Regular Synthesis for the Linear Time-Optimal Control Problem with Convex Control Constraints
Margaréta Halická · SIAM Journal on Control and Optimization · 1989
The problem of existence of a regular synthesis for the linear time-optimal control problem with convex control constraints is studied. A regular synthesis on the whole reachable set cannot be established for this problem by direct use of Brunovsky’s general existence theorem. This is in accord with the example of a nonsubanalytic reachable set due to Lojasiewicz and Sussmann [S. Lojasiewicz, Jr. and H. J. Sussmann, “Some examples of reachable sets and optimal cost functions that fail to be subanalytic,” SIAM J. Control Optim., 23 (1985), pp. 584–598]. A closed subset H of the reachable set K that has Lebesgue measure zero is constructed and the existence of a regular synthesis on $K - H$ is proved.