Continuous Time Dynamical Systems

Chapter 6

Linear-Quadratic-Gaussian Control

In this chapter, a unified approach and two recursive algorithms via BPFs and SLPs are presented to solve the LQG control problem. By using the elegant operational properties of OFs (BPFs or SLPs), computationally elegant algorithms are developed. A numerical example is included to demonstrate the validity of the unified approach and recursive algorithms.

6.1    Introduction

The LQG control problem [4] concerns linear systems disturbed by additive white Gaussian noise, incomplete state information and quadratic costs. The LQG controller is simply the combination of a LQE, i.e., a Kalman filter with a LQR. The separation principle guarantees that these can be designed and computed independently.

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