A Worst-Case Evaluation Method for Dynamic Systems

Abstract

A worst-case evaluation method is presented in this paper. The objective of this method is to identify worst-case disturbances so that the performance of dynamic systems under extreme conditions can be evaluated. Depending on the dynamics and information structure of the system, the worst-case evaluation problems are classified into four cases. Classical optimal control and game theories are used to construct algorithms to obtain linear solutions analytically. Numerical schemes to solve nonlinear worst-case problems are also presented. Two case study examples are then presented—a truck rollover problem and a vehicle stability controller evaluation problem. In both cases, a combined analytical-numerical method is used. The nonlinear plant is first linearized. The analytical solution of the linearized plant is then used as the initial guess for the numerical scheme. The final worst-case disturbance is then obtained iteratively from the numerical scheme. It was found that the proposed worst-case evaluation method is able to produce much larger unwanted plant motions (roll/side slip in the two case studies) compared with traditional evaluation maneuvers.