Dynamic positioning of an uninhabited surface vehicle using state-dependent Riccati equation and pseudospectral method

Abstract

This paper proposed a novel control method for dynamic positioning of an uninhabited surface vehicle (USV). A state-dependent Riccati equation (SDRE) technique was introduced to deal with dynamic positioning problem of the USV. A new state-dependent coefficient (SDC) matrix was built to show the relationship between variables and satisfy the control inputs saturation for practical application. In order to solve the SDRE in real time, a semi-analytical formulation was derived by using Legendre-Gauss-Radau pseudospectral method. Simulation results show that the proposed method can be applied in real time and the USV can maintain its position and heading accurately and remains stable.

On global stability of planar systems with state‐dependent Riccati equation control

“…Clearly, all the functions and parameters in ( 10) and (11) are accessible, and hence the conditions (10) and ( 11) can be checked straightforwardly, thereby further investigating the global asymptotic stability of system (2) with the SDRE controller (5).…”

“…In light of its systematic design fashion and simplicity in real-time implementation [1,4,6], a number of elegant works dedicated to SDRE design for various practical nonlinear systems have been presented in the literature; see, for example, previous works [7][8][9][10][11][12][13][14][15][16] and the references therein. However, as shown in previous works [1,2,4], the abundantly existing SDRE-based practical/application results have drastically outpaced their available theoretical foundation, including global stability, optimality, etc.…”

An approximating pseudospectral method with state‐dependent coefficient optimization for nonlinear optimal control problem

“…In order to ensure the continuity of the differential of matrix norm on 𝛼, in this paper, the 2-norm is used to measure the size of vectors and matrices. Only by establishing the minimization problem (15) and solving it with the nonlinear optimal control problem (7), can J 1 gradually converge to zero.…”

“…with boundary conditions (13). At the same time, we need to solve appropriate 𝛼 in (15). Then the optimal control law u ⋆ can be obtained.…”

Reduce energy loss with dynamic positioning controller for USV based on Hierarchical Sliding Mode Control

“…Controlling the USV is a major challenge for researchers because of the strong and complex nonlinearity of the itself model and the operating environment. There have been some studies on linear [11] and nonlinear control of USV, boats and in articles [1], [3], [4], [5].…”