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Optimal Control of Nonlinear Systems with Temporal Logic Specifications

Chapter
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 114)

Abstract

We present a mathematical programming-based method for optimal control of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite- and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite abstraction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10\(+\) continuous state) systems.

Keywords

Temporal Logic Linear Temporal Logic Propositional Formula Linear Temporal Logic Formula Flat Output 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors thank Matanya Horowitz, Scott Livingston, and Ufuk Topcu for helpful feedback. This work was supported by a NDSEG Fellowship and the Boeing Corporation.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA

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