NDLI: A numerical comparison of frozen-time and forward-propagating Riccati equations for stabilization of periodically time-varying systems

Content Provider	IEEE Xplore Digital Library
Author	Prach, A. Tekinalp, O. Bernstein, D.S.
Copyright Year	2014
Description	Author affiliation: Dept. of Aerosp. Eng., Middle East Tech. Univ., Ankara, Turkey (Prach, A.; Tekinalp, O.) \|\| Dept. of Aerosp. Eng., Univ. of Michigan, Ann Arbor, MI, USA (Bernstein, D.S.)
Abstract	Feedback control of linear time-varying systems arises in numerous applications. In this paper we numerically investigate and compare the performance of two heuristic techniques. The first technique is the frozen-time Riccati equation, which is analogous to the state-dependent Riccati equation, where the instantaneous dynamics matrix is used within an algebraic Riccati equation solved at each time step. The second technique is the forward-propagating Riccati equation, which solves the differential algebraic Riccati equation forward in time rather than backward in time as in optimal control. Both techniques are heuristic and suboptimal in the sense that neither stability nor optimal performance is guaranteed. To assess the performance of these methods, we construct Pareto efficiency curves that illustrate the state and control cost tradeoffs. Three examples involving periodically time-varying dynamics are considered, including a second-order exponentially unstable Mathieu equation, a fourth-order rotating disk with rigid body unstable modes, and a 10th-order parametrically forced beam with exponentially unstable dynamics. The first two examples assume full-state feedback, while the last example uses a scalar displacement measurement with state estimation performed by a dual Riccati technique.
Starting Page	5633
Ending Page	5638
File Size	1756220
Page Count	6
File Format	PDF
ISBN	9781479932726
ISSN	07431619
e-ISBN	9781479932740
DOI	10.1109/ACC.2014.6859066
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Riccati equations Vehicle dynamics Aerodynamics Time-varying systems Distance measurement Output feedback Optimal control Control applications
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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