Stability Verification of a Control System using the Reachability Analysis

Abstract

Model checking is a formal method technique used for the verification of safety critical and/or complex software and hardware systems. It provides accurate results by exhaustively exploring the abstract mathematical model of the system. This paper discusses the framework proposed for the verification of an underactuated inverted pendulum based two parallel wheeled vehicle. The physical model of the perceived system is designed for 2 DOF that is the pitch along x-axis and roll along y-axis. The mathematical model of the system is developed using the state-space approach and the system is analyzed using Matlab. Stability is introduced in to the system using a Linear Quadratic Regulator (LQR) with an Observer. This controlled system is analyzed and formally verified using the SpaceEx model checker. The stability verification of this system is performed using the reachability analysis. The model checker results shows the stability verification of the system over the convergence of infinite trajectories for a range of input values provided, showing advantage over simulation based techniques. The results also provide the phase portraits of the output variables in 2-D and 3-D planes.