Discrete-Time Infinite-Dimensional Adaptive Control and Rejection of Persistent Disturbances: To D or Not to D? Conference Paper

abstract

• In many cases an adaptive control must be implemented in discrete-time rather than continuous-time, aerospace applications. In the case of infinite-dimensional systems, the adaptive control theoretic problem becomes substantially different; we will emphasize those anomalies here. Given a linear discrete-time infinite dimensional plant on a Hilbert space and disturbances of known waveform but unknown amplitude and phase, we show that there exists a stabilizing discerete-time direct model reference adaptive control law with certain disturbance rejection and robustness properties. Our central result is a discrete-time version of Barbalat-Lyapunov result for infinite-dimensional Hilbert spaces. This is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively regulated. Our results are illustrated on a system described by a compact self-adjoint operator; such a description fits many discrete-time applications.

name of conference

• 21st Mediterranean Conference on Control and Automation

authors

• Balas, Mark

published proceedings

• 21st Mediterranean Conference on Control and Automation

author list (cited authors)

• Balas, M. J., & Frost, S. A.

citation count

• 1

complete list of authors

• Balas, Mark J||Frost, Susan A

publication date

• June 2013

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

keywords

• Adaptation Models
• Adaptive Control
• Aerospace Application
• Aerospace Control
• Barbalat-lyapunov Result
• Compact Self-adjoint Operator
• Continuous Time Systems
• Continuous-time Control
• Discrete Time Systems
• Discrete-time Applications
• Discrete-time Control
• Discrete-time Infinite-dimensional Adaptive Control
• Disturbance Rejection
• Frequency Modulation
• Hilbert Space
• Hilbert Spaces
• Infinite-dimensional Hilbert Spaces
• Infinite-dimensional Systems
• Linear Discrete-time Infinite Dimensional Plant
• Linear Infinite-dimensional System
• Lyapunov Methods
• Model Reference Adaptive Control Systems
• Multidimensional Systems
• Persistent Disturbances
• ROBUST CONTROL
• Robustness Property
• Stabilizing Discerete-time Direct Model Reference Adaptive Control Law
• Trajectory
• Waveform Analysis
• Waveform Disturbances

Digital Object Identifier (DOI)

• 10.1109/med.2013.6608849

start page

• 1042

end page

• 1049

URL

• http://dx.doi.org/10.1109/med.2013.6608849