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Dissertation
Design of H^[infinity] controller by energy dissipation approach
Doctor of Philosophy (Ph.D.), Drexel University
1997
DOI:
https://doi.org/10.17918/00009168
Abstract
In this thesis, a controller design based on the energy dissipation approach is proposed to solve a more general H[infinity] control problem with nonzero direct feedthrough term D11(x) from the exogenous input to the controlled output. Initially, we discuss the relationship between the dissipative system and the H[infinity] control and then formulate the H[infinity] control problem as an energy dissipation problem. Due to the requirement of the closed-loop system to be [gamma]-dissipative, the conditions for the existence of solution to the problem can be derived. With the separation principle proposed by Bail, Helton and Walker, a dissipative controller can be constructed as well. For the nonlinear system, we will derive the necessary conditions for the closed-loop system to be dissipative and present the formulas to constructing a dissipative controller. These necessary conditions involve two Hamilton Jacobi inequalities which are the counterpart of the Riccati inequalities in the linear H[infinity] control. With the proposed dissipative controller, we show that the closed-loop system is [gamma]-dissipative. The solution to the linear case of the problem will also be given. The two Hamilton Jacobi inequalities will reduce to the two Riccati inequalities in the linear case and the coupling condition between the two Hamilton Jacobi solutions corresponds to that the spectral radius of the product of the two Riccati solution is less than the square of the prescribed bound.
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Details
- Title
- Design of H^[infinity] controller by energy dissipation approach
- Creators
- Paohwa Yang
- Contributors
- Bor-Chin Chang (Advisor) - Drexel University, Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- viii, 68 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Engineering (1970-2026); Drexel University
- Other Identifier
- 991021889094804721