# Output Feedback Tracking Control for Vessel with Collision-Avoidance and Performance Constraints
###### Abstract  
This manuscript investigates an output feedback-tracking control problem of a dynamically positioned vessel with an input constraint. The vessel is exposed to model uncertainty and external disturbances. Compared with the existing results, the primary contribution is to develop a switch-control strategy for achieving collision avoidance and performance constraints by using an extended state observer (ESO), a collision-avoidance controller (CAC), a prescribed performance controller, and an auxiliary dynamic system (ADS). The switch control strategy combined two different controllers, and an extended state observer (ESO) is designed. The ESO is employed to recover velocity information as well as unknown model uncertainty and external disturbances. A collision-risk-analysis module is introduced to evaluate whether there exists a risk of collision avoidance. Based on the analysis, the CASC can choose between a CAC and a PPC. An ADS is constructed to handle the input constraints. The CAC is employed by using an artificial potential function, the ADS, and the ESO. The PPC is designed based on an error constraint function, the ADS, and the ESO. The stability of the closed-loop control system is analyzed based on the Lyapunov direct method. Simulations prove the effectiveness of the presented control strategy. dynamically positioned vessel; prescribed performance; collision avoidance; input constraint 2023201220233112852023122023122023112202  
knowledge of disturbances. To avoid this problem, an extended state observer (ESO) is developed for a dynamically positioned vessel in [17]. The observer can estimate velocities, model uncertainty, and external disturbances without using velocity measurements. In practice, owing to physical limitations, control inputs are limited by magnitude constraints. The saturated control inputs may impact the system performance [18]. To ensure a stable and efficient work system, many methods have been widely explored for vessels. Considering input constraints, a controller combined with a Gaussian function is proposed for dynamically positioned vessels [19], and the Gaussian function is designed to approximate input saturation induced by physical limitations of thrusters. A hyperbolic tangent function is employed to solve the input saturation in [20]. However, those functions limit control inputs and degrade system performance, whether the control inputs are saturated or not. To avoid this, ref. [21] proposes a robust control scheme for dynamically positioned vessels, and an auxiliary dynamic system (ADS) is used to solve input constraints. An anti-windup compensator is combined with a control design to solve the input saturation in the trajectory tracking of a dynamically positioned vessel [22; 23]. Most of the aforementioned results do not consider prescribed performance in the control design. In a complex sea environment, collisions may occur due to a larger tracking error. Ref. [24] proposes a logarithmic error mapping function to realize the prescribed control performance, and it is widely used in nonlinear systems. Furthermore, ref. [25] designs control laws with prescribed performance for nonlinear systems with strict feedback. Ref. [26] proposes the prescribed performance control for dynamically positioned vessels, where a finite-time controller combined with a nonlinear observer is constructed. Apart from the prescribed performance, the collision avoidance must be considered. An efficient collision-avoidance algorithm can enhance navigation safety. Using a path planning algorithm is one of the most popular methods [27]. The method is limited by optimization strategies; it takes a lot of time to obtain an available solution. The existing path-planning algorithms have not been able to effectively deal with complex traffic environments, and it is sometimes impossible to obtain a feasible solution within a feasible time. To solve this, some researchers have designed collision-avoidance control systems for vessels [28; 29]. Ref.