Pontryagin's Principle for Time-Optimal Problems

We consider time-optimal control problems for semilinear parabolic equations with pointwise state constraints and unbounded controls. A Pontryagin's principle is obtained in nonqualified form without any qualification condition. The terminal time, which is a control variable, satisfies an optimality condition, which seems to be new in the context of control problems for partial differential equations.

[1]  Frédéric Bonnans,et al.  An Extension of Pontryagin's Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities , 1995 .

[2]  Time-optimal control in nonlinear evolution equations , 1990 .

[3]  H. O. Fattorini.  Nonlinear infinite dimensional optimal control problems with state constraints and unbounded control sets , 1996 .

[4]  Yu.V. Yegorov.  Some problems in the theory of optimal control , 1963 .

[5]  H. Fattorini.  The maximum principle for nonlinear nonconvex systems in infinite dimensional spaces , 1985 .

[6]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[7]  Jean-Pierre Raymond,et al.  Hamiltonian Pontryagin's Principles for Control Problems Governed by Semilinear Parabolic Equations , 1999 .

[8]  H. O. Fattorini,et al.  Optimal Problems for Nonlinear Parabolic Boundary Control Systems , 1994 .

[9]  J. Diestel.  Geometry of Banach Spaces: Selected Topics , 1975 .

[10]  Jiongmin Yong,et al.  Optimal Control Theory for Infinite Dimensional Systems , 1994 .

[11]  The construction of minimizing sequences in problems of the control of systems with distributed parameters , 1982 .

[12]  Jean-Pierre Raymond.  Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints , 1997 .

[13]  Housnaa Zidani,et al.  Optimal control problem governed by a semilinear parabolic equation , 1996 .

[14]  H. Fattorini.  Invariance of the Hamiltonian in Control Problems for Semilinear Parabolic Distributed Parameter Systems , 1994 .

[15]  W. Kampowsky.  Optimal Control in Nonlinear Evolution Equations with Constraints , 1991 .

[16]  E. Casas.  Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations , 1997 .

[17]  Jiongmin Yong,et al.  Pontryagin Maximum Principle for Semilinear and QuasilinearParabolic Equations with Pointwise State Constraints , 1995 .

[18]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[19]  O. Ladyženskaja.  Linear and Quasilinear Equations of Parabolic Type , 1968 .

[20]  Viorel Barbu,et al.  Analysis and control of nonlinear infinite dimensional systems , 1993 .

[21]  Jean-Pierre Raymond,et al.  Pontryagin's Principle for State-Constrained Control Problems Governed by Parabolic Equations with Unbounded Controls , 1998 .