ABSTRACT
This chapter discusses two recursive algorithms are presented for computing the optimal control law of linear time-invariant singular systems with quadratic performance index by using the elegant properties of block-pulse functions (BPF) and shifted Legendre polynomials (SLP). Also, a unified approach is given to solve the optimal control problem of singular systems via BPFs or SLPs. Two numerical examples are included to demonstrate the validity of the recursive algorithms and unified approach. Singular systems have been of considerable importance as they are often encountered in many areas. Singular systems arise naturally in describing large-scale systems. An interconnection of state variable subsystems is conveniently described as a singular system. The singular system is called a generalized state-space system, implicit system, semi-state system, or descriptor system. A single-term Walsh series method has been applied to study the optimal control problem of singular systems. In SLPs were used to solve the same problem. However, this approach is nonrecursive in nature.
