Optimal control of a certain type of linear distributed-parameter systems

This paper treats the problem of optimal control of one-dimensional linear stationary distributed-parameter systems which are controlled by boundary control functions. The systems are assumed to be representable by means of integral operators with suitably restricted kernel function. By using the variational method, integral equations are obtained as necessary and sufficient conditions for the optimum. When the control functions are not subjected to any constraints, a Fredholm integral equation of the second kind is obtained. When the control functions are magnitude-limited, a system of nonlinear integral equations of similar form to the integral equation of the Hammerstein type is obtained. The analytical solutions and the numerical solutions to the integral equations are shown.