Direct Method of Constructing H 2-Suboptimal Controllers: Continuous-Time Systems

Z. Lin, A. Saberi, P. Sannuti and Y. A. Shamash
Additional contact information
Z. Lin: University of Virginia
A. Saberi: Washington State University
P. Sannuti: The State University of New Jersey
Y. A. Shamash: State University of New York at Stony Brook

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 3, No 2, 585-616

Abstract: Abstract An H 2-suboptimal control problem is defined and analyzed. Then, an algorithm called H 2-suboptimal state feedback gain sequence algorithm (Algorithm A1) is developed. Rather than utilizing a perturbation method, which is numerically stiff and computationally prohibitive, Algorithm A1 utilizes a direct eigenvalue assignment method to come up with a sequence of H 2-suboptimal state feedback gains. Also, although the sequence of H 2-suboptimal state feedback gains constructed by Algorithm A1 depends on a parameter ɛ, the construction procedure itself does not require explicitly the value of the parameter ɛ. Next, attention is focused on constructing a sequence of H 2-suboptimal observer-based measurement feedback controllers. Both full-order as well as reduced-order observer-based controllers are developed. For a given H 2-suboptimal state feedback gain, a sequence of observer gains for either a full-order or reduced-order observer can be constructed by merely dualizing Algorithm A1. The direct method of constructing H 2-suboptimal controllers developed here has a number of advantages over the perturbation method, e.g., it has the ability to design both full-order and reduced-order observer-based controllers while still maintaining throughout the design the computational simplicity of it.

Keywords: Continuous-time systems; H 2-suboptimal control; direct methods; low-gain designs; disturbance decoupling problem; almost disturbance-decoupling problem (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021751016836

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