Abstract
The optimal control of a bilinear distributed parameter system described by a first order partial differential equation is considered. The performance index to be minimized is the integrated square error of the state at the outlet of the system. By means of the Maximum Principle for lumped parameter systems, we have previously solved this problem under steady-state initial conditions and constant boundary conditions.
In this paper, by appling the Maximum Principle for distributed parameter systems, we solve the problem under the more general conditions where both the initial condition and the boundary condition are continuous and mildly varying.
Our main results are as follows: In order to control the system optimally, we should first use the bang-bang control until the outlet value is equal to the desired value, and then the singular control in a wide sense to maintain the desired value. Moreover, the singular control in a wide sense is reduced to the repetition of switching between the bang-bang control and the singular one in a narrow sense under steady-state initial conditions and constant conditions. The result in this case coincides with the result in our previous paper.
