Structured adaptive model inversion applied to tracing spacecraft maneuvers
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In this paper, we demonstrate global stability and bounded tracking for a class of controllers designed using Structured Adaptive Model Inversion (SAMI), in the presence of bounded disturbances and model errors. The conventional Model Reference Adaptive Control (MRAC) problem is cast into the Structured MRAC problem3,4, by imposing the condition that the kinematic differential equations are exactly known, and all the learning is restricted to the acceleration differential equations. Dynamic Model Inversion13 is applied to solve for the controls explicitly and the adaptive structure is wrapped around this controller to account for the uncertainties in the system. The controller structure is designed, seeking to drive the error between the reference and the system states to zero with specified error dynamics, and we show that the closed loop system is globally stable. In the case where control saturation occurs, we devise a methodology to impose such constraints on the adaptive control law analogous to Pontryagin's principle on optimal control to make the error energy rate as negative as possible with admissible controls. However no claim is made with regards to convergence of the adaptation rates and parameters. The control law presented here realizes linear prescribed error dynamics in the kinematic states' vector. The controller designed using SAMI enforces these desired kinematic states' error dynamics. The overall closed loop dynamics is non-linear in two respects, the non-linear plant itself and the non-linear adaptation process.
