Path Following Control of Underactuated USV Based on Backstepping Control and Disturbance Observer

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

“…)) constitutes the nonlinear matrix inequality of Λ 1 , ( 22) is difficult to be solved by LMI. Since SOS method is an important tool to solve nonlinear problems, the SOS conditions is derived from (22) to solve the controller parameters W −1 , R(y cl ), and P(x cl ).…”

“…The SOF $$$ {H}_{\infty } $$$ control system for heading angle regulation of USV is implemented in MATLAB software, including QEBRL‐SOS method for the solution of the state feedback gain matrix and HEBRL‐SOS method for the solution of the controller parameters. The parameters of the nonlinear system (10) for USV model are, 22 $$$ {m}_{11}=25.8,{m}_{22}=33.8,{m}_{33}=2.76,{m}_{23}={m}_{32}=6.2,{d}_{11}=27,{d}_{22}=17,{d}_{33}=0.5,{d}_{23}=0.2,{d}_{32}=0.5 $$$. In order to simulate the real marine environment, time‐varying disturbances are given as $$$ {\tau}_{uw}=-0.2\cos (t)\cos (1.5t),{\tau}_{vw}=0.01\sin (0.1t),{\tau}_{rw}=-0.3\sin (2t)\cos (2.3t) $$$ 23 …”

“…(35) is same as (22) and bears the BRL form (15), it means that ( 24) is the HEBRL-SOS condition to guarantee the robustness stability of nonlinear system (10). The SOS conditions (24) can be used to solve the W −1 , R(y cl ), and P(x cl ).…”

“…The SOF H ∞ control system for heading angle regulation of USV is implemented in MATLAB software, including QEBRL-SOS method for the solution of the state feedback gain matrix and HEBRL-SOS method for the solution of the controller parameters. The parameters of the nonlinear system (10) for USV model are, 22 In order to simulate the real marine environment, time-varying disturbances are given as 𝜏 uw = −0.2 cos(t) cos(1.5t), 𝜏 vw = 0.01 sin(0.1t), 𝜏 rw = −0.3 sin(2t) cos(2.3t). 23 Figure 2 is SOF H ∞ control system for heading angle regulation.…”