Heating control of a finite rod with a mobile source

Abstract

The Green’s function approach is applied for studying the exact and approximate nullcontrollability of a finite rod in finite time by means of a source moving along the rod with controllable trajectory. The intensity of the source remains constant. Applying the recently developed Green’s function approach, the analysis of the exact null-controllability is reduced to an infinite system of nonlinear constraints with respect to the control function. A sufficient condition for the approximate null-controllability of the rod is obtained. Since the exact solution of the system of constraints is a long-standing open problem, some heuristic solutions are used instead. The efficiency of these solutions is shown on particular cases of approximate controllability.

Keywords

• null-controllability
• mobile control
• nonlinear constraints
• triangular wave
• rectangular wave
• green’s function approach
• heuristic control
• lack of exact controllability