In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data generated by solving a sample of infinite- dimensional optimization problems using composite Bernstein collocation. Once trained, the Transformer efficiently generates near-optimal, feasible trajectories, making it well-suited for real-time applications. In motion planning for autonomous vehicles, for instance, these trajectories can serve to warm- start optimal motion planners or undergo rigorous evaluation to ensure safety. We demonstrate the effectiveness of this method through numerical results on a classical control problem and an online obstacle avoidance task. This data-driven approach offers a promising solution for real-time optimal control of nonlinear, nonconvex systems.

Advanced air mobility mainly uses vehicles that are capable of vertical takeoff and landing (VTOL) for the simplicity of operation and large-scale deployment. However, VTOL vehicles need specialized trajectory and command design for the transition phase, where the vehicles transition between rotor-borne flight and wing-borne flight. Since VTOL vehicles are commonly designed as over-actuated systems for redundancy, one challenge that arises is actuator ambiguity, where it is unclear how to uniquely command actuators for the VTOL vehicle to track a given trajectory. We propose a method to design optimal reference commands for the transition mode. By formulating an..1-norm cost function on the rotor thrusts of the vehicle, we can achieve economical operation of the rotors such that they only operate when necessary and efficiently use the aerodynamics to save energy from reduced rotor actuation. We validate our approach in simulations and show its benefit compared to the commonly used differential flatness-based method.

This paper presents a receding horizon model predictive control variation of the combined Bernstein polynomial optimal reciprocal collision avoidance (ORCA) differential dynamic programming (COBRA-DDP) algorithm for advanced air mobility (AAM) vehicles. Collision avoidance, in combination with effective trajectory replanning, are expected to be core components of AAM vehicles operating within a crowded airspace. This environment necessitates the use of real-time trajectory planning algorithms that are capable of planning around large numbers of stationary and moving obstacles. Previous work on COBRA-DDP demonstrated the capability of the algorithm to produce dynamically feasible trajectories for AAM vehicles and general collision avoidance. This paper improves upon the previous work by increasing the number of stationary and moving obstacles, while implementing a variation of COBRA-DDP that lends itself to real-time application. These advancements are demonstrated on an electric vertical takeoff and landing (eVTOL) vehicle simulation with highly nonlinear vehicle dynamics.

In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial properties of composite Bernstein polynomials for the solution of optimal control problems are discussed. The efficacy of the proposed approximation method is demonstrated through a bang-bang example. Lastly, we apply this method to a motion planning problem, offering a practical solution that emphasizes the ability of this method to solve complex optimal control problems.

This paper presents an L1 adaptive control augmentation for a Lift-Plus-Cruise (L+C) vehicle. This class of vehicles operates in three flight modes with different dynamic behavior: vertical, transition, and forward flight. A robust uniform controller is used as a baseline to stabilize the system throughout these flight modes. The uniform controller is a linear control law designed around trim conditions of the aircraft and includes control allocation to achieve the desired forces and moments on the vehicle. The L1 control augmentation is designed for each of these trim conditions to compensate for the nonlinear time- and state-dependent uncertainties in the vehicle dynamics. The augmented control output is then added to the desired force and moment commands on the vehicle. Simulation results demonstrate the effectiveness of control augmentation for reducing the effects of unmodeled dynamics, reduced actuator effectiveness, and time-dependent disturbances. Effectiveness is demonstrated through tracking error metrics.

We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based L-1-adaptive (CL1) control and Bayesian learning in the form of Gaussian process (GP) regression. The CL1 controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients.

Hybrid circuit quantum electrodynamics (QED) involves the study of coherent quantum physics in solid state systems via their interactions with superconducting microwave circuits. Here we present an implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction. We realize the junction by contacting a carbon nanotube with a superconducting Pd/Al bi-layer, and implement voltage tunability of the qubit frequency using a local electrostatic gate. We demonstrate strong dispersive coupling to a coplanar waveguide resonator via observation of a resonator frequency shift dependent on applied gate voltage. We extract qubit parameters from spectroscopy using dispersive readout and find qubit relaxation and coherence times in the range of $10-200~\rm{ns}$.

