BOUNDARY CONTROL PROBLEMS OF FIRST-ORDER VOLTERRA INTEGRO-DIFFERENTIAL SYSTEMS

We study the boundary control problems for the system of first-order hyperbolic Volterra partial integro-differential equations with nonlocal boundary conditions by the deformation formula method. First, we show that the free system generates a C-0-semigroup and the corresponding control system defines an abstract boundary control system in L-2-space. Next, under some additional assumption on the coefficient matrix of the system, we construct the deformation kernel by the method of characteristics. Based on the integral kernel functions and the multiplier functions, we establish the deformation formula for the nonlocal system. The formula converts the solution of original control system to the solution of a simple system of transport equations. By applying the formula, we propose the boundary feedback control law, which makes the feedback system null controllable in finite time.