An MILP approach for real-time optimal controller synthesis with Metric Temporal Logic specifications

The fundamental idea of this work is to synthesize reactive controllers such that closed-loop execution trajectories of the system satisfies desired specifications that ensure correct system behaviors, while optimizing a desired performance criteria. We define the correctness of a system's beha...

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Bibliographic Details
Published in:Proceedings of the American Control Conference pp. 1105 - 1110
Main Authors: Saha, Sayan, Julius, A. Agung
Format: Conference Proceeding Journal Article
Language:English
Published: American Automatic Control Council (AACC) 01.07.2016
Subjects:
Controllers
Dynamical systems
Dynamics
Heuristic algorithms
Indexes
Measurement
mixed integer linear programming
Modeling
reactive controller
Real time
Real-time systems
Robots
Robustness
Specifications
Temporal logic
Trajectories
Trajectory
ISSN:2378-5861
Online Access:Get full text
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Summary:The fundamental idea of this work is to synthesize reactive controllers such that closed-loop execution trajectories of the system satisfies desired specifications that ensure correct system behaviors, while optimizing a desired performance criteria. We define the correctness of a system's behavior according to the system's relation to the environment, for example, the output trajectories of the system terminate in a goal set without entering an unsafe set. Using Metric Temporal Logic (MTL) specifications we can capture complex system behaviors and timing requirements, such as the output trajectories must pass through a number of way-points within a certain time frame before terminating in the goal set. Given a Mixed Logical Dynamical (MLD) system and system specifications in terms of MTL formula or simpler reach-avoid specifications, our goal is to find a closed-loop trajectory that satisfies the specifications, in non-deterministic environments. Using an MILP framework we search over the space of input signals to obtain such valid trajectories of the system, by adding constraints to satisfy the MTL formula only when necessary, to avoid the exponential complexity of solving MILP problems. We also present experimental results for planning a path in real-time for a mobile robot through a dynamically changing environment with a desired task specification.
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ISSN:2378-5861
DOI:10.1109/ACC.2016.7525063