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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.
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.
3. 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)

   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 andmore »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%.« less
4. Hierarchically Modular Dynamical Neural Network Relaxing in a Warped Space: Basic Model and its Characteristics

   Kazuyoshi Tsutsumi, Ernst Niebur ( November 2022 , arXivorg)

   We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are connected with a layered internetwork that consists of a pair of forward and backward subnets composed of static neurons (with an instantaneous time-course). Dynamical neurons with large time constants in the internal space determine the overall time-course. The model offers a framework in which state variables in the network relax in a warped space, due to the cooperation between dynamic and static neurons. We assume that the system operates in either a learning or an association mode, depending on the presence or absence of feedback paths and input ports. In the learning mode, synaptic weights in the internetwork are modified by strong inputs corresponding to repetitive neuronal bursting, which represents sinusoidal or quasi-sinusoidal waves in the short-term average density of nerve impulses or in the membrane potential. A two-dimensional mapping relationship can be formed by employing signals with different frequencies based on the same mechanism as Lissajous curves. In the association mode, the speed of convergence to a goal point greatly varies with the mapping relationship ofmore »the previously trained internetwork, and owing to this property, the convergence trajectory in the two-dimensional model with the non-linear mapping internetwork cannot go straight but instead must curve. We further introduce a constrained association mode with a given target trajectory and elucidate that in the internal space, an output trajectory is generated, which is mapped from the external space according to the inverse of the mapping relationship of the forward subnet.« less
5. Optimal Decision Tree with Noisy Outcomes

   Jia, Su ; Nagarajan, Viswanath ; Navidi, Fatemeh ; Ravi, R ( January 2019 , Advances in neural information processing systems)

   A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis). Our new approximation algorithms provide guarantees that are nearly best-possible and work for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades smoothly with this number. Our results adapt and generalizemore »methods used for submodular ranking and stochastic set cover. We evaluate the performance of our algorithms on two natural applications with noise: toxic chemical identification and active learning of linear classifiers. Despite our logarithmic theoretical approximation guarantees, our methods give solutions with cost very close to the information theoretic minimum, demonstrating the effectiveness of our methods.« less