Efficient choice of parameters on delta-reachability bounded hybrid systems

Abstract

Hybrid systems (HS) are roughly described as a set of discrete state transitions and continuous dynamics modeled by differential equations. Parametric HS may be constructed by having parameters on the differential equations, initial conditions, jump conditions, or a combination of the previous ones. In real applications, the best solution is obtained by a set of metrics functional over the set of solutions generated from a finite set of parameters. This paper examines the choice of parameters on delta-reachability bounded hybrid systems. We present an efficient model based on the tool pHL-MT to benchmark the HS solutions (based on dReach), and a non-parametric frontier analysis approach, relying on multidirectional efficiency analysis (MEA). Three numerical examples of epidemic models with variable growth inffectivity are presented, namely: when the variable of infected individuals oscillates around some endemic (non-autonomous) equilibrium; when there is an asymptotically stable non-trivial attractor; and in the presence of bump functions.