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

Abstract

Aiming at a mass variation of unmanned surface vehicle and the poor or even unmeasurable signal of yaw rate signal, the dynamic output feedback [Formula: see text] control method is proposed for heading regulation based on improved bounded real lemma to reduce the conservativeness and guarantee the robustness. First, a linear-varying-parameter heading error model with external disturbances is established by the consideration of mass as a variable parameter. Second, the dynamic output feedback controller with [Formula: see text] performance is presented for the linear-varying-parameter heading error model, and its nonlinear matrix inequality conditions for the stability of the closed-loop system are deduced from improved bounded real lemma by parameter-dependent Lyapunov to maintain the system robustness. Furthermore, the solution of nonlinear matrix inequality conditions relies on the variable substitution method, and improved bounded real lemma reduces the conservativeness of the controller design by introducing auxiliary relaxation variables to derive the equivalent linear matrix inequality condition. Finally, the heading control simulations for unmanned surface vehicle indicate that the dynamic output feedback [Formula: see text] method based on improved bounded real lemma (IDOF) is robust to system parameter variations and external disturbances, and can effectively reduce the conservativeness of the controller design. Moreover, dynamic output feedback H∞ method based on improved bounded real lemma has faster transient processes and smaller steady-state errors.

Heading control based on extended homogeneous polynomial Lyapunov function

“…To achieve global exponential stability and H ∞ performance for the closed-loop system (7), it is necessary to design a NPV controller (6) with the conditions of ( 9) and (10). Since both the PLF and QLF methods restrict the system performance, 10,13 EHPLF matrix with full states and varying parameter for NPV system is proposed to improve system performance.…”

“…Theorem 1. NPV closed-loop system ( 7) is globally exponentially stable with a robust H ∞ performance by the form of the state feedback controller (6) under the EHPLF stability conditions as…”

“…To analyze the suppression of varying parameter of surge velocity, the external disturbance is w = 0, the desired heading angle is 𝜓 d = 𝜋∕3 rad, and the varying surge velocity is u = (sin(𝛽 2 t) + 1) m/s. 13 rates of varying parameters. Figure 4 shows the responses of the heading control system when 𝛽 2 = 2.…”

“…5 To solve the mass-varying problem of USV during navigation, a heading linear parameter-varying (LPV) model with mass-varying parameters is controlled by a dynamic output feedback H ∞ method based on improved bounded real lemma. 6 Considering the influence of varying surge velocity on heading control, a LPV model with surge velocity is established and controlled by a state feedback H ∞ heading control method to suppress the adverse effects of surge velocity changes and external disturbances on heading regulation. 7 However, it is difficult for LPV model to accurately describe the hydrodynamic nonlinear characteristics of USV.…”

“…[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). 13 However, the parameter-dependent QLF matrix is only introduced with varying parameter and without state variables, which to some extent restricts the performance on dynamic, steady-state and robustness. 14 Therefore, it is challenging to explore a Lyapunov matrix with full states and varying parameter to design a robust H ∞ control method for NPV system.…”