The time-optimal design of linear dynamic systems

Author

Horne, G.J. ; Bernholtz, B.

Author_Institution

Nova Scotia Technical College, Halifax, Nova Scotia

Volume

19

Issue

3

fYear

1974

fDate

6/1/1974 12:00:00 AM

Firstpage

258

Lastpage

259

Abstract

The following general time-optimal design problem is studied: determine a real constant square matrix, $A$ , subject to specified constraints, to minimize the transit time between specified endpoints while satisfying the vector differential equation $\\dot{x}(t) = Ax(t)$ . Two specific kinds of constraints on $A$ are considered: 1) where the individual elements of $A$ are free but the matrix as a whole must satisfy $Q(A) \\leq \\hat{Q}$ where $Q(A)$ is a specified homogeneous function of the elements of $A$ and $\\hat{Q}$ is a given upper bound and 2) where the elements of $A$ are individually bounded. Theoretical results show that both problems can be solved by first solving a related minimum cost fixed time problem. The latter problem is solved iteratively by using the generalized Newton-Raphson method for two point boundary value problems to provide a set of linear equations at each iteration. The cost function $Q$ is then minimized subject to these equations using appropriate optimization techniques.

Keywords

Linear systems, time-invariant continuous-time; Optimization methods; Parameter selection; Time-optimal control; Boundary value problems; Control systems; Cost function; Differential equations; Industrial engineering; Linear systems; Upper bound; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1974.1100539

Filename

1100539