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1. A Time-Delayed Lur’e Model with Biased Self-Excited Oscillations

   https://doi.org/10.23919/ACC45564.2020.9147761  

   Paredes, Juan; Ul Islam, Syed Aseem; Bernstein, Dennis S. (July 2020, Proc. American Control Conference)

   Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluidstructure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur’e model that exhibits biased oscillations under constant inputs. The model involves arbitrary asymptotically stable linear dynamics, time delay, a washout filter, and a saturation nonlinearity. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an oscillatory response. A bias-generation mechanism is used to specify the mean of the oscillation. The main contribution of the paper is the presentation and analysis of a discrete-time version of this model. 

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2. Output-only identification of self-excited systems using discrete-time Lur'e models with application to a gas-turbine combustor

   https://doi.org/10.1080/00207179.2022.2137702  

   Paredes, Juan A.; Yang, Yulong; Bernstein, Dennis S. (November 2022, International Journal of Control)

   A self-excited system is a nonlinear system with the property that a constant input yields a bounded, nonconvergent response. Nonlinear identification of self-excited systems is considered using a Lur'e model structure, where a linear model is connected in feedback with a nonlinear feedback function. To facilitate identification, the nonlinear feedback function is assumed to be continuous and piecewise affine (CPA). The present paper uses least-squares optimization to estimate the coefficients of the linear dynamics and the slope vector of the CPA nonlinearity, as well as mixed-integer optimization to estimate the order of the linear dynamics and the breakpoints of the CPA function. The proposed identification technique requires only output data, and thus no measurement of the constant input is required. This technique is illustrated on a diverse collection of low-dimensional numerical examples as well as data from a gas-turbine combustor. 

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3. Identification‐ and singularity‐robust inference for moment condition models

   https://doi.org/10.3982/QE1219  

   Andrews, Donald W.; Guggenberger, Patrik (January 2019, Quantitative Economics)

   This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 +  γ bounded moments for some γ  > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k  ≥  p , where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p  = 1 in the homoskedastic linear IV model. The same is true for p  ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification. 

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4. NARMAX Identification Based Closed-Loop Control of Flow Separation over NACA 0015 Airfoil

   https://doi.org/10.3390/fluids5030100  

   Obeid, Sohaib; Ahmadi, Goodarz; Jha, Ratneshwar (September 2020, Fluids)

   null (Ed.)

   A closed-loop control algorithm for the reduction of turbulent flow separation over NACA 0015 airfoil equipped with leading-edge synthetic jet actuators (SJAs) is presented. A system identification approach based on Nonlinear Auto-Regressive Moving Average with eXogenous inputs (NARMAX) technique was used to predict nonlinear dynamics of the fluid flow and for the design of the controller system. Numerical simulations based on URANS equations are performed at Reynolds number of 106 for various airfoil incidences with and without closed-loop control. The NARMAX model for flow over an airfoil is based on the static pressure data, and the synthetic jet actuator is developed using an incompressible flow model. The corresponding NARMAX identification model developed for the pressure data is nonlinear; therefore, the describing function technique is used to linearize the system within its frequency range. Low-pass filtering is used to obtain quasi-linear state values, which assist in the application of linear control techniques. The reference signal signifies the condition of a fully re-attached flow, and it is determined based on the linearization of the original signal during open-loop control. The controller design follows the standard proportional-integral (PI) technique for the single-input single-output system. The resulting closed-loop response tracks the reference value and leads to significant improvements in the transient response over the open-loop system. The NARMAX controller enhances the lift coefficient from 0.787 for the uncontrolled case to 1.315 for the controlled case with an increase of 67.1%. 

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5. Global sampled‐data stabilization via static output feedback for a class of nonlinear uncertain systems

   https://doi.org/10.1002/rnc.6542  

   Cao, Kecai; Qian, Chunjiang; Gu, Juping (December 2022, International Journal of Robust and Nonlinear Control)

   Summary This paper proposes some novel compensating strategies in output feedback controller design for a class of nonlinear uncertain system. With Euler approximation introduced for unmeasured state and coordinate transformation constructed for continuous system, sampled‐data stabilization under arbitrary sampling period is firstly realized for linear system using compensation between sampling period and scaling gain. Then global sampled‐data stabilization for a class of nonlinear system is studied using linear feedback domination of Lyapunov functions. Extension of obtained results to three‐dimensional system or systems under general assumptions are also presented. With the compensation schemes proposed in controller design, the sufficiently small sampling period or approximating step previously imposed is not required any more. The proposed controllers can be easily implemented using output measurements sampled at the current step and delayed output measurements sampled at the previous step without constructing state observers which has been illustrated by the numerical studies. 

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