ATTAINABLE SUBSPACES AND THE BANG-BANG PROPERTY OF TIME OPTIMAL CONTROLS FOR HEAT EQUATIONS

作者：Wang Gengsheng; Xu Yashan^*; Zhang Yubiao

来源：SIAM Journal on Control and Optimization, 2015, 53(2): 592-621.

DOI：10.1137/140966022

• attainable subspaces
• the bang-bang property
• time optimal controls
• heat equations

In this paper, we study two subjects on internally controlled heat equations with time varying potentials: the attainable subspaces and the bang-bang property for some time optimal control problems. We present some equivalent characterizations on the attainable subspaces and provide a sufficient condition to ensure the bang-bang property. Both the above-mentioned characterizations and the sufficient condition are closely related to some function spaces consisting of some solutions to the adjoint equations. It seems for us that the existing ways to derive the bang-bang property for heat equations with time-invariant potentials (see, for instance, [H. O. Fattorini, Infinite Dimensional Linear Control Systems: The Time Optimal and Norm Optimal Problems, Elsevier, Amsterdam 2005], [F. Gozzi and P. Loreti, SIAM J. Control Optim., 37 (1999), pp. 1195-1221], [V. Mizel and T. Seidman, SIAM J. Control Optim., 35 (1997), pp. 1204-1216], and [G. Wang, SIAM J. Control Optim., 47 (2008), pp. 1701-1720]) do not work for the case where the potentials are time varying. We provide another way to approach it in the current paper.

• 出版日期2015