AE 713, Fall 2010

Stochastic Systems, Estimation and Identification in Aerospace Engineering

Stochastic adaptive control theory is concerned with recursive estimation of unknown parameters and control for systems with uncertainties modeled as random variables or random processes. The theory is motivated by applications in such diverse areas as aerospace guidance and control, signal processing and communications, manufacturing processes, and financial economics. Mathematical theory of stochastic adaptive control for models based on stochastic difference equations such as auto-regressive processes and stochastic differential equations as Markov diffusion processes have been developed and will be presented.

This course focuses on filtering and system identification theory.

The main course topics include:

• Conditional Expectation and Martingales.
• Estimation Methods: Least Squares and Maximum Likelihood Method.
• Limit Theorems of Probability and Convergence Analysis.
• Introduction to Stochastic Processes. Basic Examples: Markov Chains and Brownian Motion.
• Linear Filtering Theory, Kalman Filter, Prediction and Smoothing.
• Introduction to System Identification: Identification of Markov Chains, Identification of Linear Systems.