Extended bounded real lemma based sum of squares for static output feedback H∞ heading control

Aim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) H-infinity control method is proposed by the sum of squares (SOS) based on two types of extended bounded real lemmas (EBRL) for heading regulation to guarantee the robustness and improve the rapidity. First, an asymmetric nonlinear heading error model with hydrodynamic parameters is established by the consideration of lack of linear velocity. Second, SOF controller with H-infinity performance is presented for the asymmetric nonlinear USV model, and it's SOS conditions to solve controller parameters is deduced from EBRL by homogeneous Lyapunov function (HERBL) to maintain the system robustness. Further, the solution of SOF H-infinity controller relies on the state feedback gain matrix, EBRL is deduced by quadratic Lyapunov function (QEBRL) to obtain the SOS conditions without the addition of an extended matrix to cut computing cost for the solution of the state feedback gain matrix. Finally, the heading control simulations for USV indicate that, QEBRL method takes less time for SOS conditions to solve the state feedback gain matrix, and SOF H-infinity system of HERBL has a superior performance on the transient response and the robustness.

Automated summary

This study proposes a heading control method for unmanned surface vehicles (USVs) to address the asymmetry and loss of linear velocity. By using SOS and EBRL methods, the control parameters of the USV model are determined, ensuring system robustness.