Abstract
Various existing approaches to unbounded observation and control action are discussed and compared with respect to their potential applications. If one is only interested in stabilizing and regulating, then an extended system idea is presented which allows one to generalize existing results for bounded control in a simple manner.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A.V. Balakrishnan, "Optimal control problems in Banach spaces", J.S.I.A.M. Control, 1965, pp. 152–179.
A.V. Balakrishnan, "Boundary control of parabolic equations: L-Q-R theory", Proc. Conf. on theory of Nonlinear Equations, Sept. 1977, Akademic Verlag, Berlin 1978.
R.F. Curtain and A.J. Pritchard, "An abstract theory for unbounded control action for distributed parameter systems", S.I.A.M. J. Control and Optim. 15 (1977) pp. 566–611.
R.F. Curtain and A.J. Pritchard, "Infinite dimensional linear systems theory". Lecture Notes in Control and Information Sciences, Vol. 8, Springer Verlag, 1978.
R.F. Curtain, "Finite dimensional compensators for parabolic distributed systems with unbounded control and observation (to appear in S.I.A.M. J. Control and Optimization).
R.F. Curtain, "Finite dimensional compensators for some hyperbolic systems with boundary control", Workshop on Distributed Parameter Systems, Vorau, Australia, July, 1982, (to appear).
R.F. Curtain, "Stabilization of parabolic systems with point observations and boundary control via integral dynamic output feedback of a finite-dimensional compensator. The 5th International conference in Analysis and Optimization of Systems, pp. 761–776. Lecture Notes in Control and Information Sciences, Vol. 44, Springer Verlag, 1982.
R.F. Curtain, "Regulation and control of boundary control systems", to appear in Matematica Aplicada e Computacional.
H.O. Fattorini, "Boundary control systems", S.I.A.M. J. Control, 6, pp.349–385 1968.
I. Lasiecka, "Unified theory for abstract parabolic boundary problem: a semigroup approach", App. Math. and Optim., 6, pp. 281–333, 1980.
I. Lasiecka and R. Triggiani, "A cosine operator approach to modelling L(O,T; L2 (Γ)) boundary input hyperbolic equations", Appl. Math. and Optim., 7, pp. 35–93, 1981.
I. Lasiecka and R. Triggiani, "Dirichelet boundary control problem for parabolic equations with quadratic cost: analycity and Riccati's feedback synthesis", S.I.A.M. J. Control and Optim. 21, pp. 41–67, 1983
I. Lasiecka and R. Triggiani, "Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations", J. Diff. Eqns. 1982
I. Lasiecka and R. Triggiani, "Hyperbolic equations with Dirichelet boundary feedback via the position vector: regularity and almost periodic stabilization Parts I–III", Appl. Math. and Optim., 8, pp. 1–37, 103–130, 199–221. 1981.
I. Lasiecka and R. Triggiani, "Stabilization and structural assignment of Dirichelet boundary feedback parabolic equations", S.I.A.M. J.Control and Optim., to appear.
J. Lions, "Optimal control of systems governed by partial differential equations", Springer Verlag, 1971.
S. Pohjolainen, "Robust multivariable controller for distributed parameter systems", Tampere University of Technology Publications, 1980.
S. Pohjolainen, "Robust multivariable P.I.-controller for infinite-dimensional systems", I.E.E.E. Trans. Autom. Control, AC-23, pp. 17–30, 1982.
A.J. Pritchard and J. Zabczyk, "Stability and Stabilizibility of infinite-dimensional systems", S.I.A.M. Review, 23, pp. 25–52, 1981.
J.M. Schumacher, "Dynamical feedback in finite and infinite-dimensional linear systems", Mathematical Centre Tracts, No. 143, Mathematisch Centrum, Amsterdam, 1981.
R. Triggiani, "Well-posedness and regularity of boundary feedback parabolic systems", J. Diff. Eqns., pp. 347–362, 1980.
R. Vinter, "Semigroups on product spaces and applications to initial value problems with non-local boundary conditions", Proc. 2nd symposium on control of distributed parameter systems, University of Warwick, England, 1977 Permagon, Press, 1978.
D.C. Washburn, "A semigroup theoretic approach to modeling boundary inputs problem", Ph.D. Thesis, U.C.L.A., 1974.
J. Zabczyk, "Stabilization of boundary control systems", Lecture Notes in Control and Information Systems, Vol. 14, pp. 321–332, 1974.
J. Zabczyk, "A semigroup approach to boundary control", idem 22.
J. Zabczyk, "On the decomposition of generators", S.I.A.M., J. Control and Optim., 16, pp. 523–534, 1978.
J. Zabczyk, "On stabilizibility of boundary control systems", C.R.M. report No. 785, Université de Montréal, 1978.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1984 Springer-Verlag
About this paper
Cite this paper
Curtain, R.F. (1984). On semigroup formulations of unbounded observations and control action for distributed systems. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031052
Download citation
DOI: https://doi.org/10.1007/BFb0031052
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13168-7
Online ISBN: 978-3-540-38826-5
eBook Packages: Springer Book Archive