Set-membership errors-in-variables identification of MIMO linear systems

Cerone, V.; Razza, Valentino; Regruto, D.

doi:10.1016/j.automatica.2017.12.042

Cited by 12 publications

(5 citation statements)

References 54 publications

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“…By Assumption 2 and [5, Th. 1], if (18) holds for some P = P T 0 and L, we have that the closedloop system is asymptotically stable (i.e., F + GK is Schur) for all F G ∈ C. Hence, the probability that the unknown closed-loop system is asymptotically stable is greater than or equal to P θ o { F G ∈ C} = P D 0 {D 0 ∈ D}. Under Assumption 3, if…”

Section: Appendixmentioning

confidence: 99%

“…IV]. Specifically, condition (18) can be used to provide robust stability guarantees in a probabilistic sense when tracking constant references, while minimizing the mismatch of the designed closed loop from a reference closed-loop model, i.e., in place of [29, Th. 1, Eq.…”

Section: Simulation Examplementioning

confidence: 99%

“…With the definitions in (16) and θ := F 1 G F 2 , (20a) rewrites Proof of Theorem 1: Under Assumption 1 it is possible to define the matrices A, B and C, which are necessary to express (18). By Assumption 2 and [5, Th.…”

Section: Appendixmentioning

confidence: 99%

“…Alternatively, noise can corrupt the input and output signals in an additive fashion in the so-called error-in-variables (EIV) setting. This setting includes the case of output-error (OE) processes where, quite naturally, measurements are considered to be composed of signal and noise; it is known to be potentially challenging [16], and was considered for set-membership identification, e.g., [17], [18]. Direct design of a dynamic compensator for superstabilization is pursued in [14] from input/output data in an EIV setting; such a design is formulated as a polynomial optimization problem, which is effectively solved via sum-of-squares hierarchies.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Data-Based Control Design for Output-Error Linear Discrete-Time Systems With Probabilistic Stability Guarantees

D'Amico

Bisoffi

Farina

2023

IEEE Control Syst. Lett.

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In this letter we propose a novel method for direct data-based design of an output feedback controller for output-error processes in the single-input-single-output case. We consider a finite number of input/output data points collected from the system. Based on them, we define a set of state-space perturbed models consistent with data, where a bound on the disturbance is obtained by scenario optimization, and the structural properties of the models in this set are theoretically analyzed. This leads to a linear matrix inequality for the design of the feedback control law with probabilistic asymptotic stability guarantees. A simulated non-minimum phase system illustrates the approach.

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Section: Appendixmentioning

confidence: 99%

Section: Simulation Examplementioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data-Based Control Design for Output-Error Linear Discrete-Time Systems With Probabilistic Stability Guarantees

D'Amico

Bisoffi

Farina

2023

IEEE Control Syst. Lett.

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“…Based on the definition of the Extended Feasible controller parameter set, we can formulate the following result. Result 4: [Structure of the Extended Feasible Controller Parameter Set for MIMO system] The extended feasible controller parameter set can be written in the equivalent form by introducing some additional variables, Z ij and Q ij , called partial outputs (see Appendix A and [11] for more details)…”

Section: B Sm-dddc For Mimo Systemsmentioning

confidence: 99%

A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

Abuabiah,

Cerone,

Pirrera

et al. 2023

IEEE Access

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This paper proposes a non-iterative direct data-driven technique that deals with linear timeinvariant (LTI) controller design by directly identifying the controller from input-output data without using plant identification. We define the feasible controller parameter set and formulate the problem of designing a controller to match the behaviour of a given reference model as an equivalent set-membership errors-invariables problem. Then we design the controller parameters by applying recent results in set-membership errors-in-variables identification. Finally, we analyse the effectiveness of the presented technique through simulation examples and experimental results.

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A unified framework for the identification of a general class of multivariable nonlinear block‐structured systems

Cerone

Razza

Regruto

2021

Intl J Robust & Nonlinear

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This article addresses the parametric identification of block-structured nonlinear systems in a general form, characterized by the feedback interconnection of a multivariable linear system and a static multivariate nonlinear map. We assume that both the input and the output collected data are affected by bounded noise, which casts the problem in the context of set-membership (SM) errors-in-variables identification. We introduce a single-stage SM identification algorithm for the computation of the parameter uncertainty intervals. The proposed solution exploits the formulation of a suitable optimization problem solved through convex relaxation techniques. Numerical simulations and an experimental test show the effectiveness of the proposed approach.

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Set-membership errors-in-variables identification of MIMO linear systems

Cited by 12 publications

References 54 publications

Data-Based Control Design for Output-Error Linear Discrete-Time Systems With Probabilistic Stability Guarantees

Data-Based Control Design for Output-Error Linear Discrete-Time Systems With Probabilistic Stability Guarantees

A Non-Iterative Approach to Direct Data-Driven Control Design of MIMO LTI Systems

A unified framework for the identification of a general class of multivariable nonlinear block‐structured systems

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