Piecewise-Affine Approximations for a Powertrain Control Verification Benchmark

Deshmukh, Jyotirmoy V.; Ito, Hideto; Jin, Xiaoqing; Kapinski, James; Butts, Ken; Gerhard, Jürgen; Samadi, Behzad; Walker, Kevin; Xie, Y.

doi:10.29007/w3x7

Cited by 1 publication

(1 citation statement)

References 14 publications

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“…It is well-known that non-compositional methods for PWA approximations are not computationally efficient for complex systems, since an acceptable accuracy requires a very large number of pieces in the piecewise-affine approximation. Very recently, [13] presented an experimental comparison of a compositional approach, similar to that presented in this paper (called nested approximation there), against a simplex-partitioning PWA hybridization, showing that the former scales much better than the latter for increasing demands on precision. The compositional PWA-approximation is presented informally, and the paper does not discuss the implications in terms of the model size, nor preserving this compositionality in the generated model.…”

Section: Related Workmentioning

confidence: 71%

Constructing verification models of nonlinear Simulink systems via syntactic hybridization

Kekatos

Forets

Frehse

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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In this paper, we present a methodology that facilitates the integration of formal verification techniques into model-based design. The focus is on set-based reachability analysis and on control systems that are described by hybrid dynamics and nonlinear components. Starting with a standard simulation model, e.g., in MATLAB/Simulink, we transform it into an equivalent verification model, formally a network of hybrid automata, in the SX format used by several reachability tools. A major obstacle here is that highly scalable reachability algorithms and tools exist for piecewise affine (PWA) dynamical models, but not for nonlinear ones. To obtain PWA overapproximations of nonlinear dynamics, we use an abstraction method known as hybridization. It consists in partitioning the state-space into a set of domains, and for each domain, approximating the nonlinear dynamics by simpler ones plus nondeterministic inputs to account for the abstraction error. Existing hybridization procedures operate on the composed (flattened) system, so the number of partitions is exponential in the number of variables. This quickly leads to intractably large models, even for small systems. To mitigate this problem, we decompose the original dynamics and carry out the statespace partitioning and PWA approximation on the components. The number of partitions in each PWA component is at most quadratic in the abstraction error so that an explosion in the number of partitions is largely avoided. Since the SX format can handle templates, several components may share the same abstraction. The result is a highly compact model that retains the modular structure of the original simulation model. If only a small subset of the partitions is reachable, the bottleneck of having excessively large PWA models can be avoided by composing the model on-the-fly during the reachability analysis.

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Section: Related Workmentioning

confidence: 71%