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

Abstract

Aim at the fore and aft asymmetry of unmanned surface vehicle (USV) and the loss of linear velocity, a static output feedback (SOF) H ∞ 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 ∞ 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 ∞ 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 ∞ system of HERBL has a superior performance on the transient response and the robustness. K E Y W O R D Sextended bounded real lemma (EBRL), heading regulation of USV, nonlinear heading error model, state feedback gain matrix, static output feedback (SOF) H ∞ control, sum of squares (SOS)

An improved bounded real lemma for H∞ robust heading control of unmanned surface vehicle

“…For the system state equation (7), if there exists a controller of the form as u ( s ) = K ( s ) y ( s ) such that the closed-loop system satisfies the following for all ρ properties 24 :…”

“…Finally, substituting equation (32) into equation ( 27), the stability condition of IDOF control system is obtained Inequality equation ( 33) is an LMI, which is the equivalent representation of inequality equation (24).…”

Heading control based on extended homogeneous polynomial Lyapunov function

“…For (7), it is useful for robust H ∞ control technology to suppress system parameter uncertainties and external disturbances. For any initial system state x(t 0 ), if the system state and the integral inequality J with the control output z and the disturbance w satisfy the inequalities 9,23 :…”

“…and 𝜅 = 1 2 𝛼, (35) is equal to (9), which means that the NPV system ( 7) is globally exponentially stable with the conditions of ( 14) and (15).…”

“…8 For the Fossen model with asymmetric inertia matrix and damping coefficient matrix, a nonlinear heading error model is established to propose a static output feedback H ∞ heading control method based on extended bounded real lemma. 9 Nonlinear parameter-varying (NPV) systems retain the advantages of both nonlinear and varying parameter, including the nonlinear problem of yaw motion and varying parameter of surge velocity. [10][11][12] The nonlinear matrix inequality (NLMI) solution conditions are derived for NPV H ∞ heading controller by constructing a parameter-dependent quadratic Lyapunov function (QLF).…”