Riemannian trust-region methods for H2 optimal model reduction

In this paper, the Riemannian trust-region method for the H2 optimal model reduction problem is proposed. The problem is regarded as optimization problems on the Stiefel and Grassmann manifolds and several geometric quantities of the problems are discussed to develop the Riemannian trust-region method. Numerical experiments show that the proposed methods can solve the H2 optimal model reduction problem effectively.

[1]  Fernando Paganini,et al.  A Course in Robust Control Theory , 2000 .

[2]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[3]  A. Antoulas,et al.  H 2 Model Reduction for Large-scale Linear Dynamical Systems * , 2022 .

[4]  Wassim M. Haddad,et al.  Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach , 2011 .

[5]  James Lam,et al.  An approximate approach to H2 optimal model reduction , 1999, IEEE Trans. Autom. Control..

[6]  Robert E. Mahony,et al.  Optimization Algorithms on Matrix Manifolds , 2007 .

[7]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[8]  Pierre-Antoine Absil,et al.  Trust-Region Methods on Riemannian Manifolds , 2007, Found. Comput. Math..

[9]  Athanasios C. Antoulas,et al.  An overview of approximation methods for large-scale dynamical systems , 2005, Annu. Rev. Control..

[10]  Xu Yuesheng,et al.  FAST OPTIMAL H2 MODEL REDUCTION ALGORITHMS BASED ON GRASSMANN MANIFOLD OPTIMIZATION , 2013 .

[11]  Takayuki Ishizaki,et al.  Model Reduction and Clusterization of Large-Scale Bidirectional Networks , 2014, IEEE Transactions on Automatic Control.

[12]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[13]  G. Dullerud,et al.  A Course in Robust Control Theory: A Convex Approach , 2005 .

[14]  Belinda B. King,et al.  Proper orthogonal decomposition for reduced basis feedback controllers for parabolic equations , 2001 .

[15]  Bamdev Mishra,et al.  Manopt, a matlab toolbox for optimization on manifolds , 2013, J. Mach. Learn. Res..

[16]  Jérôme Malick,et al.  Projection-like Retractions on Matrix Manifolds , 2012, SIAM J. Optim..

[17]  Serkan Gugercin,et al.  H2 Model Reduction for Large-Scale Linear Dynamical Systems , 2008, SIAM J. Matrix Anal. Appl..