Optimal control of a parabolic distributed parameter system via orthogonal polynomials

A class of optimal control of systems with distributed parameters is considered. The process of the systems under consideration is governed by a linear parabolic partial differential equation. By use of the modal space technique, the optimal control of a distributed parameter system is simplified into the optimal control of a linear time-invariant lumped-parameter system. Next, a direct computational method for evaluating the modal optimal control and trajectory of the linear time-invariant lumped-parameter is suggested. The method is based on using finite interpolating orthogonal polynomials to approximate modal state variables. The formulation is straightforward and convenient for digital computation. An illustrative example is given to demonstrate the advantage of this method.