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Best achievable performance: non‐switching compensation for multiple models
Author(s) -
Sourlas Dennis D.,
Manousiouthakis Vasilios
Publication year - 1999
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(19990730)9:9<521::aid-rnc416>3.0.co;2-w
Subject(s) - minimax , control theory (sociology) , mathematical optimization , computer science , nonlinear system , process (computing) , quadratic growth , compensation (psychology) , differentiable function , measure (data warehouse) , optimization problem , dynamic programming , mathematics , control (management) , algorithm , psychology , mathematical analysis , physics , quantum mechanics , database , artificial intelligence , psychoanalysis , operating system
This paper presents a solution to the best achievable performance problem for a family of process models that are simultaneously stabilized by a non‐switching LTI compensator. Specifically, a method is presented that can quantify the best dynamic performance achievable by a dynamic feedback compensator, for a finite family of process models. Closed‐loop dynamic performance is quantified through a new performance measure that guarantees performance with respect to all allowable disturbances and allows for closed‐loop response shaping with respect to fixed disturbances. The simultaneous performance problem is then formulated as a quadratically constrained minimax optimization problem that is non‐differentiable and infinite dimensional. It is shown that the simultaneous performance problem can be solved through the iterative solution of appropriately constructed finite‐dimensional nonlinear programming problems. A method that identifies ϵ ‐globally optimal solutions to this type of problems is presented. Finally, the proposed approach is demonstrated through an illustrative numerical example problem. Copyright © 1999 John Wiley & Sons, Ltd.