We address the use of second-order methods to solve optimizations of the form\begin{equation*}\mathop {\min }\limits_{u \in \mathcal{U}} \mathop {\max }\limits_{d \in \mathcal{D}} f(u,d),\tag{1}\end{equation*}for a tw...
We address the use of second-order methods to solve optimizations of the form\begin{equation*}\mathop {\min }\limits_{u \in \mathcal{U}} \mathop {\max }\limits_{d \in \mathcal{D}} f(u,d),\tagcontrol\end{equation*}for a twice continuously differentiable function $f:\mathcal{U} \times \mathcal{D} \to \mathbb{R}$ and sets $\mathcal{U} \subset {\mathbb{R}^{{n_u}}},\mathcal{D} \subset {\mathbb{R}^{{n_d}}}$. This type of optimization arises in numerous applications, including robust machine learning [1], model predictive control [2], [3], and in reformulating stochastic programming as a min-max optimizations [4], [5].When the sets $\mathcal{U}$ and $\mathcal{D}$ are compact and convex and the function f (u, d) is convex with respect to u and concave with respect to d, the min and max in (1) commute [6] and the optimization becomes relatively simple. However, we are especially interested here in problems for which such assumptions do not hold, the min and max do not commute, and for which the optimizations may have local optima that are not *** this talk, we address the design of algorithms to solve nonconvex-nonconcave min-max optimizations like (1) using second order methods. These algorithms modify the Hessian matrix to obtain a search direction that can be seen as the solution to a quadratic program that locally approximates the min-max problem. We show that by selecting this type of modification appropriately, the only stable points of the resulting iterations are local min-max points. For min-max model predictive control problems, these algorithms leads to computation times that scale linearly with the horizon *** more information please see the main tutorial paper [7].
In order to improve the control performance of vapor compression cycles (VCCs), it is often necessary to construct accurate dynamical models of the underlying thermo-fluid dynamics. These dynamics are represented by c...
In order to improve the control performance of vapor compression cycles (VCCs), it is often necessary to construct accurate dynamical models of the underlying thermo-fluid dynamics. These dynamics are represented by complex mathematical models that are composed of large systems of nonlinear and numerically stiff differential algebraic equations (DAEs). The effects of nonlinearity and stiffness may be ameliorated by using physics-based models to describe characteristic system behaviors, and approximating the residual (unmodeled) dynamics using neural networks. In these so-called ‘physics-augmented’ or ‘physics-informed’ machine learning approaches, the learning problem is often solved by jointly estimating parameters of the physics component model and weights of the network. Furthermore, such approaches also often assume the availability of full-state information, which typically are not available in practice for energy systems such as VCCs after deployment. Rather than concurrently performing state/parameter estimation and network training, which often leads to numerical instabilities, we propose a framework for decoupling the network training from the joint state/parameter estimation problem by employing state-constrained Kalman smoothers customized for VCC applications. We show the effectiveness of our proposed framework on a Julia-based, high-fidelity simulation environment calibrated to a model of a commercially-available VCC and achieve an accuracy of 98% calculated over 24 states and multiple initial conditions under realistic operating conditions.
This paper studies equality-constrained composite minimization problems. This class of problems, capturing regularization terms and convex inequality constraints, naturally arises in a wide range of engineering and ma...
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In this letter, we study distributed optimization and Nash equilibrium-seeking dynamics from a contraction theoretic perspective. Our first result is a novel bound on the logarithmic norm of saddle matrices. Second, f...
Stochastic patrol routing is known to be advantageous in adversarial settings;however, the optimal choice of stochastic routing strategy is dependent on a model of the adversary. We adopt a worst-case omniscient adver...
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To enable the computation of effective randomized patrol routes for single- or multi-robot teams, we present RoSSO, a Python package designed for solving Markov chain optimization problems. We exploit machine-learning...
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This research brief aims to study the bifurcation analysis of an electromagnetic levitation (maglev) system. The bifurcation analysis involves first performing the numerical analysis, and then the simulations using MA...
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We study the problem of inferring edge flows and nodal injections in infrastructure networks. Leveraging the Thomson’s Principle from the electric circuits literature, we setup a framework to jointly learn network pa...
We study the problem of inferring edge flows and nodal injections in infrastructure networks. Leveraging the Thomson’s Principle from the electric circuits literature, we setup a framework to jointly learn network parameters and missing states. Despite being application agnostic, the proposed approach captures the fundamental physics of the infrastructure, and is able to handle partial observation, node and edge features as well as operational constraints. The physics inspired learning framework leads to a bilevel optimization problem, which is NP hard in general. By exploiting convexity properties, we reformulate the problem as a single level optimization, composed of a graph neural network and an additional implicit layer. The resulting architecture can be trained using standard gradient-based methods. We assess the validity of the proposed approach on two different infrastructure networks (power and traffic), and show it outperforms the current state of the art.
Global stability and robustness guarantees in learned dynamicalsystems are essential to ensure well-behavedness of the systems in the face of uncertainty. We present Extended Linearized Contracting Dynamics (ELCD), t...
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Classification of electrocardiogram (ECG) signals is essential for accurate clinical diagnosis of coronary illness. Deep Neural Network (DNN) has emerged as a promising tool for feature identification in ECG signals w...
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