Preconditioned C/GMRES algorithm for nonlinear receding horizon control of hovercrafts connected by a string

This paper describes preconditioning methods for real-time algorithm of nonlinear receding horizon control. Nonlinear receding horizon control requires a solution of a finite-horizon optimal control problem at each sampling time. Although the problem can be solved by a fast algorithm called C/GMRES, calculation may fail for some stiff systems. By introducing preconditioning methods such as block Jacobi or ILU preconditioner to a part of solving linear equations in the algorithm, it is possible to obtain a more accurate solution and to make the algorithm more numerically robust. The preconditioned algorithm is evaluated in a numerical example and is demonstrated in a hardware experiment of position control for hovercrafts connected by a string.