Leakage reduction in fast superconducting qubit gates via optimal control

AbstractReaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.

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On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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The Modelling, Simulation and FPGA-Based Implementation for Stepper Motor Wide Range Speed Closed-Loop Drive System Design

Machines ◽

10.3390/machines6040056 ◽

2018 ◽

Vol 6 (4) ◽

pp. 56 ◽

Cited By ~ 1

Author(s):

Chiu-Keng Lai ◽

Jhang-Shan Ciou ◽

Chia-Che Tsai

Keyword(s):

Embedded System ◽

High Speed ◽

Closed Loop ◽

Open Loop ◽

Drive System ◽

Stepper Motor ◽

Motor Drive ◽

Digital Controllers ◽

Loop Control ◽

Wide Range

Owing to the benefits of programmable and parallel processing of field programmable gate arrays (FPGAs), they have been widely used for the realization of digital controllers and motor drive systems. Furthermore, they can be used to integrate several functions as an embedded system. In this paper, based on Matrix Laboratory (Matlab)/Simulink and the FPGA chip, we design and implement a stepper motor drive. Generally, motion control systems driven by a stepper motor can be in open-loop or closed-loop form, and pulse generators are used to generate a series of pulse commands, according to the desired acceleration/run/deceleration, in order to the drive system to rotate the motor. In this paper, the speed and position are designed in closed-loop control, and a vector control strategy is applied to the obtained rotor angle to regulate the phase current of the stepper motor to achieve the performance of operating it in low, medium, and high speed situations. The results of simulations and practical experiments based on the FPGA implemented control system are given to show the performances for wide range speed control.

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Passive optimal feedback control of an articulated flexible arm

Journal of Vibration and Control ◽

10.1177/1077546320956763 ◽

2020 ◽

pp. 107754632095676

Author(s):

Raja Tebbikh ◽

Hicham Tebbikh ◽

Sihem Kechida

Keyword(s):

Optimal Control ◽

Feedback Control ◽

Closed Loop ◽

Open Loop ◽

Optimal Feedback Control ◽

Convolution Operators ◽

High Frequencies ◽

Zero Initial Condition ◽

Flexible Arm ◽

Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

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Modeling and Analysis for Thermal Control of Spindles for Reconfigurable Machines

10.1115/imece2001/dsc-24584 ◽

2001 ◽

Author(s):

Jeffrey L. Stein ◽

John E. Harder

Keyword(s):

High Speed ◽

Metal Cutting ◽

Closed Loop ◽

Dynamic Performance ◽

Thermal Control ◽

Open Loop ◽

Limiting Factor ◽

Process Conditions ◽

Bearing Load ◽

Bearing Loads

Abstract Control of thermally induced bearing loads remains an important but unsolved problem for precision, high-speed, metal cutting, machining spindles. Spindle dynamic performance, as well as spindle life, depends on bearing loads. Because these loads can change drastically with a change in process conditions, poor spindle dynamic performance, and dramatically reduced bearing life can result. The purpose of this paper is to evaluate the feasibility of controlling bearing loads by controlling the heat generated by a thermal actuator placed around the housing of the spindle. A mathematical model of the open loop response of a laboratory prototype spindle is developed and validated. The model is then used to evaluate the closed loop performance. The results show that closed loop control of the bearing load is achievable in steady state and under bandwidth limited transient conditions. The proposed system has reasonable command authority when additional heat is required, however, it is possible for the system to lose control when the heater is required to “provide” negative heat. This situation can be mitigated by proper choice of initial preload. As expected, measurement noise limits the control gain but is not a limiting factor. More open loop tests are suggested to validate the model under a broader set of conditions. In addition, closed loop validation is suggested. However, based on results obtained it appears bearing load control is achievable by controlling the thermal field around the spindle.

