Stability and robustness for hybrid systems

Pettersson, Stefan; Lennartson, Bengt

doi:10.1109/cdc.1996.572653

Cited by 173 publications

(75 citation statements)

References 13 publications

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“…Stability analysis of switched and hybrid systems has been treated in e.g. [80,81,82,83]. See also [84] for a recent survey of the field.…”

Section: Stability Analysis Using Sum Of Squares Programmingmentioning

confidence: 99%

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

Doyle¹

2001

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The overall long-term objective of our research is to develop mathematical and software infrastructure in support of post-genomics research in systems biology. One near-term objective articulated in this abstract centers on a deeper understanding of the organizational principles of biological networks. A distinguishing theme of this work is its focus on scalable methods of robustness and model (in)validation with data, as opposed to relying purely on simulation. In computability terms, if simulation is viewed as a way to attack the NP hard side of biological problems, our approach attacks the coNP side. Much of the success of reductionist biology has depended on creative individuals who draw biologically meaningful inferences from data and computation using small scale and informal reasoning. This type of inference was critical because the reductionist research program itself offered no systematic tools to deal with complexity, only with the component parts. Far from being dispensed with, this reasoning process and its biological content must be both formalized and made rigorous, systematic, and scalable as well, and ultimately teachable. This requires the development of new mathematics as well as algorithms and software.A central goal of modeling and simulation is to connect molecular mechanisms to network function to questions of biomedical relevance. Unfortunately, many of the most critical questions involve events which are extremely rare at the individual cell level where the mechanisms act yet catastrophic to the organism. Thus simulation methods that may be adequate for studying generic or typical behavior are entirely inadequate to explore such worst-case scenarios, which with conventional methods are computational intractable. We are extending the best-practice tools and algorithms for robustness analysis that have become standards in engineering to models of biological relevance, which are typically nonlinear, hybrid, uncertain, and stochastic. This includes integrating formal inference methods from the previously fragmented theories in Computer Science with those of Control and Dynamical Systems. This involves deep mathematical challenges that parallel those for technological networks, for which we have made dramatic progress, and on which we are building new tools for systems biology.DppWTJIToM ST ýIFbr A Distriibution Un'lhrrited 20U0U50608 054

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“…Stability analysis of switched and hybrid systems has been treated in e.g. [80,81,82,83]. See also [84] for a recent survey of the field.…”

Section: Stability Analysis Using Sum Of Squares Programmingmentioning

confidence: 99%

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

Doyle¹

2001

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“…Robustness is a standard concept from control theory [12,11]. In the case of programming languages, various definitions of robustness have been considered.…”

Section: Robustness Of Floating-point Programs With Respect To the Exmentioning

confidence: 99%

Non-local Robustness Analysis via Rewriting Techniques

Gazeau

Miller

Palamidessi

2012

Electron. Proc. Theor. Comput. Sci.

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Robustness is a correctness property which intuitively means that if the inputs to a program changes less than a fixed small amount then its output changes only slightly. The study of errors caused by finite-precision semantics requires a stronger property: the results in the finite-precision semantics have to be close to the result in the exact semantics. Compositional methods often are not useful in determining which programs are robust since key constructs-like the conditional and the while-loop-are not continuous. We propose a method for proving that some while-loop programs always returns finite precision values close to the exact values. Our method uses techniques borrowed from rewriting theory to analyze the possible paths in a program's execution in order to show that while local operations in a program might not be robust, the full program might be guaranteed to be robust. This method is non-local in the sense that instead of breaking the analysis down to single lines of code, it checks certain global properties of its structure. We show the applicability of our method on two standard algorithms: the CORDIC computation of the cosine and Dijkstra's shortest path algorithm.

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“…However, the problem is that is not clear how the nonincreasing sequence can be effectively checked in general, since it would in principle require checking all possible behaviours of a hybrid system. This problem has been tackled by constructing Lyapunov functions that are either piecewise linear (Koutsoukos and Antsaklis, 2001) or piecewise quadratic (Pettersson and Lennartson, 1996;Johansson and Rantzer, 1998;Mignone et al, 2000). In the latter case the piecewise quadratic function should be continuous on the switching boundaries, which can be checked efficiently by solving a linear matrix inequality.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis for Hybrid Automata Using Conservative Gains

Langerak

Polderman

Krilavičius

2003

IFAC Proceedings Volumes

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This paper presents a stability analysis approach for a class of hybrid automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and outgoing transitions in a location a conservative estimate is made of the gain via a Lyapunov function for the dynamics in that location. It is shown how the choice of the Lyapunov function can be optimized to obtain the best possible estimate. The calculated conservative gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton.

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Stability and robustness for hybrid systems

Cited by 173 publications

References 13 publications

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

Bioinspired Concepts: Unified Theory for Complex Biological and Engineering Systems

Non-local Robustness Analysis via Rewriting Techniques

Stability Analysis for Hybrid Automata Using Conservative Gains

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