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1. Active Learning for Nonlinear System Identification with Guarantees

   Mania, Horia; Jordan, Michael I; Recht, Benjamin (February 2022, Journal of machine learning research)

   Fukumizu, Kenji (Ed.)

   While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by i.i.d. random inputs. Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs. Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs. To estimate such systems in finite time identification methods must explore all directions in feature space. We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data. We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression. 

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2. A Quadratic Program based Control Synthesis under Spatiotemporal Constraints and Non-vanishing Disturbances

   https://doi.org/10.1109/CDC42340.2020.9304071  

   Black, Mitchell; Garg, Kunal; Panagou, Dimitra (January 2020, 2020 59th IEEE Conference on Decision and Control (CDC))

   In this paper, we study the effect of non-vanishing disturbances on the stability of fixed-time stable (FxTS) systems. We present a new result on FxTS, which allows a positive term in the time derivative of the Lyapunov function with the aim to model bounded, non-vanishing disturbances in system dynamics. We characterize the neighborhood to which the system trajectories converge, as well as the convergence time. Then, we use the new FxTS result and formulate a quadratic program (QP) that yields control inputs which drive the trajectories of a class of nonlinear, control-affine systems to a goal set in the presence of control input constraints and nonvanishing, bounded disturbances in the system dynamics. We consider an overtaking problem on a highway as a case study, and discuss how to both set up the QP and decide when to start the overtake maneuver in the presence of sensing errors. 

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3. A Fixed-Time Stable Adaptation Law for Safety-Critical Control under Parametric Uncertainty

   Black, Mitchell; Arabi, Ehsan; Panagou, Dimitra (January 2021, 2021 European Control Conference)

   We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial parameter estimation error. We then synthesize the adaptation law with a robust, adaptive control barrier function (RaCBF) based quadratic program to compute safe control inputs despite the considered model uncertainty. To corroborate our results, we undertake a comparative case study on the efficacy of this result versus other recent approaches in the literature to safe control under uncertainty, and close by highlighting the value of our method in the context of an automobile overtake scenario. 

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4. Learning Linear Complementarity Systems

   Jin, Wanxin; Aydinoglu, Alp; Halm, Mathew; Posa, Michael (June 2022, Learning for Dynamics and Control Conference)

   Firoozi, Roya; Mehr, Negar; Yel, Esen; Antonova, Rika; Bohg, Jeannette; Schwager, Mac; Kochenderfer, Mykel (Ed.)

   This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode boundaries, using gradient-based methods. The proposed violation-based loss incorporates both dynamics prediction loss and a novel complementarity - violation loss. We show several properties attained by this loss formulation, including its differentiability, the efficient computation of first- and second-order derivatives, and its relationship to the traditional prediction loss, which strictly enforces complementarity. We apply this violation-based loss formulation to learn LCSs with tens of thousands of (potentially stiff) hybrid modes. The results demonstrate a state-of-the-art ability to identify piecewise-affine dynamics, outperforming methods which must differentiate through non-smooth linear complementarity problems. 

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5. 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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