, we employ an encoding similar to the one in [11] and [12], with several changes. We employ an event-driven encoding scheme that evaluates the clock valuations val(c) only when a discrete transition is taken.…”

Section: A Representation Of the Pta In Folmentioning

confidence: 99%

“…All simulations are subject to a disturbance, which is given by the guard in Fig. 2, and represents a noncatastrophic failure in AGV 3 (q 11 ). This failure allows the AGV to continue, but at a slower travel speed.…”

Section: A Simulation Setupmentioning

confidence: 99%

“…To allow the softening of constraints in PTA MPC, this brief utilizes a method modified from the existing literature to translate the automaton structure and CORA problem to a set of first-order logic (FOL) constraints, enabling the adoption of an optimization modulo theories (OMT) solver that easily admits constraint softening. While this is not the first translation of PTA/CORA into FOL [11], [12], to the best of the authors' knowledge, it is the first work to harness the FOL framework for constraint softening.…”

Section: Introductionmentioning

confidence: 98%

“…In summary, the main contributions of this work are: 1) an MPC framework for PTA to increase robustness to disturbances and 2) the application of constraint softening to CORA to increase the feasible solution set to path planning problems without increasing model complexity. To solve the MPC problem and demonstrate its application, this work introduces a modified FOL representation of PTA based on previous work in [11] and [12] for facilitating the execution of MPC and constraint softening via an OMT solver. The solver is integrated into a simulation implementation of MPC on a PTA model of a manufacturing system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Model Predictive Control of Priced Timed Automata Encoded With First-Order Logic

Balta

Kovalenko

Spiegel

et al. 2022

IEEE Trans. Contr. Syst. Technol.

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Priced timed automata (PTA) are discrete-event system models with temporal constraints and a cost function and are used to pose optimal scheduling and routing problems. To date, solutions to these problems have been found offline and executed open loop. This open-loop control strategy makes it impossible to account for disturbances, i.e., changes in costs or scheduling constraints over time. To address this shortcoming, this work's first contribution is a closed-loop model predictive control (MPC) framework for PTA, enabling decision-making based on real-time model updates. To ensure the feasibility of an MPC problem, it is often desirable to soften constraints. However, the contemporary PTA theory does not consider soft constraints. Thus, this work's second contribution is to integrate constraint softening with PTA control by harnessing the capabilities of new solvers enabled by the recasting of the models and control problem into first-order logic by employing modified encoding schemes based on existing works. Finally, the proposed control framework and implementation are demonstrated in a simulation case study on the guidance of a product through a manufacturing system.

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