Block sparse design of distributed controllers for dynamical network systems

Adachi, Ryosuke; Yamashita, Yoichi; Kobayashi, Koichi

doi:10.1002/rnc.6092

Cited by 2 publications

(3 citation statements)

References 30 publications

(87 reference statements)

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“…Most of the contributions of this Special Issue present recent methodological developments in control design techniques involving an implicit or explicit sparsification constraint. The sparse constraint is imposed either on the desired control signal 1‐3 or on the structure of the to‐be‐designed controller 4,5 . Both continuous‐time and discrete‐time systems are considered.…”

Section: Contentsmentioning

confidence: 99%

“…The sparse constraint is imposed either on the desired control signal [1][2][3] or on the structure of the to-be-designed controller. 4,5 Both continuous-time and discrete-time systems are considered. More specifically, Ref.…”

Section: Control Designmentioning

confidence: 99%

“…Ref. 4 utilizes block-sparse optimization as a tool for the design of distributed controllers. 5 designs decentralized controllers for linear time-varying systems under structural-sparsity constraints.…”

Section: Control Designmentioning

confidence: 99%

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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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Section: Contentsmentioning

confidence: 99%