New Equilibria and Dynamic Structures Under Continuous Optimal Feedback Control

Ayano Tsuruta; Mai Bando; Shinji Hokamoto; Daniel J. Scheeres

doi:10.2514/1.G008270

New Equilibria and Dynamic Structures Under Continuous Optimal Feedback Control

Ayano Tsuruta, Mai Bando, Shinji Hokamoto, Daniel J. Scheeres

Flight Dynamics Lab

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.

Original language	English
Pages (from-to)	2029-2040
Number of pages	12
Journal	Journal of Guidance, Control, and Dynamics
Volume	47
Issue number	10
DOIs	https://doi.org/10.2514/1.G008270
Publication status	Published - Oct 2024

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Aerospace Engineering
Space and Planetary Science
Applied Mathematics
Electrical and Electronic Engineering

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10.2514/1.G008270

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abstract = "In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.",

keywords = "Algebraic Riccati Equation, Aritificial Equilibrium point, Equilibrium point, Feedback Control, Hill Three-Body Problem, Invariant manifold, Low Thrust, Low Thrust Propulsion, Low Thrust Trajectory, Space Exploration and Technology",

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AU - Tsuruta, Ayano

AU - Bando, Mai

AU - Hokamoto, Shinji

AU - Scheeres, Daniel J.

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N2 - In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.

AB - In this paper, the new equilibria realized by continuous optimal control inputs and the dynamic structure around them are studied. Using the Euler–Lagrange equation, which is a necessary condition for optimal control problems, the equations of motion of a dynamic system with optimal control inputs that minimize the quadratic cost function are described in terms of state and adjoint variables. Based on the equations of motion, equilibrium conditions are derived, and the properties of equilibria are analyzed for the two-body and Hill three-body problems. The stability and dynamic structure around unstable equilibria are also characterized to get insights into the properties of optimal trajectories.

KW - Algebraic Riccati Equation

KW - Aritificial Equilibrium point

KW - Equilibrium point

KW - Feedback Control

KW - Hill Three-Body Problem

KW - Invariant manifold

KW - Low Thrust

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KW - Low Thrust Trajectory

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New Equilibria and Dynamic Structures Under Continuous Optimal Feedback Control

Abstract

All Science Journal Classification (ASJC) codes

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