2002 Fiscal Year Final Research Report Summary
Fundamental Research on Effective Methods for Analysis and Design of Control Systems Based on Duality Theory
| Project/Area Number |
11650447
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | Osaka University |
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Principal Investigator |
OHTA Yoshito Osaka University, Dept. Mechanical Eng., Professor, 大学院・工学研究科, 教授 (30160518)
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| Project Period (FY) |
1999 – 2002
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| Keywords | Control System Design / L1 control / Linear Programming / Duality / Frequency Domain Constraint / Time Domain Constraint / Duality Gap / Finite Dimensional Approximation |
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| Research Abstract |
It is often convenient to formulate the control system design and analysis problems on an infinite dimensional space even if the system is finite dimensional. When we compute a solution, we have to restrict the variables on a finite dimensional space. Hence how to approximate the original infinite dimensional problem by a finite dimensional one is of great importance from the engineering point of view. In this research, we study (i) the computational algorithm of Hankel singular values and vectors, and (ii) the multi object control system design using abstract linear programming.
As for the Hankel singular values, the orthogonal complement of shift invariant subspace is exploited. If the system consists of finite dimensional part and infinite dimensional inner part, then the finite part and its dual system are represented on the orthogonal complement of the shift invariant subspace corresponding to the inner function. Then the Hamiltonian formula for the singular values is derived based on this representation.
As for the multi objective control design, the abstract linear programming gives a powerful approach for the optimal control with time and/or frequency domain constraints. Unlike the finite dimensional case, infinite dimensional linear programming may exhibit duality gap when finite dimensional approximation is not appropriate. In this research, we showed ways to approximate dual problems without introducing duality gap. This way, we can compute the design problem within an arbitrary error using finite dimensional convex optimization problems.
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