Stochastic Optimal Digital Feedback Control

This chapter provides a synthesis of algorithmic diagrams of the fundamental constituents of the implementation of stochastic optimal control systems. These include the stochastic linear quadratic regulator (LQR), the Kalman filter and the linear quadratic and gaussian, LQG regulator. The problem of stochastic LQR involves finding a strategy of control of the dynamic process that minimizes the cost function. The chapter presents a block diagram of the stochastic linear regulator, considering full availability of the state measurements for feedback. This diagram illustrates the Certainty Equivalent Principle, according to which the stochastic LQR control law of a linear dynamic process subjected to Gaussian white noise is certainly equivalent to that of the same deterministic process controlled by LQR. The chapter explores the properties of stochastic LQR. It focuses on the presentation of the scientific context and algorithmic diagram of the Kalman filter.