ITTC Project


Control of Stochastic Systems

Project Award Date: 09-01-2011



Description

Since most controlled stochastic systems have been described with a Brownian motion, it is important to study control problems for stochastic systems with other fractional Brownian motions. These control problems require significantly different analysis methods than the well-known methods for the control of systems with Brownian motions. These major differences have resulted in few available results for the optimal control of linear systems driven by an arbitrary fractional Brownian motion.

ITTC researchers have initiated a major study of these control problems for linear systems. This study not only obtains results for an arbitrary fractional Brownian motion but also provides results for the control of linear systems driven by a wide spectrum of other continuous stochastic processes. Researchers will expand the study of control problems to other cost functionals and to other types of systems, both finite and infinite dimensional. Specifically they will determine explicit expressions for the optimal control and the optimal cost for an ergodic (or long run average) quadratic cost functional. Researchers will study the control of linear stochastic partial differential equations for both finite and infinite time horizon control problems with a quadratic cost functional. The noise stochastic process and the control are allowed to be restricted to the boundary of the domain for the partial differential equation. Typically the stochastic systems have unknown parameters so the control problems are adaptive control problems.

The research will expand the initial ITTC work on adaptive control for a scalar linear system to multidimensional linear systems with an arbitrary fractional Brownian motion. Researchers will examine the control of bilinear systems driven by a fractional Brownian motion and having a quadratic cost functional. Since some physical models require discontinuous processes, it is proposed to study a controlled linear system with a quadratic cost functional and a discontinuous stochastic process, such as a Levy process. Some computationally related aspects of these control problems are also proposed such as the discretization of continuous time algorithms and the control of discrete time linear systems.


Investigators

Faculty Investigator(s): Tyrone Duncan (PI), Bozenna Pasik-Duncan

Student Investigator(s): Cody Clifton, Theodore Lindsey, Collin Eubanks, Jonathan Bush, Yi Yan


Project Sponsors


Primary Sponsor(s): National Science Foundation (NSF)


Partner with ITTC

The Information and Telecommunication Technology Center at the University of Kansas has developed several assistance policies that enhance interactions between the Center and local, Kansas, or national companies. 

ITTC assistance includes initial free consulting (normally one to five hours). If additional support is needed, ITTC will offer one of the following approaches: 

Sponsored Research Agreement

Individuals and organizations can enter into agreements with KUCR/ITTC and provide funds for sponsored research to be performed at ITTC with the assistance of faculty, staff and students.

Licensing and Royalty/Equity Agreement

An ITTC goal is the development of investment-grade technologies for transfer to, and marketing by, local, Kansas, and national businesses. To enhance this process, the Center has developed flexible policies that allow for licensing, royalty, and equity arrangements to meet both the needs of ITTC and the company.

Commercialization Development

Companies with a technology need that can be satisfied with ITTC's resources can look to us for assistance. We can develop a relationship with interested partners that will provide for the development of a technology suited for commercialization.

ITTC Resource Access

ITTC resources, including computers and software systems, may be made available to Kansas companies in accordance with the Center's mission and applicable Regents and University policies.

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