Time-varying bang-bang property of time optimal controls for heat equation and its application

Abstract In this paper, the bang–bang property of time optimal controls for heat equation is established. Compared with the existing results on these problems, the bound of control variables is not a constant but a time-varying function. As an application of the bang–bang property, some kind of relation between the time optimal control problem and its corresponding target optimal control problem is considered.

[1]  Lijuan Wang,et al.  Bang-bang property for time optimal control of semilinear heat equation , 2014 .

[2]  Lijuan Wang,et al.  Bang-Bang Property of Time Optimal Null Controls for Some Semilinear Heat Equation , 2016, SIAM J. Control. Optim..

[3]  J. Yong,et al.  Exact Controllability of Linear Stochastic Differential Equations and Related Problems , 2016, 1603.07789.

[4]  Karl Kunisch,et al.  TIME OPTIMAL CONTROL OF THE HEAT EQUATION WITH POINTWISE CONTROL CONSTRAINTS , 2013 .

[5]  R. Bellman,et al.  On the “bang-bang” control problem , 1956 .

[6]  Yubiao Zhang,et al.  Decompositions and bang-bang properties , 2016, 1603.05362.

[7]  Enrique Zuazua,et al.  On the Equivalence of Minimal Time and Minimal Norm Controls for Internally Controlled Heat Equations , 2012, SIAM J. Control. Optim..

[8]  T. Seidman,et al.  An Abstract Bang-Bang Principle and Time-Optimal Boundary Control of the Heat Equation , 1997 .

[9]  Ionel Roventa,et al.  Time optimal boundary controls for the heat equation , 2012 .

[10]  Enrique Zuazua,et al.  Null and approximate controllability for weakly blowing up semilinear heat equations , 2000 .

[11]  B. Guo,et al.  Optimal Actuator Location of the Minimum Norm Controls for Heat Equation with General Controlled Domain , 2015, 1501.05448.

[12]  Qi Lü,et al.  Bang-bang principle of time optimal controls and null controllability of fractional order parabolic equations , 2010 .

[13]  E. Schmidt,et al.  The “Bang-Bang” Principle for the Time-Optimal Problem in Boundary Control of the Heat Equation , 1980 .

[14]  G. Lebeau,et al.  Contróle Exact De Léquation De La Chaleur , 1995 .

[15]  Marius Tucsnak,et al.  Maximum Principle and Bang-Bang Property of Time Optimal Controls for Schrödinger-Type Systems , 2013, SIAM J. Control. Optim..

[16]  Gengsheng Wang,et al.  Equivalence of Three Different Kinds of Optimal Control Problems for Heat Equations and Its Applications , 2013, SIAM J. Control. Optim..

[17]  J. Apraiz,et al.  Observability Inequalities and Measurable Sets , 2012, 1202.4876.

[18]  H. Fattorini.  Time and norm optimal controls: A survey of recent results and open problems , 2011 .

[19]  Paola Loreti,et al.  Regularity of the Minimum Time Function and Minimum Energy Problems: The Linear Case , 1999 .

[20]  Bao-Zhu Guo,et al.  Optimal actuator location for time and norm optimal control of null controllable heat equation , 2015, Math. Control. Signals Syst..

[21]  Karl Kunisch,et al.  Bang-bang property of time optimal controls of semilinear parabolic equation , 2015 .

[22]  Gengsheng Wang,et al.  Linfinity-Null Controllability for the Heat Equation and Its Consequences for the Time Optimal Control Problem , 2008, SIAM J. Control. Optim..

[23]  Yanqing Wang,et al.  THE NORM OPTIMAL CONTROL PROBLEM FOR STOCHASTIC LINEAR CONTROL SYSTEMS , 2015 .

[24]  Jean-Pierre Puel,et al.  Approximate controllability of the semilinear heat equation , 1995, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[25]  Jie Zhong,et al.  Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications , 2016, SIAM J. Control. Optim..