Abstract: A control system for controlling stick-slip oscillations in a drilling system is disclosed. The control system includes a processor and a memory communicatively coupled to the processor with computer program instructions stored therein. The instructions are configured to, when executed by the processor, cause the processor to receive a communication including a value of a drilling system parameter, determine based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, and transmit to a drive system the value for the torque to be applied by the drive system. The value for the torque to be applied by the drive system is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality.

Abstract: A control system for controlling stick-slip oscillations in a drilling system is disclosed. The control system includes a processor and a memory communicatively coupled to the processor with computer program instructions stored therein. The instructions are configured to, when executed by the processor, cause the processor to receive a communication including a value of a drilling system parameter, determine based on the value of the drilling system parameter, a value for a torque to be applied to a drill string to reduce the effect of stick-slip oscillations, and transmit to a drive system the value for the torque to be applied by the drive system. The value for the torque to be applied by the drive system is determined by solving a set of linear matrix inequalities including a disturbance minimization linear matrix inequality, a first magnitude constraint linear matrix inequality, and a second magnitude constraint linear matrix inequality.

Abstract: A method and apparatus for landing a spacecraft having thrusters with non-convex constraints is described. The method first computes a solution to a minimum error landing problem for a convexified constraints, then applies that solution to a minimum fuel landing problem for convexified constraints. The result is a solution that is a minimum error and minimum fuel solution that is also a feasible solution to the analogous system with non-convex thruster constraints.

Abstract: A method and apparatus for landing a spacecraft having thrusters with non-convex constraints is described. The method first computes a solution to a minimum error landing problem for a convexified constraints, then applies that solution to a minimum fuel landing problem for convexified constraints. The result is a solution that is a minimum error and minimum fuel solution that is also a feasible solution to the analogous system with non-convex thruster constraints.