Mixed discrete/continuous specifications in sampled-data H2-optimal control

Abstract The increasing use of digital equipment in control in the last half century made a tremendous impact on controller design methodology. On the other hand, it had little effect on the control problem formulation: the control goals to a large extent still remain those of the analog world. The goal of this paper is to introduce and justify a new approach to sampled-data control system design, which enables one to account for the special opportunities, introduced by the employment of digital equipment. The essence of this approach is the simultaneous treatment of both continuous- and discrete-time performance requirements; hence, mixed discrete/continuous specifications (MDCS). In the paper, the sampled-data H 2 MDCS problem is formulated and solved. As a by-product of the MDCS treatment several novel technical results are obtained. Illustrative examples, demonstrating the potential benefits of the proposed approach are presented.

[1]  D. G. Meyer,et al.  Cost translation and a lifting approach to the multirate LQG problem , 1992 .

[2]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[3]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[4]  Hannu T. Toivonen,et al.  Sampled-data control of continuous-time systems with an H∞ optimality criterion , 1992, Autom..

[5]  I. Gohberg,et al.  Classes of Linear Operators , 1990 .

[6]  K. Poolla,et al.  Robust control of linear time-invariant plants using periodic compensation , 1985 .

[7]  M. A. Kaashoek,et al.  Classes of Linear Operators Vol. I , 1990 .

[8]  P. Kabamba.  Control of Linear Systems Using Generalized Sampled-Data Hold Functions , 1987, 1987 American Control Conference.

[9]  Bassam Bamieh,et al.  A general framework for linear periodic systems with applications to H/sup infinity / sampled-data control , 1992 .

[10]  Tomomichi Hagiwara,et al.  FR-operator approach to the H2 analysis and synthesis of sampled-data systems , 1995, IEEE Trans. Autom. Control..

[11]  D. G. Meyer.  A parametrization of stabilizing controllers for multirate sampled-data systems , 1990 .

[12]  Li Qiu,et al.  𝓗2-optimal Design of Multirate Sampled-data Systems , 1994, IEEE Trans. Autom. Control..

[13]  Tongwen Chen,et al.  Linear time-varying H2-optimal control of sampled-data systems , 1991, Autom..

[14]  Pramod P. Khargonekar,et al.  H 2 optimal control for sampled-data systems , 1991 .

[15]  Israel Gohberg,et al.  Time varying linear systems with boundary conditions and integral operators. I. The transfer operator and its properties , 1984 .

[16]  B. Francis,et al.  A lifting technique for linear periodic systems with applications to sampled-data control , 1991 .

[17]  Yutaka Yamamoto,et al.  A function space approach to sampled data control systems and tracking problems , 1994, IEEE Trans. Autom. Control..

[18]  Bassam Bamieh,et al.  The 2 problem for sampled-data systems , 1992, Systems & Control Letters.

[19]  G. E. Taylor,et al.  Computer Controlled Systems: Theory and Design , 1985 .

[20]  Munther A. Dahleh,et al.  H∞ and H2 optimal controllers for periodic and multirate systems , 1994, Autom..

[21]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[22]  Shinji Hara,et al.  A hybrid state-space approach to sampled-data feedback control , 1994 .

[23]  Bassam Bamieh,et al.  The H 2 problem for sampled-data systems m for sampled-data systems , 1992 .

[24]  Mituhiko Araki,et al.  Recent Developments in Digital Control Theory , 1993 .

[25]  Pramod P. Khargonekar,et al.  Synthesis of H/sub 2/ optimal controllers for sampled-data systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[26]  Leonid Mirkin,et al.  A New Representation of Lifted Systems with Applications , 1998 .

[27]  Petros G. Voulgaris,et al.  Optimal H ∞ and H 2 control of hybrid multirate systems , 1993 .

[28]  H. L. Trentelman,et al.  Sampled-Data and Discrete-Time $H_2$ Optimal Control , 1995 .

[29]  Gilead Tadmor,et al.  H ∞ optimal sampled-data control in continuous time systems , 1992 .

[30]  B. Francis,et al.  Stability Theory for Linear Time-Invariant Plants with Periodic Digital Controllers , 1988, 1988 American Control Conference.

[31]  B. Francis,et al.  H/sub 2/-optimal sampled-data control , 1991 .