Beyond HyTech: Hybrid Systems Analysis Using Interval Numerical Methods

Henzinger, Thomas A.; Horowitz, Benjamin; Majumdar, Rupak; Wong-Toi, Howard

doi:10.1007/3-540-46430-1_14

Cited by 110 publications

(77 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Under the assumption that Table 1. Summary of different verified methods for non-smooth IVPs: R (Rihm, 1993), RS , NM (Nedialkov and von Mohrenschildt, 2002), H (Henzinger et al, 2000), I (Ishii, 2010), MC (Mahmoud and Chen, 2008), EE (Eggers et al, 2009), and RA (Ratschan, 2012 …”

Section: Then the Following Relations Hold For The Unknown Stepsizes Hmentioning

confidence: 99%

A verified method for solving piecewise smooth initial value problems

Auer

Kiel

Rauh

2013

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.

show abstract

Section: Then the Following Relations Hold For The Unknown Stepsizes Hmentioning

confidence: 99%

A verified method for solving piecewise smooth initial value problems

Auer

Kiel

Rauh

2013

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

show abstract

“…IA has proven to be a valuable tool in a variety of engineering applications [16]. More related to our work is the application of IA to reachability problems [14], [28].…”

Section: A Interval Arithmeticmentioning

confidence: 99%

Robustness of Model-Based Simulations

Fainekos¹,

Sankaranarayanan²,

Ivančić³

et al. 2009

2009 30th IEEE Real-Time Systems Symposium

View full text Add to dashboard Cite

Abstract-This paper proposes a framework for determining the correctness and robustness of simulations of hybrid systems. The focus is on simulations generated from model-based design environments and, in particular, Simulink. The correctness and robustness of the simulation is guaranteed against floatingpoint rounding errors and system modeling uncertainties. Toward that goal, self-validated arithmetics, such as interval and affine arithmetic, are employed for guaranteed simulation of discrete-time hybrid systems. In the case of continuous-time hybrid systems, self-validated arithmetics are utilized for overapproximations of reachability computations.

show abstract

“…This equation implicitly determines the maximal controlled invariant set and the least restrictive feedback control map. Due to the complexity of exactly solving the HJB equation, researchers have been investigating approximate algorithms for computing inner-approximations of the maximal controlled invariant set [30,31,44,50]. Termination of the algorithm that computes the maximal controlled invariant set is often an issue and work has been investigating special classes of systems that allow to prove termination [46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Safety Control of Hidden Mode Hybrid Systems

Verma

Vecchio

2012

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-In this paper, we consider the safety control problem for Hidden Mode Hybrid Systems (HMHSs), which are a special class of hybrid automata in which the mode is not available for control. For these systems, safety control is a problem with imperfect state information. We tackle this problem by introducing the notion of non-deterministic discrete information state and by translating the problem to one with perfect state information. The perfect state information control problem is obtained by constructing a new hybrid automaton, whose discrete state is an estimate of the HMHS mode and is, as such, available for control. This problem is solved by computing the capture set and the least restrictive control map for the new hybrid automaton. Sufficient conditions for the termination of the algorithm that computes the capture set are provided. Finally, we show that the solved perfect state information control problem is equivalent to the original problem with imperfect state information under suitable assumptions. We illustrate the application of the proposed technique to a collision avoidance problem between an autonomous vehicle and a human driven vehicle at a traffic intersection.Index Terms-Mode estimation, dynamic feedback, multiagent systems.

show abstract

Beyond HyTech: Hybrid Systems Analysis Using Interval Numerical Methods

Cited by 110 publications

References 18 publications

A verified method for solving piecewise smooth initial value problems

A verified method for solving piecewise smooth initial value problems

Robustness of Model-Based Simulations

Safety Control of Hidden Mode Hybrid Systems

Contact Info

Product

Resources

About