Time-optimality by distance-optimality for parabolic control systems

Abstract

The equivalence of time-optimal and distance-optimal control problems is shown for a class of parabolic control systems. Based on this equivalence, an approach for the efficient algorithmic solution of time-optimal control problems is investigated. Numerical examples are provided to illustrate that the approach works well is practice.1991 Mathematics Subject Classification. 49K20, 49M15.

Error Estimates for Space-Time Discretization of Parabolic Time-Optimal Control Problems with Bang-Bang Controls

“…In an outer loop the optimal time is determined by a Newton method. For further details we refer to [3]. The computations are performed in MATLAB.…”

“…In this section we describe an alternative approach based on an equivalent reformulation. For further details we refer to [3]. B.1.…”

“…We verify the theoretical results by numerical examples. In order to solve the optimization problem ( P ), we employ the equivalence of time-and distance optimal control problems summarized in Appendix B (see also [3]), and solve a sequence of optimization problems with a fixed time. The resulting convex sub-problems for a fixed time are solved by an accelerated conditional gradient method.…”

“…Concerning the numerical realization, we use the bilevel algorithm from [3] that is based on an equivalent reformulation of (P ). In the outer loop we employ a Newton method to find the root of a certain value function.…”