Worst-case design in the time domain: The maximum principle and the standardH ∞ problem

Mathematics of Control, Signals and Systems - Tập 3 Số 4 - Trang 301-324 - 1990
Gilead Tadmor1
1Department of Mathematics, The University of Texas at Dallas, Richardson, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

A. Ball and N. Cohen, Sensitivity minimization in anH ∞ norm: paramentrization of all suboptimal solutions,Internat. J. Control.,46 (1987), 785–816.

J. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, State-space solutions to standardH 2 andH ∞ control problems,Proceedings of the 1988 American Control Conference, pp. 1691–1696. (Expanded version inIEEE Trans. Automat. Control,34 (1989), 831–846.

B. A. Francis,A Course in H ∞ Control, Lecture Notes in Control and Informations Sciences, vol. 88, Springer-Verlag, Berlin, 1987.

B. A. Francis and J. Doyle, Linear control theory with anH ∞ optimality criterion, Systems Control Group Report #8501, University of Toronto.

K. Glover and J. C. Doyle, State-space formalae for all stabilizing controllers that satisfy anH ∞-norm bound and relations to risk sensitivity,Systems Control Lett.,11 (1988), 167–172.

J. W. Helton, Worst case analysis in the frequency domain: TheH ∞ approach to control,IEEE Trans. Automat. Control.,30 (1985), 1154–1170.

R. E. Kalman, P. L. Falb and M. A. Arbib,Topics in Mathematical System Theory, McGraw-Hill, New York 1969.

P. P. Khargonekar, I. R. Petersen, and M. A. Rotea,H ∞ optimal control and state feedback,IEEE Trans. Automat. Control,33 (1988), 786–788.

P. P. Khargonekar, I. R. Petersen and K. Zhou, Robust stabilization of uncertain systems, preprint, 1987.

H. Kwakernaak and R. Sivan,Linear Optimal Control Systems, Wiley, New York, 1972.

E. B. Lee and L. Markus,Foundations of Optimal Control Theory, Wiley, New York, 1967.

D. J. N. Limebeer, E. M. Kasenally, and M. G. Safonov, A characterization of all solutions to the four block general distance problem, preprint, 1987.

E. F. Margeirou, Values and strategies for infinite time linear quadratic games,IEEE Trans. Automat. Control,21 (1976), 547–550.

J. Medanic, Bounds on the performance index and the Riccati equation in differential games,IEEE Trans. Automat. Control,12 (1967), 613–614.

C. N. Nett. C. A. Jacobson, and A. T. Miller, An integrated approach to controls and diagnostics: the 4-parameter controller, preprint.

I. R. Petersen, Disturbance attenuation andH ∞ optimization: a design method based on the algebraic Riccati equation,IEEE Trans. Automat. Control,32 (1987), 427–429.

J. E. Potter, Matrix quadratic solutions,SIAM J. Appl. Math.,14 (1966), 496–501.

I. B. Rhodes and D. G. Luenberger, Differential games with imperfect state information,IEEE Trans. Automat. Control,14 (1969), 29–38.

G. Tadmor,H ∞ in the time domain: the four block problem, Technical Report, LCDS/CCS #88-21, Brown University, July 1988.

M. S. Verma and J. C. Romig, Reduced order controller inH ∞-optimal synthesis methods of the first kind, preprint, University of Texas, December 1987.

K. Zhou and P. P. Khargonekar, An algebraic Riccati equation approach toH ∞-optimization,Systems Control Lett.,11, (1988), 85–92.