Scalable identification of stable positive systems

Umenberger, Jack; Manchester, Ian R.

doi:10.1109/cdc.2016.7798974

Cited by 15 publications

(36 citation statements)

References 33 publications

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“…For identification of 'large scale' systems (e.g. models of high dimension n x ), it is possible to use only gradient information, if moderate-accuracy is acceptable, e.g., gradient descent or BFGS approximation of the Hessian, as in [40].…”

Section: A Complexity Of Each Newton Iterationmentioning

confidence: 99%

“…simulation error decreases) monotonically with increasing model complexity. In contrast, performance of models fit by minimization of EE is more erratic and exhibits (40). Parenthesized numbers denote the degrees of the polynomials (e,f,g) for models of the form (39).…”

Section: B Comparison To Rie and Equation Errormentioning

confidence: 99%

“…Sections VI, VII, and VIII present empirical comparisons to established methods on a number of example problems, and finally Section IX offers concluding remarks. Preliminary work on specialized algorithms in the linear setting was presented in [40], which employed BFGS [41, §6]) approximations of the Hessian.…”

Section: Introductionmentioning

confidence: 99%

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Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Umenberger

Manchester

2019

IEEE Trans. Automat. Contr.

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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.

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Section: A Complexity Of Each Newton Iterationmentioning

confidence: 99%

Section: B Comparison To Rie and Equation Errormentioning

confidence: 99%

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Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Umenberger

Manchester

2019

IEEE Trans. Automat. Contr.

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“…Another motivating application is nonlinear system identification with guaranteed model stability, building on the results of Tobenkin et al (2017). Recent results allow scalable computation for linear systems (Umenberger and Manchester, 2016). With separable contraction metrics, these could be extended to identification of large-scale nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

Manchester

Slotine

2017

IFAC-PapersOnLine

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Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are exponentially stable, can have that property verified by a separable metric. Making use of recent results in the theory of positive linear systems and separable Lyapunov functions, we prove several new results showing when this is possible, and discuss the application of to nonlinear distributed control design via convex optimization.

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“…The structure learning problem for distributed dynamical systems is a precursor to inference in systems that are not fully observable. This case encompasses many practical problems of known artificial, biological and chemical systems, such as neural networks [5,6,7], multi-agent systems [8,9,10,11] and various others [1]. Modelling a partially observable system as a dynamical network presents a challenge in synthesising these models and capturing their global properties [1].…”

Section: Introductionmentioning

confidence: 99%

An Information Criterion for Inferring Coupling of Distributed Dynamical Systems

Cliff

Prokopenko

2016

Front. Robot. AI

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The behavior of many real-world phenomena can be modeled by non-linear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical system. Specifically, we study the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph. Unlike established structure learning procedures that find locally maximum posterior probabilities of a network structure containing latent variables, our work exploits the properties of dynamical systems to compute globally optimal approximations of these distributions. We arrive at this result by the use of time delay embedding theorems. Taking an information-theoretic perspective, we show that the log-likelihood has an intuitive interpretation in terms of information transfer.

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Scalable identification of stable positive systems

Cited by 15 publications

References 33 publications

Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

Specialized Interior-Point Algorithm for Stable Nonlinear System Identification

On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

An Information Criterion for Inferring Coupling of Distributed Dynamical Systems

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