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Generalized Composite Noncertainty-Equivalence Adaptive Control of Orbiting Spacecraft in Vicinity of Asteroid

The Journal of the Astronautical Sciences volume 67, pages 1021–1043 (2020)Cite this article

Abstract

The paper presents composite noncertainty-equivalence adaptive control (NCEA) systems for the closed orbit and hovering control of spacecraft in the vicinity of a uniformly rotating asteroid. In this study, the asteroid’s mass and moment of inertia matrix, and the mass of the spacecraft are treated as unknown constant parameters. The objective is to control the orbit of the spacecraft, despite uncertainties in the gravitational force of asteroid. For the trajectory control of the spacecraft, first a generalized composite noncertainty-equivalence adaptive (NCEA) control system - based on the immersion and invariance theory - is developed. This system consists of a control module for stabilization and an identifier for the estimation of parameters. The identifier includes a dynamic integral type parameter adaptation law, which is formed by combining the update laws of the NCEA system, gradient algorithm-based identification scheme, and classical certainty-equivalence adaptive system. The classical component of the composite update law is used to cancel certain sign-indefinite functions in the derivative of a Lyapunov function. The full estimate of each unknown parameter is the sum of an algebraic function, and a signal generated by the composite integral type adaptation law. The gradient algorithm-based update rule is a function of the estimation model error. Then, by a proper choice of adaptation gains of the generalized control system, two additional composite control systems - (i) an NCEA system with gradient algorithm-based adaptation law, and (ii) an NCEA controller with classical update law - are derived. By the Lyapunov analysis, it is shown that in each composite closed-loop system, all of the signals are bounded, and the trajectory tracking error asymptotically converges to zero. Interestingly, composite systems, including gradient-based adaptation, have two attractive manifolds to which certain vector functions converge, but the composite system, without gradient-based update law, has a single attractive manifold. Numerical results are presented, which show that robust orbit control of the spacecraft around 433 Eros and hovering control in the vicinity of Ida are accomplished, despite parameter uncertainties and perturbing disturbance forces on the spacecraft.

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Authors and Affiliations

  1. Department of Electronic Engineering, Catholic Kwandong University, Gangwon, 25601, Republic of Korea

    Keum W. Lee

  2. Department of Electrical and Computer Engineering, University of Nevada Las Vegas, Las Vegas, NV, 89154-4026, USA

    Sahjendra N. Singh

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  1. Keum W. Lee
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  2. Sahjendra N. Singh
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Correspondence to Sahjendra N. Singh.

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Lee, K.W., Singh, S.N. Generalized Composite Noncertainty-Equivalence Adaptive Control of Orbiting Spacecraft in Vicinity of Asteroid. J Astronaut Sci 67, 1021–1043 (2020). https://doi.org/10.1007/s40295-019-00207-x

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  • DOI: https://doi.org/10.1007/s40295-019-00207-x

Keywords

  • Composite adaptive spacecraft control
  • Asteroid orbiting spacecraft
  • Composite gradient-based adaptation
  • Composite noncertainty-equivalence adaptive system
  • Immersion and invariance-based orbit control
  • Composite nonlinear adaptive control

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