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Stochastic Adaptive Control


Stochastic adaptive control methods. Stochastic processes such as Markov chains and Brownian motion, martingales and estimation techniques. Identification of discrete and continuous time linear stochastic systems. Specific applications and simulation results of stochastic adaptive control theory. Introduction to Control Theory.


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MATH 627 or 727 or equivalent.

Credit Hours: 

Adaptive control is the identification and control of the system. In some applications we have to identify the system and to adjust the control in accordance with the model which is supposed to be approaching the true system during the process of identification. This is why there has been tremendous interest in identification and adaptive control for stochastic systems from both theorists and practitioners, in particular, mathematicians, engineers, economists, biologists, environmental scientists and others.

The opening lectures will present preliminaries such as the fundamentals of probability theory and both classical and refined results in martingale limit theory and estimation theory. Subsequent lectures will give a comprehensive and systematic treatment of the main topics.


Input-output models Martingales Adaptive control of Markov chains Filtering Theory Linear System Identification Optimal control for state-space models Self-tuning and self-optimizing controls Estimation and Control of Linear Stochastic Systems and Applications

The area of adaptive systems has been one of the most active in identification and control theory of the past decade. The main aim of this course is to show an application of probability theory, statistics, stochastic processes and control to stochastic adaptive control theory. The core mathematical statistics topics of estimation, testing, and confidence intervals are covered. Following the core topics such modern topics as ranking and selection procedures are covered. Computer-assisted data analysis is discussed at several points, since it is very important for students of modern probability and mathematical statistics to have a comprehensive view that includes a glimpse of the importance of statistical computation to the field.

(Pasik-Duncan 2015 )


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