Reachability and Control Synthesis for Piecewise-Affine Hybrid Systems on Simplices

Habets, L.C.G.J.M.; Collins, Pieter; Schuppen, Jan H. van

doi:10.1109/tac.2006.876952

Cited by 232 publications

(213 citation statements)

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“…Also, we plan to link our work to hybrid systems: a refinement of the spatial reasoning in this paper to the car dynamics is of interest. There we could benefit from the work of [7,8,9].…”

Section: Resultsmentioning

confidence: 99%

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Proving Safety of Traffic Manoeuvres on Country Roads

Hilscher

Linker

Olderog

2013

Theories of Programming and Formal Methods

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Abstract.We adapt the Multi-lane Spatial Logic MLSL, introduced in [1] for proving the safety (collision freedom) of traffic manoeuvres on multi-lane motorways, where all cars drive in one direction, to the setting of country roads with two-way traffic. To this end, we need suitably refined sensor functions and length measurement in MLSL. Our main contribution is to show that also here we can separate the purely spatial reasoning from the underlying car dynamics in the safety proof.

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“…Also, we plan to link our work to hybrid systems: a refinement of the spatial reasoning in this paper to the car dynamics is of interest. There we could benefit from the work of [7,8,9].…”

Section: Resultsmentioning

confidence: 99%

“…In [7] the authors introduce abstraction and refinement in a hierarchical design of hybrid control systems. In [8] the synthesis of control laws for piecewise-affine hybrid systems is introduced. In [9] controller patterns were proposed to simplify safety proofs for two cooperating traffic agents.…”

Section: Introductionmentioning

confidence: 99%

Proving Safety of Traffic Manoeuvres on Country Roads

Hilscher

Linker

Olderog

2013

Theories of Programming and Formal Methods

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“…The theoretical background of the algorithms in Con-PAHS has been developed in several papers (see [8], [9], [10], [11]). In this section, an overview is presented of the problem statements and results in these papers.…”

Section: Control Of Piecewise-affine Hybrid Systemsmentioning

confidence: 99%

“…Such sufficient conditions for control of piecewise-affine hybrid systems on polytopes have been developed by several of the authors, see [8], [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

ConPAHS - A Software Package for Control of Piecewise-Affine Hybrid Systems

Collins¹,

Habets²,

Kuut³

et al. 2006

2006 IEEE Conference on Computer-Aided Control Systems Design

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Abstract-The software package ConPAHS facilitates control design of continuous-time piecewise-affine hybrid systems on polytopes. For the control objective of reaching a particular state from a specified initial state, the output of the package is a piecewise-affine control law. After a short review of the control theory for this problem, the paper presents the functional specification of ConPAHS, the objected oriented software principles used, the program structure, and the design choices. Three examples including simulations are provided to illustrate the use of ConPAHS.

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“…The set of states can be seen as a set of labels for the regions in the partition, and each transition corresponds to a controller driving the vehicle between two adjacent regions. By partitioning the environment into simplicial or rectangular regions, continuous feedback controllers that drive a robotic system from any point inside a region to a desired facet of an adjacent region have been developed for linear ( Kloetzer & Belta, 2008a), multi-affine (Habets, Collins, & van Schuppen, 2006), piecewise-affine (Desai, Ostrowski, & Kumar, 1998;Habets, Kloetzer, & Belta, 2006;Wongpiromsarn, Topcu, & Murray, 2009), and non-holonomic (unicycle) (Belta, Isler, & Pappas, 2005;Lindemann, Hussein, & LaValle, 2007) dynamical models. By relating the initial continuous dynamical system and the abstract discrete finite system through simulation or bisimulation relations (Milner, 1989), the abstraction process allows one to replace the original more complex continuous system with the ''equivalent'' abstract system when solving a control synthesis problem.…”

Section: Introductionmentioning

confidence: 99%