Adaptive Control of Uncertain Hamiltonian Multi-Input Multi-Output Systems: With Application to Spacecraft Control

Abstract—A novel adaptive tracking control law for nonlinear Hamiltonian multi-input–multi-output (MIMO) systems with un-certain parameters in the actuator modeling as well as the inertia and/or the Coriolis and centrifugal terms is developed. The phys-ical properties of the Hamiltonian systems are effectively used in the control design and the stability analysis. The number of the pa-rameter estimates is significantly lowered as compared to the con-ventional adaptive control methods which are based on the state-space form. The developed control scheme is applied for attitude control of a spacecraft with both the inertia and the actuator un-certainties, and numerical examples show that the controller suc-cessfully deals with the unknown inertia/actuator parameters. Index Terms—Actuator uncertainty, adaptive control, Hamil-tonian system, multiple-input–multiple-output (MIMO) system control, smooth projection algorithm, spacecraft attitude control. I