View Video Presentation: https://doi.org/10.2514/6.2021-0586.vid In this paper, we propose a method for generating dynamically feasible trajectories for an acoustically aware vehicle with propeller phase control. The trajectory generation procedure allows both propeller phase control and navigation objectives to be considered simultaneously. The presented method is demonstrated where the mission objectives are given as a desired position and phase trajectory. From these trajectories, the full desired state of the vehicle is calculated. Furthermore, the control inputs that realize the desired mission objectives are computed. The acoustic performance for the given trajectory is estimated in terms of sound pressure level as a function of tracking performance. The method is demonstrated in simulation, where the vehicle must navigate through an urban environment with both spatial and acoustic constraints. In the presented scenario, the vehicle must follow a given flight path, and can only reduce sound pressure level by changing the propeller phase targets.

Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher noise levels can still converge to useful parameters. Our findings show that noisy quantum computers can be used in applications for state discrimination and for classifiers of the output of quantum generative adversarial networks.

Matthias Mergenthaler, 2, ∗ Ani Nersisyan, Andrew Patterson, Martina Esposito, Andreas Baumgartner, Christian Schönenberger, G. Andrew D. Briggs, Edward A. Laird, 2 and Peter J. Leek † Clarendon Laboratory, Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom (Dated: April 21, 2021)

In 2020, the coronavirus disease 2019 (COVID-19) pandemic interrupted the administration of the APPLIED Examination, the final part of the American Board of Anesthesiology (ABA) staged examination system for initial certification. In response, the ABA developed, piloted, and implemented an Internet-based "virtual" form of the examination to allow administration of both components of the APPLIED Exam (Standardized Oral Examination and Objective Structured Clinical Examination) when it was impractical and unsafe for candidates and examiners to travel and have in-person interactions. This article describes the development of the ABA virtual APPLIED Examination, including its rationale, examination format, technology infrastructure, candidate communication, and examiner training. Although the logistics are formidable, we report a methodology for successfully introducing a large-scale, high-stakes, 2-element, remote examination that replicates previously validated assessments.

In this work, several neural network function approximations are compared for interpolating, storing, and sampling acoustic source spheres with applications to propeller noise estimation. These methods are compared using an acoustic model of the three-bladed GL-10 propeller at different flight conditions, with training data generated using NASA's ANOPP-PAS module. The source spheres used to train the networks capture the tonal propeller noise due to both the blade thickness and loading. This tonal noise prediction method allows the vehicle noise to be estimated for auralization and acoustic control. Three radial basis function neural network architectures are compared in this work. The first two networks directly estimate the parameters of the source sphere at different flight conditions but differ in the number of layers used. The third network estimates the parameters of the source sphere using a weighted combination of spherical basis functions. These networks are trained on numerically generated source spheres, with operating points given in terms of the propeller rotation rate, freestream speed, and propeller angle of attack. The performance of the neural network is determined using a validation dataset of withheld data points. This performance is quantified in terms of the approximation error, training time, and sample time. The third network, which estimates the weights of the spherical basis functions, performs the best in both average and maximum approximation errors in all cases. This network's worst case performance is 5.6% relative difference of a model parameter associated with acoustic pressure. The direct estimation network with a single layer has the worst approximation error in all cases. Additionally, the spherically defined network has the slowest sample time at 0.05 seconds per thousand points. Both direct estimation methods produce one thousand sample points in approximately 0.01 seconds.

