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Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.
PyZebrascope: An Open-Source Platform for Brain-Wide Neural Activity Imaging in Zebrafish
Understanding how neurons interact across the brain to control animal behaviors is one of the central goals in neuroscience. Recent developments in fluorescent microscopy and genetically-encoded calcium indicators led to the establishment of whole-brain imaging methods in zebrafish, which record neural activity across a brain-wide volume with single-cell resolution. Pioneering studies of whole-brain imaging used custom light-sheet microscopes, and their operation relied on commercially developed and maintained software not available globally. Hence it has been challenging to disseminate and develop the technology in the research community. Here, we present PyZebrascope, an open-source Python platform designed for neural activity imaging in zebrafish using light-sheet microscopy. PyZebrascope has intuitive user interfaces and supports essential features for whole-brain imaging, such as two orthogonal excitation beams and eye damage prevention. Its camera module can handle image data throughput of up to 800 MB/s from camera acquisition to file writing while maintaining stable CPU and memory usage. Its modular architecture allows the inclusion of advanced algorithms for microscope control and image processing. As a proof of concept, we implemented a novel automatic algorithm for maximizing the image resolution in the brain by precisely aligning the excitation beams to the image focal plane. PyZebrascope enables whole-brain neural activity imaging in fish behaving in a virtual reality environment. Thus, PyZebrascope will help disseminate and develop light-sheet microscopy techniques in the neuroscience community and advance our understanding of whole-brain neural dynamics during animal behaviors.
A stochastic scan strategy for grain structure control in complex geometries using electron beam powder bed fusion
Spatial control of microstructure within a three-dimensional component has been a dream of materials scientists for centuries. However, limitations in traditional manufacturing processes prevent detailed control over the distribution of microstructures in a single part. Here, we demonstrate the ability to control grain structure and crystallographic texture during metal additive manufacturing for arbitrary cross-sections of a practical size, with profound implications for the design and optimization of next-generation products. The key to this advance is a new geometry agnostic scan path algorithm that manipulates the spatial distribution of solidification conditions. Utilizing a fundamental understanding of solidification dynamics and a model of the heat transfer during processing, we have designed this algorithm to manipulate the natural competition between epitaxial dendrite growth and grain nucleation. With this algorithm, we successfully controlled the grain structure of Ni-based superalloy IN718 in the shape of the Mona Lisa.
DOE Express Quantum Computing Application Teams (QCAT FY20 Report)
The QCOR project consists of 4 main research tasks: 1) scientific applications and algorithm development for machine learning (ML) and quantum theories of condensed matter systems and lattice gauge theories; 2) high-level quantum-classical (HLQC) language and domain specific language (DSL) development; 3) compiler and interfaces development for the HLQC language; and 4) hardware-level control, optimization, and algorithms libraries. In the succeeding sections we report on progress towards our research tasks during the 2020 calendar year.
Deep Reinforcement Learning Based Control of Wind Turbines for Fast Frequency Response
In order to fulfill vital auxiliary grid services, such as load regulation, spin and non-spin reserve provision, and frequency support during emergencies, there is often a requirement for certain wind farms to operate in de-loaded modes. Leveraging the swift response capabilities of wind farms, this study demonstrates that reserving power in de-loaded modes can significantly enhance power grid stability and reliability during system contingencies. Controlling wind farms optimally for frequency support is intricate due to the nonlinearity of models and controllers and the complexity of wind farm interactions with power systems. Here, to address this challenge, this paper introduces a novel approach that integrates wind turbines into reinforcement learning-based solutions for frequency response. This innovative methodology utilizes the state-of-the-art reinforcement learning algorithm known as the surrogate-gradient-based evolutionary strategy. The proposed learning-based algorithm provides continuous control of wind farm output to rapidly stabilize system frequency and prevent unnecessary trips of under-frequency load shedding relays. To facilitate efficient training, parallel computing techniques are employed. The proposed methodology is evaluated on a modified IEEE-39 bus system, and simulation results reveal its efficacy in reliably supporting power system frequency and preventing the need for unnecessary load shedding.
