  In this paper, two robust model predictive control (MPC) schemes are proposed
for tracking control of nonholonomic systems with bounded disturbances:
tube-MPC and nominal robust MPC (NRMPC). In tube-MPC, the control signal
consists of a control action and a nonlinear feedback law based on the
deviation of the actual states from the states of a nominal system. It renders
the actual trajectory within a tube centered along the optimal trajectory of
the nominal system. Recursive feasibility and input-to-state stability are
established and the constraints are ensured by tightening the input domain and
the terminal region. While in NRMPC, an optimal control sequence is obtained by
solving an optimization problem based on the current state, and the first
portion of this sequence is applied to the real system in an open-loop manner
during each sampling period. The state of nominal system model is updated by
the actual state at each step, which provides additional a feedback. By
introducing a robust state constraint and tightening the terminal region,
recursive feasibility and input-to-state stability are guaranteed. Simulation
results demonstrate the effectiveness of both strategies proposed.
