Real-time optimal control of a special distributed parameter system

The problem of constructing positional solutions under the real-time optimal control of a parabolic system is considered. A method for finding an approximate solution of the problem is justified. According to the method, the problem is reduced to the optimal control problem for a large dynamical ordinary differential system, which is solved by applying a dynamical version of the dual linear programming method. The fundamental matrix of the homogeneous part of the system is quasi-decomposed to save computation time at the iterations of the method. An optimal controller is described whereby the current optimal feedback values (positional solution) are constructed in real time. Numerical results are presented for the control of thermal processes in a rod.