# Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships
## 1 Introduction  
Marine vessels and ships have been widely used for offshore exploration, deep-sea mining, military operations, rigs-drilling and offshore wind farm constructions [1]. For such activities to be operated under safe and stable conditions, the vessels need to be equipped with advanced motion-control systems [2]. This has led to increasing demands for dynamic positioning (DP) systems to regulate the vessels' plane motions in order to maintain its position and heading. The dynamic positioning systems automatically control and maintain the ship's position and heading by means of computers, thrusters, propellers, filters, sensors and other components [3]. The capability of the ship for maneuvering and maintaining its position precisely depends on the efficiency and capacity of the components of the DP system. Precise operations require expensive hardware components (sensors, filters, etc) whose functionality and performance are degraded over time as the vessel maneuvers in the water [4]. Furthermore, the complexity and nonlinearity of the vessel dynamics and the fact that environment conditions of the sea/ocean (due to wind, waves and currents) are changeable and unpredictable have brought about new challenges on the design of DP systems [4]. The obvious alternative solution is the design of advanced and intelligent control system. Various advanced control techniques have been thoroughly discussed in literature and successfully applied to DP systems. A comprehensive literature survey for the control methods of DP systems until 2011 have been discussed in [3]. Further review and comparison of different control techniques have been presented in the recent review in [1]. The single-input-single-output PID control is afirst reported method used for DP system regulation [1; 5]. A low-pass filter was combined to the PID controller to control the motion of the DP system in the 3-degrees-of-freedom (DOF) horizontal plane. PID controllers have also been used in the nonlinear PID-control approach as proposed in [6], and model free multivariable PID controller tuning method with a capability of online tuning of DP control systems [7]. The emergence of Kalman filter and optimal theories was utilized to establish more advanced control design in [8] which was adopted and further improved and extended in the works of [9; 10; 11; 12] and the references therein. To deal with the exact dynamics of the vessel/ship (i.e., ship's nonlinear hydrodynamics), a number of nonlinear control methods have been proposed. State and input/output feedback linearization control methods have been discussed in [6; 13; 14]. Lyapunov-based design techniques including: nonlinear (passive) observer based on Lyapunov theory with wave filtering and full-scale experimental results [15], Asymmetric Barrier Lyapunov Function with Neural Networks have been deployed to control a vessel with output constraints and uncertainties [16], a combination of backstepping technique and Barrier Lyapunov Function with a passive observer to estimate some states [17]. Considering the robustness of DP system to variations in environmental and loading conditions, sliding mode control has been developed in [18; 19]. Fuzzy-logic and neural network algorithm methods have the ability to reduce the complex nonlinear characteristics of the DP system controller (by means of approximation of nonlinear function) without heavy/ tedious online computation requirements [20; 21]. This enables online estimation with time-saving in case of dynamics variations of the DP systems due to ex. disturbances which clarifies the wide use of such methods in various control-related problems of the DP systems as in [2; 5; 22; 23] and the references therein. Model-predictive control (MPC) is another popular control method that has recently been reported in the literature by a number of authors.