Lyapunov-Based Model Predictive Control for Dynamic Positioning and Trajectory-Tracking Control of an AUV

In this chapter, an LMPC-based DP control algorithm is firstly proposed for an AUV. A nonlinear Proportional-derivative (PD) control law is exploited to construct the contraction constraint in optimization problem that is associated with the LMPC. A quasi-global closed-loop stability property can be claimed for the closed-loop LMPC-based DP control system. Secondly, the LMPC is applied to solve the AUV trajectory tracking control problem. An auxiliary nonlinear tracking control law is designed using the backstepping technique and then used to construct the contraction constraint. Conditions for recursive feasibility and closed-loop stability are derived. In both DP and tracking control, the TA subproblem is solved simultaneously with the LMPC control, which reduces the conservativeness brought by conventional TA solutions. Essentially, the proposed LMPC method builds on the existing AUV control system and incorporates online optimization to improve the control performance. Since the closed-loop stability does not rely on the exact solution of the optimization, the LMPC creates a trade-off between computational complexity and control performance. We can easily control the computational complexity by specifying the maximum iteration number meanwhile guaranteeing the control performance no worse than the existing AUV motion controller.