Fuzzy H∞ tracking control for spacecraft orbit transfer via T-S fuzzy model with pole assignment

A robust fuzzy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> control for spacecraft orbit transfer is investigated in this paper, which includes output tracking, disturbance attenuation, input constraint, and pole assignment. Spacecraft dynamics is modeled using the Keplerian two-body problem in polar coordinates, enabling long-range maneuvers in a circular orbit, while the relative motion between spacecraft is particularly useful for proximity operations. Utilizing the fuzzy theory approach, a Takagi-Sugeno (T-S) fuzzy model is constructed through the gain-scheduling technique, which involves selecting multiple operating points to develop a linearized model of the equation of motion. An output tracking reference is incorporated to enable the spacecraft to follow and reach its final position. Using the parallel distributed compensation (PDC) approach, sufficient conditions for the design of a robust fuzzy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> controller are derived to guarantee the asymptotic stability of the closed-loop system. This controller minimizes fuel consumption, attenuates external disturbances, and restricts system poles within a specified region. Using Lyapunov theory, the orbit transfer problem is addressed as a convex optimization problem, with the controller’s objectives expressed as linear matrix inequalities (LMIs). Numerical simulations demonstrate the effectiveness of the proposed controller, efficiently transferring the spacecraft to its final orbit while using limited thrust and minimizing the disturbance index.