Optimal control of linear systems with delays in state and control via Walsh functions

The paper presents a parameter-embedding approach to the optimal control of linear time-delay systems, and develops a simple computational algorithm via Walsh functions. The algorithm employs the concept of Walsh operational matrices for delay and advance. These operational matrices provide us with a means of numerically integrating differential equations with delayed and advanced arguments; a major task in the process of computing optimal controls for time-delay systems. An attractive feature of the present method is its ultimate simplicity and the resulting piecewise constant controls are convenient in practical implementation.