On sparsity‐inducing methods in system identification and state estimation

Bako, Laurent

doi:10.1002/rnc.5995

Cited by 4 publications

(6 citation statements)

References 61 publications

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“…with order and singular order (n, q) = (3, 1). From (41), and with m = 1 + qn = 4, this yield the pencil problem [Φ 4 0,k + 𝜆 k Φ 4 1,k ]𝜃 = 0, and the matrix in Step 1 of Algorithm 1 consists of the 4 × 6 matrix:…”

Section: 11mentioning

confidence: 99%

“…In a linear discrete time (DT) setting, system identification in the presence of impulsive disturbances has been studied in References 1‐4. These approaches, based on nonsmooth optimization (e.g.,

{l}_1

norm minimization), are generally developed in a batch mode and the reader may consult the survey paper 5 for a complete and comprehensive description of these optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

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Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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Online parameters estimation algorithms are proposed for continuous time systems subject to structured perturbations. Using a distribution framework, a matrix pencil structure, whose polynomial order is characterized by the nature of the singularities describing the impulsive effects, is proposed for the modeling of perturbed systems with different disturbance types. Then, using an appropriate projection subspace, the rectangular pencils are reformulated as square generalized eigenvalue problems subject to linear constraints, from which unperturbed regression are derived. This approach allows for the implementation of recursive estimation schemes, free of penalty terms. An identifiability analysis is also conducted, and theoretical results are illustrated with experimental and simulated data.

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Section: 11mentioning

confidence: 99%

{l}_1

norm minimization), are generally developed in a batch mode and the reader may consult the survey paper 5 for a complete and comprehensive description of these optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

Online continuous time system identification in the presence of impulsive terms

Belkoura

2022

Adaptive Control & Signal

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“…Another important problem considered in this Special Issue is that of state estimation in the face of impulsive noise or sparse adversarial attacks. In this context, Ref 9 . surveys the application of sparsity‐inducing methods in robust regression, hybrid system identification and secure state estimation.…”

Section: Contentsmentioning

confidence: 99%

“…In this context, Ref. 9 surveys the application of sparsity-inducing methods in robust regression, hybrid system identification and secure state estimation. Ref.…”

Section: State Estimationmentioning

confidence: 99%

Special Issue on Sparsity‐inducing Methods in Control Theory

Pham

Nagahara

2022

Intl J Robust & Nonlinear

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Modern control theory is challenged by an increasing complexity of the systems to be controlled and meanwhile by the increasing level of demanded performance. In effect, the control performance specification comes with various other design requirements related to energy consumption, communication network topology, computational efficiency, fault-tolerance, robustness/resilience and diverse hard constraints with respect to size, cost, compliance to norms, etc. It can be observed that a significant number of performance specifications admit a mathematical formalization which involves implicitly or explicitly some structural sparsity requirements (e.g., design of network topology with minimum communication links, estimation in the presence of sporadic data losses, impulsive noise-tolerant control, identification of switched systems, etc). Furthermore, sparsity constraints can arise as a mere methodological device induced by the intrinsic nature of the control engineering problem, as well as from sparse uncertainties which can take the form of parametric inaccuracies in the system model or sparse disturbances affecting the measurements and the control signals. For example, a large-scale control system, such as a chemical plant or a power grid, could be subject to a myriad of failures, but it is very rare that a large number of faults occur simultaneously. Meanwhile, sparsity constraints can be leveraged to model critical situations where the sensory and control channels are under an integrity attack from a resource-constrained adversary, who can only break the encryption on a small subset of the signals. In all these situations, the structural sparsity, whether induced by intermittent errors, spatially distributed faults or adversary attacks, can usually be represented by additive sparse or low-rank matrices.From a methodological viewpoint, sparsity-inducing optimization is a powerful paradigm for developing control and estimation schemes that are robust to the aforementioned sparse uncertainties. Sparse optimization refers to a mathematical optimization framework in which the to-be-optimized objective function or the associated constraints involve an sparsity measure on the data such as the rank of a matrix, the "zero-norm" of a vector or the cardinality of a set. Although most of the sparse optimization problems are combinatorial in nature, recent advancements, such as 𝓁 1 relaxation and basis pursuit, have greatly reduced the computational complexity of sparse optimization for many practical problems. For example, compressed sensing has leveraged sparsity to bring a remarkable methodological shift in the way of acquiring, representing and processing information-bearing signals. Even though sparse optimization has been initially investigated in the communities of signal processing, information theory and machine learning, it has now been successfully applied to many other fields including the field of control systems design. For example, sparsity-inducing optimization has proven to be a powerful principle for devel...

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“…Unless there is only one submodel, the LLS model delivered by this scheme will not be isomorphic to the targeted LSS. We refer the interested reader to the recent survey 46 for applications of the sparsity‐inducing methods to system identification.…”

Section: Introductionmentioning

confidence: 99%

Basis transform in linear switched system models from input–output data

Bencherki,

Türkay,

Akçay

2023

Adaptive Control & Signal

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SummaryThis article addresses the problem of basis correction in the context of linear switched‐system (LSS) identification from input–output data. It is often the case that identification algorithms for the LSSs from input–output data operate locally. The local submodel estimates, identified individually by subspace algorithms from the input‐output data, reside in different‐state bases, which mandates performing a basis correction that facilitates their coherent patching for the ultimate goal of performing output predictions for arbitrary inputs and switching sequences. We formulate a persistence of excitation condition for the inputs and the switching sequences that guarantees the presented approach's success. These conditions are mild in nature, which proves the practicality of the devised algorithm. We supplement the theoretical findings with an elaborating numerical simulation example.

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On sparsity‐inducing methods in system identification and state estimation

Cited by 4 publications

References 61 publications

Online continuous time system identification in the presence of impulsive terms

Online continuous time system identification in the presence of impulsive terms

Special Issue on Sparsity‐inducing Methods in Control Theory

Basis transform in linear switched system models from input–output data

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