Techniques for Verified Reachability Analysis of Quasi-Linear Continuous-Time Systems

Abstract

Quasi-linear continuous-time state-space representations are common for a large variety of dynamic systems described by ordinary differential equations (ODEs) with continuously differentiable smooth right-hand sides. Such models arise, for example, after representing technical systems by the use of first-principle techniques and subsequently factoring out the state vectors so that a set of ODEs is obtained that has a structure similar to linear dynamics. However, in the case of quasi-linear ODEs, the system matrix (as well as the corresponding input matrix) are explicit functions of the state variables. Thus, analytic solutions to corresponding initial value problems (IVPs) are, even in cases of a-priori defined closed-form control inputs, hardly available. Therefore, this paper aims at giving an overview of interval-based techniques which allow for determining outer enclosures of the reachable states by either numerical iteration procedures or by similarity transformations of the state equations.