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1. Identification of Self-Excited Systems Using Discrete-Time, Time-Delayed Lur’e Models

   Paredes, Juan; Bernstein, Dennis S. (May 2021, Proceedings of the American Control Conference)

   null (Ed.)

   This paper considers system identification for systems whose output is asymptotically periodic under constant inputs. The model used for system identification is a discretetime Lur’e model consisting of asymptotically stable linear dynamics, a time delay, a washout filter, and a static nonlinear feedback mapping. For sufficiently large scaling of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an asymptotically oscillatory output. A leastsquares technique is used to estimate the coefficients of the linear model as well as the parameters of a piecewise-linear approximation of the feedback mapping. 

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2. 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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3. Aeroelastic force prediction via temporal fusion transformers

   https://doi.org/10.1111/mice.13381  

   Cid_Montoya, Miguel; Mishra, Ashutosh; Verma, Sumit; Mures, Omar_A; Rubio‐Medrano, Carlos_E (November 2024, Computer-Aided Civil and Infrastructure Engineering)

   Abstract Aero‐structural shape design and optimization of bridge decks rely on accurately estimating their self‐excited aeroelastic forces within the design domain. The inherent nonlinear features of bluff body aerodynamics and the high cost of wind tunnel tests and computational fluid dynamics (CFD) simulations make their emulation as a function of deck shape and reduced velocity challenging. State‐of‐the‐art methods address deck shape tailoring by interpolating discrete values of integrated flutter derivatives (FDs) in the frequency domain. Nevertheless, more sophisticated strategies can improve surrogate accuracy and potentially reduce the required number of samples. We propose a time domain emulation strategy harnessing temporal fusion transformers (TFTs) to predict the self‐excited forces time series before their integration into FDs. Emulating aeroelastic forces in the time domain permits the inclusion of time‐series amplitudes, frequencies, phases, and other properties in the training process, enabling a more solid learning strategy that is independent of the self‐excited forces modeling order and the inherent loss of information during the identification of FDs. TFTs' long‐ and short‐term context awareness, combined with their interpretability and enhanced ability to deal with static and time‐dependent covariates, make them an ideal choice for predicting unseen aeroelastic forces time series. The proposed TFT‐based metamodel offers a powerful technique for drastically improving the accuracy and versatility of wind‐resistant design optimization frameworks. 

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4. Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty

   https://doi.org/10.23919/ACC53348.2022.9867457  

   Sinha, Rohan; Harrison, James; Richards, Spencer M.; Pavone, Marco (June 2022, American Control Conference)

   We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems commonly model the nonlinear effects of an unknown environment on a nominal system. We optimize over a class of nonlinear feedback policies inspired by certainty equivalent "estimate-and-cancel" control laws pioneered in classical adaptive control to achieve significant performance improvements in the presence of uncertainties of large magnitude, a setting in which existing learning-based predictive control algorithms often struggle to guarantee safety. In contrast to previous work in robust adaptive MPC, our approach allows us to take advantage of structure (i.e., the numerical predictions) in the a priori unknown dynamics learned online through function approximation. Our approach also extends typical nonlinear adaptive control methods to systems with state and input constraints even when we cannot directly cancel the additive uncertain function from the dynamics. Moreover, we apply contemporary statistical estimation techniques to certify the system’s safety through persistent constraint satisfaction with high probability. Finally, we show in simulation that our method can accommodate more significant unknown dynamics terms than existing methods. 

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5. Control-Coherent Koopman Modeling: A Physical Modeling Approach

   Asada, Harry; Solano--Castellanos, Jose (December 2024, IEEE)

   The modeling of nonlinear dynamics based on Koopman operator theory, originally applicable only to autonomous systems with no control, is extended to nonautonomous control system without approximation of the input matrix. Prevailing methods using a least square estimate of the input matrix may result in an erroneous input matrix, misinforming the controller. Here, a new method for constructing a Koopman model that yields the exact input matrix is presented. A set of state variables are introduced so that the control inputs are linearly involved in the dynamics of actuators. With these variables, a lifted linear model with the exact input matrix, called a Control-Coherent Koopman Model, is constructed by superposing control input terms, which are linear in local actuator dynamics, to the Koopman operator of the associated autonomous nonlinear system. As an example, the proposed method is applied to multi degree-of-freedom robotic arms, which are controlled with Model Predictive Control (MPC). It is demonstrated that the prevailing Dynamic Mode Decomposition with Control (DMDc) using an approximate input matrix does not provide a satisfactory result, while the Control-Coherent Koopman Model performs well with the correct input matrix, even performing better than the bilinear formulation of the Koopman operator. 

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