Stability Analysis and T-S Fuzzy Dynamic Positioning Controller Design for Autonomous Surface Vehicles Based on Sampled-Data Control

Abstract

This paper investigates the stability analysis and the fuzzy dynamic positioning (DP) controller design for an autonomous surface vehicle (ASV) based on sampled-data. Firstly, the Takagi-Sugeno (T-S) fuzzy model for the ASV with dynamic positioning system (DPS) is established. Then the criteria for asymptotically stability analysis and controller synthesis are provided by means of linear matrix inequalities. And less conservative results can be obtained by introducing convex reciprocal inequalities. Finally, simulation result is shown that the fuzzy sampled-data controller is effective to guarantee that the states of the ASV are stable and have good DP performance under the external disturbance. INDEX TERMS Autonomous surface vehicles, dynamic positioning system, T-S fuzzy model, sampleddata control.

Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models

“…From Table 1, the maximum sampling internal is d = 0.681. Note that results in [37][38][39] are 0.25, 0.264, and 0.532, respectively. This means that the sampling internal in this paper improves [37][38][39] by 160.8, 146.97, and 22.56%, respectively.…”

“…Note that results in [37][38][39] are 0.25, 0.264, and 0.532, respectively. This means that the sampling internal in this paper improves [37][38][39] by 160.8, 146.97, and 22.56%, respectively. It also shows that the proposed controllers play an important role in obtaining a longer sampling interval.…”

“…In [37], the fault-tolerant control problem of a sampled-data DPS was studied using actuator failure. Reference [38] established fuzzy models for a sampled-data DPS, and convex reciprocal inequalities were used to obtain the stability condition. Reference [39] investigated the non-periodic sampling tracking control problem of a DPS using actuator faults, and by introducing a new LKF, the mean square exponential stability criterion was obtained.…”

“…Compared with the LKF in [38,39], more available matrices, such as Q, R, X, U, are effectively used in the LKF. If we let R 12 = R 22 = Z = Q = 0 and U 13 = U 12 = U 22 = X 13 = X 23 = X 33 = 0, the LKF will be reduced to those in [38,39], which means that the proposed LKF has a more general form. Moreover, free matrices M ij and N ij are introduced into the differentiation of the LKF.…”

“…Remark 4. In the process of derivative and further proof of the LKF in [38,39], the positive definite requirement of the matrix is necessary. In this paper, X-dependent terms are introduced in V 1 (t) and are not required to be positive definite, which means that the limitation conditions of the matrices are overcome.…”