Computing Abstractions of Nonlinear Systems

Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid systems and to design finite state controllers that provably e...

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Veröffentlicht in:IEEE transactions on automatic control 2011-11, Vol.56 (11), p.2583-2598
1. Verfasser: Reissig, G.
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description Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid systems and to design finite state controllers that provably enforce predefined specifications. We present a novel algorithm to compute such finite state models for nonlinear discrete-time and sampled systems which depends on quantizing the state space using polyhedral cells, embedding these cells into suitable supersets whose attainable sets are convex, and over-approximating attainable sets by intersections of supporting half-spaces. We prove a novel recursive description of these half-spaces and propose an iterative procedure to compute them efficiently. We also provide new sufficient conditions for the convexity of attainable sets which imply the existence of the aforementioned embeddings of quantizer cells. Our method yields highly accurate abstractions and applies to nonlinear systems under mild assumptions, which reduce to sufficient smoothness in the case of sampled systems. Its practicability in the design of discrete controllers for nonlinear continuous plants under state and control constraints is demonstrated by an example.
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subjects Accuracy
Applied sciences
Approximation methods
Attainability
attainable set
Automata
Computational modeling
Computer science
control theory
systems
Control system synthesis
Control theory. Systems
Controllers
Design engineering
discrete abstraction
Dynamical systems
Exact sciences and technology
formal verification
Half spaces
Mathematical analysis
Mathematical models
Modelling and identification
motion planning
Nonlinear dynamics
nonlinear system
Nonlinear systems
Nonlinearity
polyhedral over-approximation
Quantization
Robotics
Studies
symbolic control
symbolic model
Trajectory
title Computing Abstractions of Nonlinear Systems
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