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Moment matching based reduced closed-loop design to achieve asymptotic performance (2405.02253v1)
Published 3 May 2024 in math.OC and math.DS
Abstract: In this paper, the moment matching techniques are adopted to obtain reduced-order closed-loop systems with reduced-order controllers that maintain the closed-loop stability and guarantee desired asymptotic performance, after revealing the relationship between the Internal Model Principle used in control design and the time-domain moment matching problem. As a result, the design of a low order controller can be done starting from considering the achieving of asymptotic performance as a moment matching problem, resulting in a reduced order closed-loop system.
- B. D. O. Anderson and Y. Liu. Controller reduction: concepts and approaches. IEEE Trans. Autom. Contr., 34(8):802–812, 1987.
- B. D. O. Anderson and Y. Liu. Controller reduction: concepts and approaches. In IEEE Proc. of American Control Conference, pages 1–9, 1987.
- A. C. Antoulas. Approximation of large-scale dynamical systems. SIAM, Philadelphia, 2005.
- A. Astolfi. Model reduction by moment matching for linear and nonlinear systems. IEEE Trans. Autom. Contr., 50(10):2321–2336, 2010.
- A. Astolfi. Model reduction by moment matching, steady-state response and projections. In Proc. 49th IEEE Conf. on Decision and Control, pages 5344 – 5349, 2010.
- E. de Souza and S. P. Bhattacharyya. Controllability, observability and the solution of AX−XB=C𝐴𝑋𝑋𝐵𝐶{AX}-{XB}={C}italic_A italic_X - italic_X italic_B = italic_C. Linear Algebra & Its App., 39:167–188, 1981.
- Feedback control theory. Macmillan Publishing Co., New York, 1992.
- Internal model principle of control theory. Automatica, 12:457–465, 1976.
- Model reduction of MIMO systems via tangential interpolation. SIAM J. Matrix Anal. Appl., 26(2):328–349, 2004.
- Sylvester equations and projection based model reduction. J. Comp. Appl. Math., 162:213–229, 2004.
- A Hessenberg-Schur method for tehe problem AX+XB=C𝐴𝑋𝑋𝐵𝐶{AX}+{XB}={C}italic_A italic_X + italic_X italic_B = italic_C. IEEE Trans. Autom. Contr., 24(6):909–913, 1979.
- Data-driven modeling and control of large-scale dynamical systems in the Loewner framework, 2021.
- Krylov-based controller reduction for large-scale systems. In Proc. of 43rd Conf. on Decision and Contr., volume 3, pages 3074–3077, 2004.
- M. L. J. Hautus. A frequency domain treatment of disturbance decoupling and output stabilization. In Lectures in Applied Mathematics, volume 18. American Mathematical Societies, 1980.
- D. Y. Hu. Krylov-subspace methods for the Sylvester equation. Linear Algebra & its Applications, 172:283–313, 1992.
- Families of moment matching based, low order approximations for linear systems. Systems & Control Letters, 64:47–56, 2014.
- Balancing as a moment matching problem. In Proc. 20th Int. Symp. on Mathematical Theory of Networks and Sys., 2012.
- From reference model selection to controller validation: Application to loewner data-driven control. IEEE Control Systems Letters, 3(4):1008–1013, 2019.
- Y. Liu and B. D. O. Anderson. Controller reduction via stable factorization and balancing. Int. J. Control, 44:507–531, 1986.
- A. Medvedev and G. Hillerström. An external model control system. Control-Theory and Advanced Technology, 10(4):1643–1665, 1995.
- Feedback systems. Princeton Univ. Press, 2012.
- T. Reis and T. Stykel. Stability analysis and model order reduction for coupled systems. Math. Comput. Model. Dyn. Syst., 13(5):413–436, 2007.
- H. Sandberg. An extension to balanced truncation with application to structured model reduction. IEEE Trans. Autom. Contr., 55(4):1038–1043, 2010.
- H. Sandberg and R. M. Murray. Model reduction of interconnected linear systems. Optimal Control, App. and Methods, 30(3):225–245, 2009. Special Issue on Directions, Applications and Methods and Robust Control.
- G. Schelfourt and B. De Moor. A note on closed-loop balanced truncation. IEEE Trans. Autom. Contr., 41(10):1498–1500, 2002.
- A. Vandendorpe and P. Van Dooren. Model reduction of interconnected systems. In Model order reduction: theory, research aspects and applications, volume 13 of Mathematics in industry, pages 305–321. 2008.
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