The method of parameterization in the quadratic optimal control problem

Срочко, В. А.; Antonik, V. G.; Aksenyushkina, E. V.

doi:10.1088/1742-6596/1847/1/012023

Cited by 1 publication

(2 citation statements)

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“…11 and 12 ) constrained with the linearized dynamics of Eq. 6 with costate parameters p(t) used in the Hamiltonian problem formulation leads to time-optimal control ( Flugge-Lotz, 1953 ; Pontryagin et al, 1962 ; Boltyanskii, 1971 ; Sands et al, 2009 ; Sands and Ghadawala, 2011 ; Duprez et al, 2017 ; Heidlauf and Cooper, 2017 ; Baker et al, 2018 ; Sands, 2019 ; Smeresky et al, 2020 ; Arguchintsev and Poplevko, 2021 ; Malecek, 2021 ; Srochko et al, 2021 ).

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Section: Methodsmentioning

confidence: 99%

“… Arguchintsev and Poplevko (2021 ) proposed an optimal control for linear hyperbolic systems of ordinary differential equations by estimating the residuals in terms of the value that characterizes the smallness of the measure of the domain of the needle variation of control. Emphasis was placed on problem formulation by Srochko et al (2021 ), but the focus was parameterizing the cost functional rather than the nonlinear constraint function as done in this work.…”

Section: Introductionmentioning

confidence: 99%

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Treatise on Analytic Nonlinear Optimal Guidance and Control Amplification of Strictly Analytic (Non-Numerical) Methods

Sands

2022

Front. Robot. AI

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Optimal control is seen by researchers from a different perspective than that from which the industry practitioners see it. Either type of user can easily become confounded when deciding which manner of optimal control should be used for guidance and control of mechanics. Such optimization methods are useful for autonomous navigation, guidance, and control, but their performance is hampered by noisy multi-sensor technologies and poorly modeled system equations, and real-time on-board utilization is generally computationally burdensome. Some methods proposed here use noisy sensor data to learn the optimal guidance and control solutions in real-time (online), where non-iterative instantiations are preferred to reduce computational burdens. This study aimed to highlight the efficacy and limitations of several common methods for optimizing guidance and control while proposing a few more, where all methods are applied to the full, nonlinear, coupled equations of motion including cross-products of motion from the transport theorem. While the reviewed literature introduces quantitative studies that include parametric uncertainty in nonlinear terms, this article proposes accommodating such uncertainty with time-varying solutions to Hamiltonian systems of equations solved in real-time. Five disparate types of optimum guidance and control algorithms are presented and compared to a classical benchmark. Comparative analysis is based on tracking errors (both states and rates), fuel usage, and computational burden. Real-time optimization with singular switching plus nonlinear transport theorem decoupling is newly introduced and proves superior by matching open-loop solutions to the constrained optimization problem (in terms of state and rate errors and fuel usage), while robustness is validated in the utilization of mixed, noisy state and rate sensors and uniformly varying mass and mass moments of inertia. Compared to benchmark, state-of-the-art methods state tracking errors are reduced one-hundred ten percent. Rate tracking errors are reduced one-hundred thirteen percent. Control utilization (fuel) is reduced eighty-four percent, while computational burden is reduced ten percent, simultaneously, where the proposed methods have no control gains and no linearization.

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