ABSTRACT
This chapter deals with optimal control of time-delay/delay free, time-invariant/time-varying systems via block-pulse functions (BPF) and shifted Legendre polynomials (SLP). It considers time-varying systems containing delays and reverse time terms in state and control. The chapter discusses Based on using BPFs or SLPs, two unified approaches to compute optimal control law of linear time-delay dynamic systems with quadratic performance index. The problem of finding the optimal control law is reduced to the problem of solving algebraic equations obtained via the operational matrices. Time-delay systems are those systems in which time delays exist between the application of input or control to the system and its resulting effect on it. They arise either as a result of inherent delays in the components of the system or as a deliberate introduction of time delay into the system for control purpose.
