access icon free Reduced optimal models via cross Gramian for continuous linear time-invariant systems

© The Institution of Engineering and Technology
Received 01/11/2016, Accepted 09/05/2017, Revised 17/04/2017, Published 01/06/2017

In this study, the authors focus on the problem of model order reduction (MOR) suitable for continuous linear time-invariant (LTI) systems. Specifically, for single-input single-output (SISO) LTI systems, a couple of MOR algorithms via the cross Gramian are presented. The authors first give a cross Gramian-based optimal MOR iterative algorithm to reduce the SISO system. Further, the authors explore the optimisation problem on the Stiefel manifold. Based on the geometric notions on this manifold, a conjugate gradient iterative algorithm (CGIAHM) is proposed. The conjugate gradient direction used to search for the minimiser is derived by applying the notion of vector transport. It is worth mentioning that the conjugate gradient used in the CGIAHM algorithm is a decent direction for the cost function due to the ingenious construction of this algorithm. In addition, the authors’ algorithms are extended to solve the optimal MOR problem for general LTI systems. Finally, two numerical examples demonstrate the effectiveness of their algorithms.

Inspec keywords: conjugate gradient methods; minimisation; optimal systems; H2 control; reduced order systems; linear systems; continuous systems; search problems

Other keywords: single-input single-output LTI systems; SISO LTI systems; H2 optimisation problem; model order reduction; H2 minimiser search; geometric notions; cross Gramian-based H2 optimal MOR iterative algorithm; vector transport; continuous linear time-invariant systems; conjugate gradient iterative algorithm; Stiefel manifold; reduced H2 optimal models; cost function; CGIAHM algorithm; continuous LTI systems

Subjects: Linear control systems; Linear algebra (numerical analysis); Interpolation and function approximation (numerical analysis); Optimisation techniques; Optimal control

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