Computation of optimal control for linear systems with delay

Abstract

A numerical algorithm is presented to calculate an optimal control recursively for linear multivariable systems with delay. The algorithm is based on the method of steepest descent in Hilbert space. The optimal control of a multivariable system with delay for a quadratic criterion function is given by the Riccati partial differential equations. These are simultaneous partial differential equations which are difficult to solve numerically. In most computational algorithms, errors are inevitable, a vast memory is required, and a lot of computational time is needed. This makes it impractical to use available computers for these algorithms. The algorithm presented here gives optimal control effectively without a large memory requirement. It also provides a practical computational method for obtaining the optimal control of multivariable systems with delay. Several numerical computations are performed to show how the effectiveness of the algorithm compares with other methods.