Hybrid circuit QED involves the study of coherent quantum physics in solid-state systems via their interactions with superconducting microwave circuits. Here we present a crucial step in the implementation of a hybrid superconducting qubit that employs a carbon nanotube as a Josephson junction. We realize the junction by contacting a carbon nanotube with a superconducting Pd/Al bilayer, and implement voltage tunability of the quantum circuit's frequency using a local electrostatic gate. We demonstrate a strong dispersive coupling to a coplanar waveguide resonator by investigating the gate-tunable resonator frequency. We extract qubit parameters from spectroscopy using dispersive readout and find qubit relaxation and coherence times in the range of 10-200 ns.

The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present a quantum algorithm to perform dynamical mean field theory (DMFT) calculations for condensed matter systems on currently available quantum computers, and demonstrate it on two quantum hardware platforms. DMFT is required to properly describe the large class of materials with strongly correlated electrons. The computationally challenging part arises from solving the effective problem of an interacting impurity coupled to a bath, which scales exponentially with system size on conventional computers. An exponential speedup is expected on quantum computers, but the algorithms proposed so far are based on real time evolution of the wavefunction, which requires high-depth circuits and hence very low noise levels in the quantum hardware. Here we propose an alternative approach, which uses the variational quantum eigensolver (VQE) method for ground and excited states to obtain the needed quantities as part of an exact diagonalization impurity solver. We present the algorithm for a two site DMFT system, which we benchmark using simulations on conventional computers as well as experiments on superconducting and trapped ion qubits, demonstrating that this method is suitable for running DMFT calculations on currently available quantum hardware.

This paper presents Power Amplifier solutions for 5G using GaN SiC HEMT technology. The difference in performance between 0.15 μm and 0.25 μm GaN HEMT devices is discussed. Measurements show 0.25 μm GaN HEMTs provide good performance for applications up to 18 GHz, including excellent performance in the Sub-6 GHz 5G bands. 0.15 μm GaN HEMTs currently offer good performance for applications to more than 32 GHz, including excellent performance in the 24-28 GHz 5G mm-wave band. Variations on the 0.15 μm process are also being developed to extend the operation frequency to cover the US 5G mm-wave band at 39 GHz and operation over 40 GHz to include Q band Satellite. This paper discusses performance of a discrete GaN power transistor (power bar) DC - 14GHz, with high power density and PAE in a single stage transistor that offers strong performance suitable for Sub-6 GHz 5G. It also discusses performance of a 2-stage 5W PA MMIC 24-28 GHz which is ideally suited for mm-wave 5G.

Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for replanning and collision avoidance. The information needed to predict collisions can be learned from previously observed vehicle trajectories in a specific environment, generating a traffic model. The learned traffic model can then be incorporated as prior knowledge into any trajectory estimation method being used in this environment. This work presents a Gaussian process based probabilistic traffic model that is used to quantify vehicle behaviors in an intersection. The Gaussian process model provides estimates for the average vehicle trajectory, while also capturing the variance between the different paths a vehicle may take in the intersection. The method is demonstrated on a set of time-series position trajectories. These trajectories are reconstructed by removing object recognition errors and missed frames that may occur due to data source processing. To create the intersection traffic model, the reconstructed trajectories are clustered based on their source and destination lanes. For each cluster, a Gaussian process model is created to capture the average behavior and the variance of the cluster. To show the applicability of the Gaussian model, the test trajectories are classified with only partial observations. Performance is quantified by the number of observations required to correctly classify the vehicle trajectory. Both the intersection traffic modeling computations and the classification procedure are timed. These times are presented as results and demonstrate that the model can be constructed in a reasonable amount of time and the classification procedure can be used for online applications.

We present ℒ_1-𝒢𝒫, an architecture based on ℒ_1 adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the ℒ_1 adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the ℒ_1 control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.

We present $\mathcal{L}_1$-$\mathcal{GP}$, an architecture based on $\mathcal{L}_1$ adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the $\mathcal{L}_1$ adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the $\mathcal{L}_1$ control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.

We present L-1 -GP, an architecture based on L-1 adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the L-1 adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the L-1 control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.