Computing reachable sets for uncertain nonlinear monotone systems

Ramdani, Nacim; Meslem, Nacim; Candau, Yves

doi:10.1016/j.nahs.2009.10.002

Cited by 45 publications

(42 citation statements)

References 43 publications

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“…Usually, time-consuming interval arithmetic is used to overapproximate the set of linearization errors. In this work, we were able to take advantage of monotonicity properties of the Lagrange remainder, which make it possible to compute variable ranges of functions by simply evaluating the corner cases (see [17]). The detailed discussion is skipped since it would require deriving all second-order derivatives…”

Section: Parallelizationmentioning

confidence: 99%

Set-based computation of vehicle behaviors for the online verification of autonomous vehicles

Althoff

Dolan

2011

2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC)

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Abstract-We compute the set of all possible behaviors of an autonomous vehicle using reachability analysis. A reachable set is the set of states a system can possibly reach for a given set of initial states, disturbances, and sensor noise values. We consider autonomous vehicles which plan trajectories for a certain lookahead horizon which are followed using feedback control. While a perfectly followed trajectory might not violate specified safety properties (e.g. lane departures or vehicle collisions), there might exist a violating deviation from the planned trajectory. Given the mathematical model of the controlled vehicle and bounds on uncertainty, our approach detects any possible violation. In addition, the approach provides results faster than real time such that maneuvers of vehicles can be checked before they are fully executed.

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Section: Parallelizationmentioning

confidence: 99%

Set-based computation of vehicle behaviors for the online verification of autonomous vehicles

Althoff

Dolan

2011

2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC)

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“…One way to address this shortcoming, while deriving guaranteed results, is to use the bracketing approach introduced in [16,17], which relies on the classical Müller's existence theorem [11,10]. Given the IVP (2), the bracketing method analyzes the signs of the partial derivatives ∂f i /∂x l , evaluated over the enclosure for all t ∈ [t j , t j+1 ].…”

Section: Using Bracketing Systems As Enclosuresmentioning

confidence: 99%

Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

Eggers

Ramdani

Nedialkov

et al. 2011

Software Engineering and Formal Methods

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Abstract. Aiming at automatic verification and analysis techniques for hybrid systems, we present a novel combination of enclosure methods for ordinary differential equations (ODEs) with the iSAT solver for large Boolean combinations of arithmetic constraints. Improving on our previous work, the contribution of this paper lies in combining iSAT with VNODE-LP, as a state-of-the-art enclosure method for ODEs, and with bracketing systems which exploit monotonicity properties to find enclosures for problems that VNODE-LP alone cannot enclose tightly. We apply our method to the analysis of a non-linear hybrid system by solving predicative encodings of an inductive stability argument and evaluate the impact of different methods and their combination.

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“…This idea ultimately leads to robustness guarantees under parametric uncertainty. These results are in the spirit of [8,19], where the authors considered the problem of computing reachability sets of a monotone system. Some parallels can be also drawn with [15,5], where feedback controllers for monotone systems were proposed.…”

Section: Introductionmentioning

confidence: 98%

Shaping pulses to control bistable systems: Analysis, computation and counterexamples

et al. 2016

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In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation.

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Computing reachable sets for uncertain nonlinear monotone systems

Cited by 45 publications

References 43 publications

Set-based computation of vehicle behaviors for the online verification of autonomous vehicles

Set-based computation of vehicle behaviors for the online verification of autonomous vehicles

Improving SAT Modulo ODE for Hybrid Systems Analysis by Combining Different Enclosure Methods

Shaping pulses to control bistable systems: Analysis, computation and counterexamples

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