ABSTRACT
This chapter presents a unified approach and two recursive algorithms via block-pulse functions (BPF) and shifted Legendre polynomials (SLP) to solve the linear-quadratic-Gaussian (LQG) control problem. By using the elegant operational properties of orthogonal functions (OF) (BPFs or SLPs), computationally elegant algorithms are developed. A numerical example is included to demonstrate the validity of the unified approach and recursive algorithms. The LQG control problem concerns linear systems disturbed by additive white Gaussian noise, incomplete state information and quadratic costs. The LQG controller is simply the combination of a linear-quadratic-estimator, a Kalman filter with a LQR. The separation principle guarantees that these can be designed and computed independently. The chapter deals with the LQG control design problem. It presentds the method of obtaining a solution of the LQG control design problem, which contain a unified approach and two recursive algorithms, respectively. A numerical example is included and demonstrates the effectiveness of unified approach and recursive algorithms.
