Abstract
In this paper we study the following question: given a finite dimensional linear system together with a finite horizon (possibly indefinite) quadratic cost functional, when does the corresponding optimal cost converge to the optimal cost of the corresponding infinite horizon problem, as the length of the horizon tends to infinity? For the case that the linear quadratic problems are regular we establish necessary and sufficient conditions for this convergence to hold.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.W. Brockett, Finite Dimensional Linear Systems, New York, Wiley, 1970.
F.M. Callier & J.L. Willems, ‘Criterion for the convergence of the solution of the Riccati differential equation’ IEEE Trans. Aut. Control, AC-26, p. 1232–1242, 1981.
W.A. Coppel, ‘Matrix quadratic equation’, Bull. Austral. Math Soc., Vol. 10, p. 377–401, 1974.
O. Hijab, Stabilization of Control Systems, New York, Springer Verlag, 1987.
H. Kwakernaak & R. Sivan, Linear Optimal Control Systems, Wiley, New York, 1972.
K. Mârtensson, ‘On the matrix Riccati equation’, Information Sciences, Vol. 3, p. 17–49, 1971.
M Shayman, ‘Geometry of the algebraic Riccati equation–part 1’, SIAM Journal of. Contr. & Opt., Vol. 21, no 3, p. 375–393, 1983.
J.M. Soethoudt & H.L. Trentelman. ‘The regular indefinite linear quadratic problem with linear endpoint constraints’, Systems & Contr. Letters, Vol 12, No. 1, p. 23–31, 1989.
H.L. Trentelman ‘The regular free-endpoint linear quadratic problem with indefinite cost’, SIAM Journal of Cont. & Opt., Vol 27, No. 1, p. 27–42, 1989.
J.C. Willems, ‘Least squares stationary optimal control and the algebraic Riccati equation’, IEEE Trans. Aut. Control, AC 16, no. 6, p. 621–634, 1971.
J.L. Willems & F.M. Callier, ‘Large finite horizon and infinite horizon LQ-optimal control problems’, Optimal Contr. Appl. & Meth., Vol. 4, p 31–45, 1983.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Trentelman, H.L., Soethoudt, J.M. (1990). Convergence Properties of Indefinite Linear Quadratic Problems with Receding Horizon. In: Kaashoek, M.A., van Schuppen, J.H., Ran, A.C.M. (eds) Robust Control of Linear Systems and Nonlinear Control. Progress in Systems and Control Theory, vol 4. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4484-4_16
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4484-4_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8839-8
Online ISBN: 978-1-4612-4484-4
eBook Packages: Springer Book Archive