Phase-space reconstruction: a path towards the next generation of nonlinear differential equation based models and its implications towards non-uniform sampling theory

Tolle, Charles R.; Pengitore, Mark

doi:10.1109/isrcs.2009.5251347

Cited by 1 publication

(2 citation statements)

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“…Many of these issues are well known within the regression community. For a bit more insight into the dynamical issues please see [20]. Without some type of weighting scheme the amount of data contained within the slower evolving portions of the phase-space can simply just smooth out the effects of other portions of the phase-space.…”

Section: Discussionmentioning

confidence: 99%

“…Without some type of weighting scheme the amount of data contained within the slower evolving portions of the phase-space can simply just smooth out the effects of other portions of the phase-space. In previous work [20], the author has discussed some of these affects under the guise of the need for multiple sample times within different portions of a system's phase-space. There are numerous directions one can take, again this paper is meant as a starting point not a complete summery of completed research results.…”

Section: Discussionmentioning

confidence: 99%

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Musings on persistent excitation prompts new weighted least squares SysID method for nonlinear differential equation based systems

Tolle

2012

2012 5th International Symposium on Resilient Control Systems

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The Control community relies heavily on good System Identification (SysID) for finding the plant models needed to develop a good controller. However over time the SysID process and controller development process have remained generally separate activities. One reason for this is that SysID and Control are disparate in their fundamental nature. For good SysID, one is faced with the challenge of persistently exciting plant dynamics; while a good control system attempts to constrain or suppress much of a plant's natural dynamics with desired dynamics. It is this inherent conflict that separates the two practices. But for many plants, their inherent instabilities makes trajectory collection difficult, thus there is a desire to perform data collection while under some simple form of control. Nevertheless, in order to perform solid SysID one must sample the very dynamics one might need to suppress; how then can this be achieved? This paper will explore the notation of persistent excitation, its relationship to phase space trajectories, and how one might recover the most nonlinear dynamics information for SysID while remaining under the linearizing based control region -the very place that those dynamics are most suppressed.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%