Abstract
This paper is concerned with the distributed control of a vibration process that can be described by a differential equation for a Hilbert-spacevalued functiony: [0, ∞) → H. The control functions on the right-hand side of this equation are taken fromL∞([0, ∞),H) equipped with the essential supremum norm. To be solved is the problem of time-minimal null-controllability by norm-bounded controls. This problem is essentially reduced to solving the problem of minimum norm control on a given time interval. This is solved via its dual problem which is approximately solved by truncation and discretization. Numerical results are presented for a vibrating string and a vibrating beam.
Similar content being viewed by others
References
Fattorini HO (1977) The time optimal problem for distributed control of systems governed by the wave equation. In: Aziz AK, Wingate JW, Balas MJ (eds) Control Theory of Systems Governed by Partial Differential Equations. Academic Press, New York
Krabs W (1981) Time minimal controllability in view of optimization. In: Auslender A, Oettli W, Stoer J (eds) Optimization and Optimal Control. Lecture Notes in Control and Information Sciences, vol 30. Springer-Verlag, Berlin, pp 211–277
Krabs W (1982) Convex optimization and approximation. In: Korte B (ed) Modern Applied Mathematics: Optimization and Operations Research. North-Holland, Amsterdam, pp 327–357
Krabs W (1985) On time-minimal distributed control of vibrating systems governed by an abstract wave equation. Appl Math Optim 13:137–149
Krabs W (1989) On time-minimal distributed control of vibrations. Appl Math Optim 19:65–73
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krabs, W., Yan, Z. Numerical solution of minimum norm problems of distributed control of vibrations. Appl Math Optim 21, 243–264 (1990). https://doi.org/10.1007/BF01445165
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01445165