Abstract
This paper presents a simple method for determining a minimum-energy input function that takes a controllable linear time-invariant system to any desired state. The method is based upon the idea of formulating the problem as a variational problem under constraint of integral type. The solution is constructive and highly suited to presentation in undergraduate classes in linear systems and control theory, offering a good pedagogical approach for this topic.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Polak
E.
Wong
E.
, A First Course on Linear Systems (Van Nostrand Reinhold , New York , 1970 ).
2.
Fortmann
T. E.
Hitz
K. L.
, An Introduction to Linear Control Systems (Marcel Dekker , New York , 1977 ).
3.
Friedland
B.
, Control Systems Design , 2nd edn (MacGraw-Hill , Singapore , 1987 ).
4.
Kamen
E. W.
, Signals and Systems , 2nd edn (Macmillan , New York , 1990 ).
5.
Chen
C. T.
, Linear System Theory and Design (Holt, Rinehart and Winston , New York , 1984 ).
6.
Rugh
W. J.
, Linear System Theory , 2nd edn (Prentice Hall , Upper Saddle River, NJ , 1996 ).
7.
Luenberger
D. G.
, Optimization by Vector Space Methods (John Wiley , New York , 1969 ).
8.
Zeidler
E.
, Applied Functional Analysis, Applications to Mathematical Physics (Springer , New York , 1995 ).
9.
Kubrusly
C. S.
, Elements of Operator Theory (Birkhäuser , Boston , 2001 ).
10.
Weinstock
R.
, Calculus of Variations (Dover , New York , 1974 ).