Trajectory sensitivity analysis of hybrid systems with sliding motion

Abstract

This paper concerns hybrid control systems exhibiting the sliding motion. It is assumed that the system’s motion on the switching surface is described by index-2 differential–algebraic equations (DAEs), which guarantee the accurate tracking of the sliding motion surface. For those systems the sensitivity analysis is performed with the help of solutions to system’s linearized equations. The paper states conditions under which the solutions to the linearized equations for original DAEs and the solutions to linearized equations for underlying ordinary differential equations (ODEs) exhibit similar properties. Due to the presence of sliding motion, we restrict the class of admissible control functions to piecewise differentiable functions. The presented sensitivity analysis might be useful in deriving the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding motion and in establishing the global convergence of algorithms for solving those problems.