A Constraint Generation Approach to Learning Stable Linear Dynamical Systems

By Sajid M. Siddiqi, Byron Boots, Geoffrey J. Gordon. 2007

149 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Ocean Engineering

How researchers see this paper

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

In Artificial Intelligence

In Control and Systems Engineering

In Ocean Engineering

Citations in the corpus

Hilbert Space Embeddings of Predictive State Representations (2013, methodology): “aximize each model’s performance: a 5-dimensional nonlinear model using a kernelized version of linear system identication (K-LDS) [22], ing a stabilized version of spectral subspace identi- cation [23, 24] with Hankel matrices of 10 time steps; and a 50-state input-output HMM (IO-HMM) trained via E”
Bayesian reasoning and machine learning (2012, unknown): “3 Subspace Methods An alternative to EM and Maximum Likelihood training of an LDS is to use a subspace method[281, 249].”
Convergent Fitted Value Iteration with Linear Function Approximation (2011, methodology): “Explicitly enforcing all of these constraints is intractable, so we employ a constraint-generation approach [20].”
Hilbert Space Embeddings of Hidden Markov Models (2010, methodology): “In each case we compare the learned embedded HMM to several alternative time series models including (I) linear dynamical systems (LDS) learned by Subspace Identification (Subspace ID) (Van Overschee & De Moor, 1996) with stability constraints (Siddiqi et al., 2008), (II) discrete HMMs learned by EM”
A Regularized Linear Dynamical System Framework for Multivariate Time Series Analysis (2015, methodology): “(Boots, Gordon, and Siddiqi 2007) develops a spectral algorithm that is able to learn a stable LDS by limiting the largest eigenvalue of transition matrix A to be less than 1.”
Learning Stable Deep Dynamics Models (2020, background): “Alternatively, past work has also looked at different heuristics, such as approximately projecting a dynamics function A onto the (non-convex) stable set of matrices with eigenvalues Re(λi(A)) < 0 [3].”
Layered Dynamic Textures (2005, methodology): “For example, Siddiqi et al. [ 23 ] learn a stable DT, which is more suitable for synthesis, by iteratively adding constraints to the least-squares problem of [7].”
Modeling Video Dynamics with Deep Dynencoder (2014, background): “Stable LDS [4] tries to solve this by adding constraints on the eigenvalues.”
Learning to Filter with Predictive State Inference Machines (2015, background): “Such systems have been studied in the literature as time-series modeling or system identification problems (Siddiqi et al., 2007; Chan and Vasconcelos, 2007).”
Model Regularization for Stable Sample Rollouts (2014, background): “Siddiqi et al. (2007) addressed the problem of learning stable dynamics models of linear dynamical systems.”
Kernel Learning for Dynamic Texture Synthesis (2016, methodology): “Although introducing a feedback control mode [21] or adding constraints to a relaxed system solution [24] can make LDS more stable, these mechanisms can only guarantee limited number of eigenvalues close to one, which may also cause the synthesized sequence to decay gradually.”
Improved Learning of Dynamics Models for Control (2016, background): “Some of these approaches [13, 14] can provide performance guarantees in the infinite-data and model-realizable case (i.”