Simulation of hybrid systems based on hierarchical interval constraints

Abstract

We propose a framework called HydLa for simple modeling and reliable simulation of hybrid systems which involve discrete and continuous changes over time. HydLa employs interval constraints as a central principle to express uncertainties in modeling, error bounds in the computation of nonlinear continuous changes, and reachable state sets that play key roles in verification. In this research, we propose a modeling language with hierarchical interval constraints to facilitate well-defined modeling, and its implementation which uses machine-representable interval constraints to enclose computation errors with intervals or boxes. The implementation is based on the integration of a consistency technique for nonlinear interval constraints and a technique for solving ordinary differential equations. We also present a method for solving constraint hierarchies among interval constraints.

A Comprehensive Method for Reachability Analysis of Uncertain Nonlinear Hybrid Systems

“…We consider the uncertain model of a ball that bounces on a sinusoidal surface (modified from [54]). It is described by four variables We took a constant integration time step h = 0.1 for ϕ QR (Algorithm 2) and set threshold for time interval bisection to ε T = 0.005 in Hybrid-Transition (Algorithm 6).…”

“…In the nonlinear case, one may proceed with guaranteed linearization and use the above methods [51], but at the cost of overapproximating the reachable sets. Thus, the most promising approach relies on constraint propagation methods, amongst others, Constraint Satisfaction Problems (CSP) [46], Hybrid Constraint Satisfaction (HCS) [54] and nonlinear differential equation numerical integration. This is directly applicable to nonlinear systems and naturally takes into account the presence of uncertainty.…”