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates
This work develops a new multi delity ensemble Kalman lter (MFEnKF) algorithm based on linear control variate framework. The approach allows for rigorous multi delity extensions of the EnKF, where the uncertainty in coarser delities in the hierarchy of models represent control variates for the uncertainty in ner delities. Small ensembles of high delity model runs are com- plemented by larger ensembles of cheaper, lower delity runs, to obtain much improved analyses at only small additional computational costs. We investigate the use of reduced order models as coarse delity control variates in the MFEnKF, and provide analyses to quantify the improvements over the traditional ensemble Kalman lters. We apply these ideas to perform data assimilation with a quasi-geostrophic test problem, using direct numerical simulation and a corresponding POD-Galerkin reduced order model. Numerical results show that the two- delity MFEnKF provides better analyses than existing EnKF algorithms at comparable or reduced computational costs.
Chaos control of Hastings–Powell model by combining chaotic motions
In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings–Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: “losing + losing = winning.” If “loosing” is replaced with “chaos” and, “winning” with “order” (as the opposite to “chaos”), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write “chaos + chaos = regular.” Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.
A VSM-Based DER Dispatch MINLP for Volt-VAR Control in Unbalanced Power Distribution Systems
This paper presents an optimal dispatch algorithm to coordinate customer-owned controllable loads and smart solar inverters with utility-owned voltage regulators and capacitors to meet voltage control objectives. The optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) problem. A voltage sensitivity matrix (VSM) is used to linearize the effect of control actions on the voltage at customer nodes when solving the MINLP. The VSM is recalculated at each time step to improve the computational accuracy. Both discrete switching actions of the capacitor and VRs and the continuous adjustment of real and reactive power from load and smart inverters are considered in the MINLP volt-var problem formulation. The objective function minimizes the cost of all control actions and the magnitude of voltage fluctuations from the previous time period. Constraints ensure that the voltage at each node is maintained within ANSI limits and the feeder power factor is controlled within the desired range. The algorithm is tested using an actual 3-phase unbalanced distribution feeder model. Simulation results demonstrate that the proposed algorithm is computationally feasible on real circuits and improves voltage control while minimizing operational costs.
Automated Price and Demand Response Demonstration for Large Customers in New York City using OpenADR
Open Automated Demand Response (OpenADR), an XML-based information exchange model, is used to facilitate continuous price-responsive operation and demand response participation for large commercial buildings in New York who are subject to the default day-ahead hourly pricing. We summarize the existing demand response programs in New York and discuss OpenADR communication, prioritization of demand response signals, and control methods. Building energy simulation models are developed and field tests are conducted to evaluate continuous energy management and demand response capabilities of two commercial buildings in New York City. Preliminary results reveal that providing machine-readable prices to commercial buildings can facilitate both demand response participation and continuous energy cost savings. Hence, efforts should be made to develop more sophisticated algorithms for building control systems to minimize customer's utility bill based on price and reliability information from the electricity grid.
A Data-Driven Algorithm for Enabling Delay Tolerance in Resilient Microgrid Controls Using Dynamic Mode Decomposition
The increased implementation of smart grid technologies in the power distribution grid presents unique opportunities that enable resiliency, but also brings challenges motivating needs for novel solutions and mitigation techniques. The bi-directional power and data flow allow for the grid to operate with increased resiliency, which is the ability to avoid discontinuity of service to end-use loads during extreme events. However, in applications where control of the distribution grid or microgrid relies on communication networks, the degradation of communication systems in the form of loss or high latency can cause maloperation and result in loss of end-use loads. Here this paper presents a novel framework to enable delay tolerance of centralized microgrid control schemes to mitigate communication system latency impacts and guarantee successful control action. We demonstrate the delay tolerance on a control scheme that operates a battery energy storage system (BESS) to offset the sudden loss of generation and maintain system frequency. During periods of severely degraded communication system performance, the proposed delay-tolerant algorithm compensates for the latency by utilizing a data-driven model generated at the device level using dynamic mode decomposition (DMD) to determine the performance of the communications. The DMD technique predicts the system’s frequency using device-level terminal measurements and provides updated control signals. The HELICS cosimulation platform evaluates the cyber-physical interaction of the power system model in GridLAB-D, the centralized control agent in Python, and the discrete network model in NS-3. The framework is tested and validated on the IEEE-123 node system modified to represent a networked remote microgrid model, and the results show an improvement in the dynamic performance
System and method for microwave volumetric additive manufacturing
The present disclosure relates to a volumetric additive manufacturing system for forming a structure from a volume of resin using microwave energy. The system makes use of an electronic controller and at least one beam forming algorithm accessible by the electronic controller for generating information relating to an amplitude and a time delay for forming a microwave signal, where the microwave signal will be used in irradiating a build volume, and where the build volume is formed by the volume of resin. A microwave signal generating subsystem is included which is responsive to the information generated by the beam forming algorithm, and which generates a microwave signal using the amplitude and the time delay determined by the beam forming algorithm. An antenna is used to receive the microwave signal and project the microwave signal as a microwave beam, in accordance with the amplitude and time delay, into the build volume to form the structure.
