BOUNDED CONTROLS IN DISTRIBUTED-PARAMETER SYSTEMS

Control systems with distributed parameters, described by partial differential equations, solvable with respect to the first or second time derivative, are considered. The controls on the right-hand sides of the equations are assumed to be bounded in absolute magnitude. A control method is proposed which brings the controlled system into the null state in a finite time. The proposed approach is based on decomposing the system and applying the time-optimal control for each mode of motion obtained by Fourier-expanding the solution. Estimates for the duration of the control process are obtained. Sufficient conditions for the problem to be solvable are given. Examples are presented.