A subspace approach to balanced truncation for model reduction of nonlinear control systems

By Sanjay Lall, Jerrold E. Marsden, Sonja Glavaski. 2002

601 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanical Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c2f5609fc33af8af4f7d1db022abd8f3dc3dff03

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

In Mechanical Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Proper orthogonal decomposition for optimality systems (2008, neutral): “Received March 24, 2006.”
Simplified and effective motor control based on muscle synergies to exploit musculoskeletal dynamics (2009, background): “Balanced truncation is one such reduction procedure, with the goal of identifying a low-dimensional representation of a system’s input–output dynamics* (22, 38).”
Model-reduced gradient-based history matching (2011, methodology): “It has been shown in Lall et al. (2002) that for a stable, linear system using impulse inputs, the empirical Gramian is identical to the controllability Gramian.”
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition (2008, neutral): “Improvements in the numerical efficiency of reduced-order models have been focused mostly on the development of alternative, more efficient methods to compute the approximating basis functions [15], [30], [41].”
Constraint reduction procedures for reduced‐order subsurface flow models based on POD–TPWL (2015, methodology): “(including balanced POD [27, 28], in which POD is used to approximate the Gramians in the balanced truncation method), the appropriate constraint reduction matrix is provided from theory [29].”
A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations (2005, methodology): “Many model-order reduction techniques for time-dependent systems are proposed in the literature: the most well-known are proper orthogonal decomposition (POD or Karhunen-Loève decomposition) [40], balanced truncation [26], and various related hybrid [19,45] techniques; see also [20,33] for an applic”
Power System Dynamic State Estimation: Motivations, Definitions, Methodologies, and Future Work (2019, background): “The empirical observability Gramian [62], [63] provides a way to analyze the state-output behavior of a nonlinear system.”
Equation-free: The computer-aided analysis of complex multiscale systems (2004, methodology): “The use of observer theory (e.g., Luenberger, 1964; Krener, 2003) and realization balancing (e.g., Moore, 1981; Lall et al., 2002) arises naturally: the microscopic system dynamics are observed on the macroscopic variables, but are realized through the microscopic simulator.”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, methodology): “It was proposed in [75] to use the same balanced truncation POD method for dealing also with nonlinear flows.”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, methodology): “Common choices for computing the reduced-basis matrix Φ when the velocity is linear in its first argument include balanced truncation [52], rational interpolation [4, 31], the reduced-basis method [59, 64], Rayleigh–Ritz eigenvectors [20]; common choices when the velocity is nonlinear include POD [3”
Generalizing Koopman Theory to Allow for Inputs and Control (2016, methodology): “The method, however, requires a linear adjoint calculation [28, 49, 40, 20], which is not possible in typical data-driven experiments.”
Dynamic model reduction: An overview of available techniques with application to power systems (2012, background): “However, in the case of controlled systems, one is concerned with modelling the relationship between the system behaviour and the system inputs and outputs, or actuators and sensors [7].”
Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control (2013, methodology): “Proper orthogonal decomposition, model-order reduction, apriori and a-posteriori error analysis, linear-quadratic optimal control, primal-dual active set strategy.”