Title :
Discretized switching time optimization problems
Author :
Flasskamp, Kathrin ; Murphey, Todd ; Ober-Blobaum, Sina
Author_Institution :
Dept. of Math., Univ. of Paderborn, Paderborn, Germany
Abstract :
A switched system is defined by a family of vector fields together with a switching law which chooses the active vector field at any time. Thus, the switching law encoding the switching times and the sequence of modes may serve as a design parameter. Switching time optimization (STO) focuses on the optimization of the switching times in order to govern the system evolution to a desired behavior described by some cost function. However, it is rare that a STO problem can be solved analytically leading to the use of numerical approximation methods. In this contribution, we directly start with applying integration schemes to approximate the system´s state and adjoint trajectories and study the effect of this discretization. It turns out that in contrast to the continuous time problem, the discretized problem loses differentiability with respect to the optimization variables. The isolated nondifferentiable points can be precisely identified though. Nevertheless, to solve the STO problem, nonsmooth optimization techniques have to be applied which we illustrate using a hybrid double pendulum.
Keywords :
approximation theory; continuous time systems; integration; optimisation; time-varying systems; vectors; STO problem; active vector field; continuous time problem; cost function; discretized switching time optimization; hybrid double pendulum; integration scheme; nonsmooth optimization technique; numerical approximation method; switching law; Cost function; Equations; Switched systems; Switches; Trajectory; Vectors;
Conference_Titel :
Control Conference (ECC), 2013 European
Conference_Location :
Zurich