Quantum control theory and applications: a survey

Lower-limb exoskeletons are widely researched to improve walking performance and mobility. Low-level sensor-less exoskeleton motor control is attractive for consumer applications due to reduced device complexity and cost, but complex and variable transmission system configurations make the development of effective open-loop motor controllers that are responsive to user input challenging. The objective of this study was to develop and validate an open-loop motor control framework resulting in similar or greater performance vs. closed-loop torque control. We used generalized linear regression to develop two open-loop controllers by modeling motor current during exoskeleton-assisted walking; a "complex" model used desired torque and estimated ankle angular velocity as inputs, while a "simple" model used desired torque alone. Five participants walked at 1.0-1.3 m/s on a treadmill with closed-loop and both open-loop controllers providing ankle exoskeleton assistance. Both open-loop current controllers had similar root-mean-squared torque tracking error (p=0.23) compared to the closed-loop torque-feedback controller. Both open-loop controllers had improved relative average torque production (p<0.001 complex, p=0.022 simple), lower power consumption (p<0.001 for both), and reduced operating noise (p=0.002 complex, p<0.001 simple) over the closed-loop controller. New control models developed for a different ankle exoskeleton configuration showed similar improvements (lower torque error, greater average and peak torque production, lower power consumption) over closed-loop control during over-ground walking. These results demonstrate that our framework can produce open-loop motor controllers that match closed-loop control performance during exoskeleton operation.

Robust quantum control is crucial for realizing practical quantum technologies. Energy landscape shaping offers an alternative to conventional dynamic control, providing theoretically enhanced robustness and simplifying implementation for certain applications. This work demonstrates the feasibility of robust energy landscape control in a practical implementation with ultracold atoms. We leverage a digital mirror device (DMD) to shape optical potentials, creating complex energy landscapes. To achieve a desired objective, such as efficient quantum state transfer, we formulate a novel hybrid optimization approach that effectively handles both continuous (laser power) and discrete (DMD pixel activation) control parameters. This approach combines constrained quasi-Newton methods with surrogate models for efficient exploration of the vast parameter space. Furthermore, we introduce a framework for analyzing the robustness of the resulting control schemes against experimental uncertainties. By modeling uncertainties as structured perturbations, we systematically assess controller performance and identify robust solutions. We apply these techniques to maximize spin transfer in a chain of trapped atoms, achieving high-fidelity control while maintaining robustness. Our findings provide insights into the experimental viability of controlled spin transfer in cold atom systems. More broadly, the presented optimization and robustness analysis methods apply to a wide range of quantum control problems, offering a toolkit for designing and evaluating robust controllers in complex experimental settings.

Step motors are widely used in motion control systems. The step motor controller must perform high-precision positioning and smooth movement operation. In motion systems applying velocity profile control, the velocity of the motor gradually increases or decreases, to avoid the negative effect caused by the sudden change in velocity. Previous research proposes several step motor controller designs, that contain several modules, including a velocity profile generator, step motor driver, and feedback counter. These controllers are able to perform precise positioning and provide smooth motion operation. However, because these controllers operate in an open-loop control so the synchronous condition can be lost when disturbances in load torque exist. This paper presents the application of closed-loop control in the step motor controller. The control algorithm is based on two mode operations: open-loop and closed-loop. The controller operates in open-loop mode when it remains synchronized, and switches to closed-loop mode when it loses synchronization. This paper presents an algorithm for generating various velocity profiles and closed-loop control algorithms. The experiment is performed on a 16-b DSP, to verify the performance of the design. The experimental results show a velocity profile of unsymmetrical shape and demonstrate effective closed-loop control in an actual step motor system

Layer-to-layer closed-loop feedback control application for inter-layer temperature stabilization in laser powder bed fusion

Closed-loop fluid flow control using a low dimensional model

This paper presents an experimental study of laser interferometry-based closed-loop motion tracking for flexure-based four-bar micro/nano manipulator. To enhance the accuracy of micro/nano manipulation, laser interferometry-based motion tracking control is established with experimental facility. The authors present and discuss open-loop control, model-based closed-loop control, and robust motion tracking closed-loop control for flexure-based mechanism. A comparative error analysis for closed-loop control with capacitive position sensor and laser interferometry feedback is discussed and presented. Model-based closed-loop control shows improvement in position and motion tracking over open-loop control. Robust control demonstrates high precise and accurate motion tracking of flexure-based mechanism compared to the model-based control. With this experimental study, this paper offers evidence that the laser interferometry-based closed-loop control can minimize positioning and tracking errors during dynamic motion, hence realizing high precision motion tracking and accurate position control.

The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed.

Quantum control theory has been developed in the past few years [1] by extending the control theory of classical systems into the quantum domain. It has lead to new insights into the way in which matter can be manipulated that may have important consequences for chemistry, biology, materials science and possibly optical communications and computing.