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Experimental Implementation of a Hybrid Nonlinear Control Design for Magnetostrictive Actuators

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3089560 ◽

2009 ◽

Vol 131 (4) ◽

Cited By ~ 17

Author(s):

William S. Oates ◽

Phillip G. Evans ◽

Ralph C. Smith ◽

Marcelo J. Dapino

Keyword(s):

Optimal Control ◽

Nonlinear Control ◽

Tracking Control ◽

High Speed ◽

Control Design ◽

Nonlinear Optimal Control ◽

Open Loop ◽

Energy Model ◽

Switching Behavior ◽

Homogenized Energy Model

A hybrid nonlinear optimal control design is experimentally implemented on a magnetostrictive Terfenol-D actuator to illustrate enhanced tracking control at relatively high speed. The control design employs a homogenized energy model to quantify rate-dependent nonlinear and hysteretic ferromagnetic switching behavior. The homogenized energy model is incorporated into a finite-dimensional nonlinear optimal control design to directly compensate for the nonlinear and hysteretic magnetostrictive constitutive behavior of the Terfenol-D actuator. Additionally, robustness to operating uncertainties is addressed by incorporating proportional-integral (PI) perturbation feedback around the optimal open loop response. Experimental results illustrate significant improvements in tracking control in comparison to PI control. Accurate displacement tracking is achieved for sinusoidal reference displacements at frequencies up to 1 kHz using the hybrid nonlinear control design, whereas tracking errors become significant for the PI controller for frequencies equal to or greater than 500 Hz.

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Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

Acta Cybernetica ◽

10.14232/actacyb.285798 ◽

2021 ◽

Author(s):

Etienne Bertin ◽

Elliot Brendel ◽

Bruno Hérissé ◽

Julien Alexandre dit Sandretto ◽

Alexandre Chapoutot

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Closed Loop ◽

Minimum Principle ◽

Open Loop ◽

Pontryagin Minimum Principle ◽

Interval Method ◽

Bounded Uncertainties ◽

The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

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Approximating open-loop and closed-loop optimal control by model predictive control

2020 European Control Conference (ECC) ◽

10.23919/ecc51009.2020.9143615 ◽

2020 ◽

Author(s):

Asen L. Dontchev ◽

Ilya V. Kolmanovsky ◽

Mikhail I. Krastanov ◽

Vladimir M. Veliova

Keyword(s):

Optimal Control ◽

Model Predictive Control ◽

Predictive Control ◽

Closed Loop ◽

Open Loop

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A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331220977433 ◽

2020 ◽

pp. 014233122097743

Author(s):

Mohamed Sadok Attia ◽

Mohamed Karim Bouafoura ◽

Naceur Benhadj Braiek

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Sufficient Conditions ◽

Open Loop ◽

System Stability ◽

Gronwall Lemma ◽

Interconnected System ◽

Control Approach ◽

State Dependent ◽

And Control

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

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The Optimal Adaptive Sampled-Data Regulator

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3426811 ◽

1974 ◽

Vol 96 (3) ◽

pp. 334-340

Author(s):

R. A. Schlueter ◽

A. H. Levis

Keyword(s):

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Closed Loop ◽

Open Loop ◽

Sampled Data ◽

Threshold Values ◽

Regulator Problem

The optimal control problem for sampled-data processes in which sampling is not triggered by a timer, but occurs when one or more outputs attain preset threshold values is formulated as an adaptive optimal sampled-data regulator problem. Both open loop and closed loop solutions are determined and a comparison of a system’s performance with adaptive and with periodic sampling is presented.

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Approximately Optimal Control of Nonlinear Dynamic Stochastic Problems with Learning: The OPTCON Algorithm

Algorithms ◽

10.3390/a14060181 ◽

2021 ◽

Vol 14 (6) ◽

pp. 181

Author(s):

Dmitri Blueschke ◽

Viktoria Blueschke-Nikolaeva ◽

Reinhard Neck

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Numerical Solutions ◽

Optimization Problems ◽

Economic Models ◽

Open Loop ◽

Parameter Uncertainties ◽

Information Patterns ◽

Loop Feedback ◽

Dynamic Stochastic

OPTCON is an algorithm for the optimal control of nonlinear stochastic systems which is particularly applicable to economic models. It delivers approximate numerical solutions to optimum control (dynamic optimization) problems with a quadratic objective function for nonlinear economic models with additive and multiplicative (parameter) uncertainties. The algorithm was first programmed in C# and then in MATLAB. It allows for deterministic and stochastic control, the latter with open loop (OPTCON1), passive learning (open-loop feedback, OPTCON2), and active learning (closed-loop, dual, or adaptive control, OPTCON3) information patterns. The mathematical aspects of the algorithm with open-loop feedback and closed-loop information patterns are presented in more detail in this paper.

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