Robust Multi-Stage Nonlinear Model Predictive Control Using Sigma Points

Thangavel, S.; Paulen, Radoslav; Engell, Sebastian

doi:10.3390/pr8070851

Cited by 5 publications

(4 citation statements)

References 69 publications

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“…Whereas the sampling method penalizes the deviations of the sample states from the target state, the unscented sampling method penalizes the deviations of the sample states from the nominal state [68][69][70]. Accordingly, the cost function we add to the objective takes the form…”

Section: B Unscented Sampling Methodsmentioning

confidence: 99%

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Robust Quantum Optimal Control with Trajectory Optimization

Propson¹,

Jackson²,

Koch³

et al. 2021

Preprint

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The ability to engineer high-fidelity gates on quantum processors in the presence of systematic errors remains the primary barrier to achieving quantum advantage. Quantum optimal control methods have proven effective in experimentally realizing high-fidelity gates, but they require exquisite calibration to be performant. We apply robust trajectory optimization techniques to suppress gate errors arising from system parameter uncertainty. We propose a derivative-based approach that maintains computational efficiency by using forward-mode differentiation. Additionally, the effect of depolarization on a gate is typically modeled by integrating the Lindblad master equation, which is computationally expensive. We employ a computationally efficient model and utilize time-optimal control to achieve high-fidelity gates in the presence of depolarization. We apply these techniques to a fluxonium qubit and suppress simulated gate errors due to parameter uncertainty below 10 −7 for static parameter deviations on the order of 1%.

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Section: B Unscented Sampling Methodsmentioning

confidence: 99%

“…2. An unscented sampling method [68][69][70] adapted from the unscented transform [71,72] used in state estimation.…”

Section: Introductionmentioning

confidence: 99%

Robust Quantum Optimal Control with Trajectory Optimization

Propson¹,

Jackson²,

Koch³

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…In the literature, there exist different stochastic sample-based optimization approaches for a predictive optimal controller design; see, e.g., [45][46][47][48][49][50]. However, these approaches are computationally tractable only for a shorter prediction horizon.…”

Section: Linear Approximation Of the State Dynamics Around The Expect...mentioning

confidence: 99%

“…Among the several approaches to cope with stochastic dynamics [44], we mention two groups of techniques, which are popular in control theory. First, the particle-based approaches [45][46][47][48][49] with scenario trees allow coping with general (not necessarily Gaussian) models. Secondly, the tube-based approaches [50][51][52][53] approxi-mate each predicted state and input by a Gaussian distribution.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

2022

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In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

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