Anatoly Zlotnik

Kaarthik Sundar, Anatoly Zlotnik

We formulate two estimation problems for pipeline systems in which measurements of compressible gas flow through a network of pipes is affected by time-varying injections, withdrawals, and compression. We consider a state estimation problem that is then extended to a joint state and parameter estimation problem that can be used for data assimilation. In both formulations, the flow dynamics are described on each pipe by space- and time-dependent density and mass flux that evolve according to a system of coupled partial differential equations, in which momentum dissipation is modelled using the Darcy-Wiesbach friction approximation. These dynamics are first spatially discretized to obtain a system of nonlinear ordinary differential equations on which state and parameter estimation formulations are given as nonlinear least squares problems. A rapid, scalable computational method for performing a nonlinear least squares estimation is developed. Extensive simulations and computational experiments on multiple pipeline test networks demonstrate the effectiveness of the formulations in obtaining state and parameter estimates in the presence of measurement and process noise.

Anatoly Zlotnik, Jr-Shin Li

An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are indexed by a parameter set, by applying the same open-loop control. The subject originates from the study of complex spin dynamics in Nuclear Magnetic Resonance (NMR) spectroscopy and imaging (MRI). A fundamental question concerns ensemble controllability, which determines the existence of controls that transfer the system between desired initial and target states. For ensembles of finite-dimensional time-varying linear systems, the necessary and sufficient controllability conditions and analytical optimal control laws have been shown to depend on the singular system of the operator characterizing the system dynamics. Because analytical solutions are available only in the simplest cases, there is a need to develop numerical methods for synthesizing these controls. We introduce a direct, accurate, and computationally efficient algorithm based on the singular value decomposition (SVD) that approximates ensemble controls of minimum norm for such systems. This method enables the application of ensemble control to engineering problems involving complex, time-varying, and high-dimensional linear dynamic systems.

Anatoly Zlotnik, Jr-Shin Li

We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space representation of the oscillator is reduced to a linearized phase model, and the optimal periodic control is computed from the phase response curve using formal averaging and the calculus of variations. Computational methods are used to calculate the periodic orbit and the phase response curve, and a numerical method for approximating the optimal controls is introduced. Our method is applied to asymptotically control the period of spiking neural oscillators modeled using the Hodgkin-Huxley equations. This example illustrates the optimality of entrainment controls derived using phase models when applied to the original state space system.

Noah Rhodes, Sachin Shivakumar, Luke S. Baker et al.

We examine market outcomes in energy transport networks with a focus on gas-fired generators, which are producers in a wholesale electricity market and consumers in the natural gas market. Market administrators monitor bids to determine whether a participant wields market power to manipulate the price of energy, reserves, or financial transmission rights. If economic or physical withholding of generation from the market is detected, mitigation is imposed by replacing excessive bids with reference level bids to prevent artificial supply shortages. We review market monitoring processes in the power grid, and present scenarios in small interpretable test networks to show how gas-fired generators can bid in the gas market to alter outcomes in a power market. We develop a framework based on DC optimal power flow (OPF) and steady-state optimal gas flow (OGF) formulations to represent two interacting markets with structured exchange of price and quantity bids. We formulate optimization-based methods to identify market power in a power grid, as well as to identify market conditions that indicate market power being exerted by a generator using gas market bids.

Alpha Renner, Forrest Sheldon, Anatoly Zlotnik et al.

The capabilities of natural neural systems have inspired new generations of machine learning algorithms as well as neuromorphic very large-scale integrated (VLSI) circuits capable of fast, low-power information processing. However, it has been argued that most modern machine learning algorithms are not neurophysiologically plausible. In particular, the workhorse of modern deep learning, the backpropagation algorithm, has proven difficult to translate to neuromorphic hardware. In this study, we present a neuromorphic, spiking backpropagation algorithm based on synfire-gated dynamical information coordination and processing, implemented on Intel's Loihi neuromorphic research processor. We demonstrate a proof-of-principle three-layer circuit that learns to classify digits from the MNIST dataset. To our knowledge, this is the first work to show a Spiking Neural Network (SNN) implementation of the backpropagation algorithm that is fully on-chip, without a computer in the loop. It is competitive in accuracy with off-chip trained SNNs and achieves an energy-delay product suitable for edge computing. This implementation shows a path for using in-memory, massively parallel neuromorphic processors for low-power, low-latency implementation of modern deep learning applications.