ISSN:
1573-2878
Keywords:
Distributed-parameter systems
;
optimal control
;
maximum principle
;
singular mass matrix
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939535
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