NDLI: Direct Method of Constructing H $_{2}$-Suboptimal Controllers: Discrete-Time Systems

Content Provider	Springer Nature Link
Author	Lin, Z. Saberi, A. Sannuti, P. Shamash, Y. A.
Copyright Year	1998
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.
Starting Page	617
Ending Page	653
Page Count	37
File Format	PDF
ISSN	00223239
Journal	Journal of Optimization Theory and Applications
Volume Number	99
Issue Number	3
e-ISSN	15732878
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	1998-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Applications of Mathematics Optimization Calculus of Variations and Optimal Control Engineering Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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