Stabilogram-diffusion analysis was used to examine how prolonged periods in microgravity affect the open-loop and closed-loop postural control mechanisms. It was hypothesized that following spaceflight: (1) the effective stochastic activity of the open-loop postural control schemes in astronauts is increased; (2) the effective stochastic activity and uncorrelated behavior, respectively, of the closed-loop postural control mechanisms in astronauts are increased; and (3) astronauts utilized open-loop postural controls schemes for shorter time intervals and smaller displacements. Four crew members and two alternates from the 14-day Spacelab Life Sciences 2 Mission were included in the study. Each subject was tested under eyes-open, quiet-standing conditions on multiple preflight and postflight days. The subjects' center-of-pressure trajectories were measured with a force platform and analyzed according to stabilogram-diffusion analysis. It was found that the effective stochastic activity of the open-loop postural control schemes in three of the four crew members was increased following spaceflight. This result is interpreted as an indication that there may be in-flight adaptations to higher-level descending postural control pathways, e.g., a postflight increase in the tonic activation of postural muscles. This change may also be the consequence of a compensatory (e.g., "stiffening") postural control strategy that is adopted by astronauts to account for general feeling of postflight unsteadiness. The crew members, as a group, did not exhibit any consistent preflight/postflight differences in the steady-state behavior of their closed-loop postural control mechanisms or in the functional interaction of their open-loop and closed-loop postural control mechanisms. These results are interpreted as indications that although there may be in-flight adaptations to the vestibular system and/or proprioceptive system, input from the visual system can compensate for such changes during undisturbed stance.

The reduction of drag force and suppression of vortex shedding on a circular cylinder in electrically poorly-conducting water can be realized by utilizing the Lorentz forces. In order to control the cylinder wake effectively, three kinds of control approach, i.e. open-loop, closed-loop and optimal control methods, are proposed and discussed in the present paper. Constant Lorentz forces are used in the open-loop control process, and Lorentz forces are varied to target the zero total drag or the zero pressure drag coefficients during the control process in two closed-loop control procedures. The purpose of optimal flow control is to determine controls that effectively tailor the flow, and the key element of an optimal flow control is the minimization of a cost functional that provides a quantitative measure of the objective. Numerical simulation of the theoretical models is performed in the exponential–polar coordinates system, from which it has been shown that the above three methods can suppress the vortex shedding successfully; moreover, during the control process, the optimal control needs less energy than the closed-loop control method targeting a zero total drag or pressure drag coefficients.

Stochastic dynamic programming has been. extensively used in the optimization of long term hydrothermal scheduling problems due to its ability to cope with the nonlinear and stochastic characteristics of such problems, and the fact that it provides a closed-loop feedback control policy. Its computational requirements, however, tend to be heavy even for systems with a small number of hydroplants, requiring some sort of modeling manipulation in order to be able to handle real systems. An alternative to closed-loop optimization is an approach that combines a deterministic optimization model with an inflow forecasting model in a partial open-loop feedback control framework. At each stage in this control policy, a forecast of the inflows during the period of planning is made, and an operational decision for the following stage is obtained by a deterministic optimization model. The present paper compares such closed-loop and partial open-loop feedback control policies in long term hydrothermal scheduling, using a single hydroplant system as a case study to focus the comparison on the feedback control performance. The comparison is made by simulation using data from historical and synthetical inflow sequences in the consideration of three different Brazilian hydroplants located in different river basins. Results have demonstrated that the performance of the partial open-loop feedback control policy is similar to that of the closed-loop control policy, and is even superior in dry streamflow periods.

Study on the Simulation for Closed-Loop Control Based on Synchronous Rotating Coordinate for MC

The global carbon-climate system is a complex dynamical system with multiple feedbacks among components, and to steer this system away from dangerous climate change, it may not be enough to prescribe action according to long-term scenarios of fossil fuel emissions. We introduce here concepts from control theory, a branch of applied mathematics that is effective at steering complex dynamical systems to desired states, and distinguish between open- and closed-loop control. We attempt (1) to show that current scientific work on carbon-climate feedbacks and climate policy more closely resembles the conceptual model of open- than closed-loop control, (2) to introduce a mathematical generalization of the carbon-climate system as a compartmental dynamical system that can facilitate the formal treatment of the closed-loop control problem, and (3) to formulate carbon-climate control as a congestion control problem, discussing important concepts such as observability and controllability. We also show that most previous discussions on climate change mitigation and policy development have relied on an implicit assumption of open-loop control that does not consider frequent corrections due to deviations of goals from observations. Using a reduced complexity model, we illustrate that the problem of managing the global carbon cycle can be abstracted as a network congestion problem, accounting for nonlinear behavior and feedback from a global carbon monitoring system. As opposed to scenarios, the goal of closed-loop control is to develop rules for continuously steering the global carbon-climate system away from dangerous climate change.

In this article, average large signal modeling technique is applied to develop the various transfer function models of the DC–DC buck converter. With the help of transfer function, Proportional—Integral-Derivative (PID) and PID with filter co-efficient (N) so-called PIDN controller is designed for voltage mode closed-loop control in both analog and digital domain. Bode plots are developed to show the open-loop and closed-loop control in both analog and digital domains. Similarly, Pole-zero plots in both analog and digital domains in order to demonstrate the stability of the buck converter. The obtained model is simulated in two variants; (1) Simulink environment. (2) Text-based computational implementation technique. Simulation results in both the variants show that with PIDN control, the steady-state and dynamic response of the buck converter is increased compared to PID control since PIDN offers wider bandwidth and high gain. The filter co-efficient “N value” is taken higher, the derivative filter term “ ” will become ‘s’ which is an ideal derivative term. This ideal derivative has very high gain for high-frequency signals therefore high-frequency measurement noise will generate large variations of the control signal (PWM signal) which results in erroneous system operation. To prevent this situation, the value of filter co-efficient ‘N’ is taken to be low. Here low value of ‘N’ is 22765.4257546504 which is obtained by tuning process and the whole process is demonstrated. These models pave the way in the design, development analysis of closed-loop embedded control of DC–DC converters in the platforms like DSP- and FPGA-based systems.

Optimal control of batch electrochemical reactor using K–L expansion