Performance and Robustness of Adaptive Controllers for Linear Stochastic Systems

In this thesis we address the twin questions of performance as well as robustness of an adaptive controller for linear stochastic systems. Regarding the performance problem, we consider the issue of convergence of the parameter estimates with respect to the stochastic gradient algorithm and the modified least squares algorithm. As to the linear model following problem, we have shown that under certain conditions, both algorithms are strongly consistent. For the general tracking problem, if the reference trajectory is sufficiently rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the robustness problem, we have presented a robust adaptive controller. Its mean square stabilizes the ideal system optimally if the noise signal satisfies a positive real condition. It can also stabilize a non-ideal system if the system is in a certain graph topological neighborhood of an ideal system.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Lin, Sheng-Fuu

Contributors dc:contributor

• Kumar, P.R.

• Engineering, Electronics and Electrical

Identifier

(UMI)AAI8908755

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69414