Neural-network diagnostics of electrochemical machining
In the high-precision electrochemical shaping of new high-strength and hard materials, diagnostics may be based on neural-network identification algorithms incorporated in the automated control system of the equipment.
Matlab Based LOCO
The LOCO algorithm has been used by many accelerators around the world. Although the uses for LOCO vary, the most common use has been to find calibration errors and correct the optics functions. The light source community in particular has made extensive use of the LOCO algorithms to tightly control the beta function and coupling. Maintaining high quality beam parameters requires constant attention so a relatively large effort was put into software development for the LOCO application. The LOCO code was originally written in FORTRAN. This code worked fine but it was somewhat awkward to use. For instance, the FORTRAN code itself did not calculate the model response matrix. It required a separate modeling code such as MAD to calculate the model matrix then one manually loads the data into the LOCO code. As the number of people interested in LOCO grew, it required making it easier to use. The decision to port LOCO to Matlab was relatively easy. It's best to use a matrix programming language with good graphics capability; Matlab was also being used for high level machine control; and the accelerator modeling code AT, [5], was already developed for Matlab. Since LOCO requires collecting and processing a relative large amount of data, it is very helpful to have the LOCO code compatible with the high level machine control, [3]. A number of new features were added while porting the code from FORTRAN and new methods continue to evolve, [7][9]. Although Matlab LOCO was written with AT as the underlying tracking code, a mechanism to connect to other modeling codes has been provided.
A new method for tracking organ motion on diagnostic ultrasound images
Purpose: Respiratory-gated irradiation is effective in reducing the margins of a target in the case of abdominal organs, such as the liver, that change their position as a result of respiratory motion. However, existing technologies are incapable of directly measuring organ motion in real-time during radiation beam delivery. Hence, the authors proposed a novel quantitative organ motion tracking method involving the use of diagnostic ultrasound images; it is noninvasive and does not entail radiation exposure. In the present study, the authors have prospectively evaluated this proposed method. Methods: The method involved real-time processing of clinical ultrasound imaging data rather than organ monitoring; it comprised a three-dimensional ultrasound device, a respiratory sensing system, and two PCs for data storage and analysis. The study was designed to evaluate the effectiveness of the proposed method by tracking the gallbladder in one subject and a liver vein in another subject. To track a moving target organ, the method involved the control of a region of interest (ROI) that delineated the target. A tracking algorithm was used to control the ROI, and a large number of feature points and an error correction algorithm were used to achieve long-term tracking of the target. Tracking accuracy was assessed in terms of how well the ROI matched the center of the target. Results: The effectiveness of using a large number of feature points and the error correction algorithm in the proposed method was verified by comparing it with two simple tracking methods. The ROI could capture the center of the target for about 5 min in a cross-sectional image with changing position. Indeed, using the proposed method, it was possible to accurately track a target with a center deviation of 1.54 ± 0.9 mm. The computing time for one frame image using our proposed method was 8 ms. It is expected that it would be possible to track any soft-tissue organ or tumor with large deformations and changing cross-sectional position using this method. Conclusions: The proposed method achieved real-time processing and continuous tracking of the target organ for about 5 min. It is expected that our method will enable more accurate radiation treatment than is the case using indirect observational methods, such as the respiratory sensor method, because of direct visualization of the tumor. Results show that this tracking system facilitates safe treatment in clinical practice.
AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems
Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.