Abstract
AbstractThe type of system approximation in which the system state space x is mapped into a scalar domain V by a quadratic transformation where Q is appropriately determined, is used to develop a suboptimal control procedure for unconstrained lumped parameter dynamic systems via the application of Pontryagin's Maximum Principle. The optimization problem in the scalar domain becomes an initial value problem when the scalar adjoint variable is held constant through out the course of control. The resulting computational scheme includes an effective and simple way to construct the transformation matrix Q and a straightforward minimum seeking approach to locate the best constant overall average scalar adjoint parameter. For the class of problems with quadratic performance index, system equation approximation further reduces the determination of Q to the solution of a matrix Riccati equation.The application of the proposed suboptimal control procedure to four chemical engineering systems shows that the procedure is simple direct, and efficient and works particularly well for problems where the final time is large.
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