Journal article
Direct Method of Constructing H 2-Suboptimal Controllers: Discrete-Time Systems
Journal of optimization theory and applications, Vol.99(3), pp.617-653
12/1998
Handle:
https://hdl.handle.net/2376/108406
Abstract
For discrete-time systems, an H
2-suboptimal control problem is defined and analyzed. Then, an algorithm called H
2-suboptimal state feedback gain sequence (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 estimator-based measurement feedback controllers. Three different estimator structures (prediction, current, and reduced-order estimators) are considered. For a given H
2-suboptimal state feedback gain, a sequence of estimator gains for any of the three estimators considered 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 all three types of estimator-based controllers while still maintaining throughout the design the computational simplicity of it. This paper is the discrete-time version of Ref. 1. There are some conceptual similarities as well as fundamental differences between the H
2-suboptimal control problems for continuous-time and discrete-time systems. The fundamental differences arise mainly from the fact that, in contrast to continuous-time systems, for discrete-time systems the infimum of the H
2-norm over the class of strictly proper controllers is in general different from the infimum of the H
2-norm over the class of proper controllers.
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Details
- Title
- Direct Method of Constructing H 2-Suboptimal Controllers: Discrete-Time Systems
- Creators
- Z Lin - Department of Electrical Engineering University of Virginia Charlottesville VirginiaA Saberi - School of Electrical Engineering and Computer Science Washington State University Pullman WashingtonP Sannuti - Department of Electrical and Computer Engineering, Rutgers The State University of New Jersey Piscataway New JerseyY Shamash - College of Engineering and Applied Sciences State University of New York at Stony Brook Stony Brook New York
- Publication Details
- Journal of optimization theory and applications, Vol.99(3), pp.617-653
- Academic Unit
- Electrical Engineering and Computer Science, School of
- Publisher
- Kluwer Academic Publishers-Plenum Publishers; New York
- Identifiers
- 99900546734001842
- Language
- English
- Resource Type
- Journal article