A cutting plane method for solving KYP-SDPs

Self Cite

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem.

Section: Sparse Formulationmentioning

confidence: 99%

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

Andersen

Pakazad

Hansson

et al. 2014

Self Cite

“…Exploiting this structure for distributed computing as discussed in [26], or combining the SSS framework with other LMI solution techniques (e.g. [62]) to approach such problems seems promising, and should be investigated.…”

Section: Discussionmentioning

confidence: 99%

Distributed Control: A Sequentially Semi-Separable Approach for Spatially Heterogeneous Linear Systems

Rice

Verhaegen

2009

Abstract-We consider the problem of designing controllers for spatially-varying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis, analysis and sub-optimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example.

“…Our contribution can therefore be seen in the context of a growing body of research on specialized solvers for special classes of SDPs appearing in robustness analysis via integral quadratic constraints and the Kalman-Yakubovich-Popov lemma, e.g. [32], [33], [34], [35]. Of more direct relevance to system identification is [36], which develops a custom interior point method (exploiting structure in the Nesterov-Todd equations) for nuclear norm approximation with application to subspace identification.…”

Section: Introductionmentioning

confidence: 99%

Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Umenberger

Manchester

2019

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.