# Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships
## 1 Introduction
Enhancement in control performance of the DP systems can be achieved deploying this method due to its systematic way in handling various (inputs, outputs and states) constraints [24], its model/performance optimization capabilities as well as its robustness against external disturbances and unmodeled dynamics [1; 4]. The tracking MPC control problem of underactuated surface vessels has been proposed in [20]. In [24], both linear and nonlinear MPC approaches have been investigated for the trajectory tracking problem of autonomous vessels. Considering uncertain environmental disturbances, measurement errors and partially measured states, two robust control methods based on MPC and using a simple Luenberger observer for DP systems control problem of autonomous surface vessels have been discussed in [4]. Passivity-based control (PBC) is another class of nonlinear control methods that have received a lot of interest due to its advantages in reducing the complexity in the control design [3] exploiting intrinsic system properties. By invoking the physically motivated principles of energy dissipation and transformation, the stabilization of the dynamical system is achieved fulfilling its passivity property which is related to the stability properties of the systems [25]. The PBC problem aims at making the closed loop system passive by shaping both the energy and internal interconnection structure of the system. The most notable example of the PBC approach is the interconnection and damping assignment-passivity based control (IDA-PBC) which has already been successfully applied to various dynamical systems adopting port-Hamiltonian (PH) formalism [26]. In addition to energy and structural shaping of the PH model, damping is injected by means of feedback control to ensure asymptotic stability of the closed-loop system. Passivity theory has been used in [6] to establish a passive nonlinear observer and in [27] a passivity-based controller based on IDA-PBC method has been proposed to stabilize a DP system of ship. Focusing on enhancement of the control performance, optimization techniques have been widely used and applied. They provide systematic procedure for designing of controllers, tuning the parameters and gains, and online estimation/calibration for unknown parameters caused by environmental changes or disturbances [21; 28]. In the literature, various optimization algorithms have been developed to improve the quality of the closed-loop system such as Artificial Bee Colony (ABC) algorithm [29], Ant Colony Optimization (ACO) algorithm [30], Bacterial Foraging Optimization (BFO)algorithm [31], Multi-Verse Optimization (MVO) algorithm [32] and Gravitational Search Algorithm (GSA) [33]. Particle Swarm Optimization (PSO) is one of the effective optimization methods that has been successfully used in tuning PID controllers as in [34], for quadrotor stabilization based on integral backstepping control design [35], for tuning the parameters of fuzzy PD controller with minimization of integral square error cost function in [36], to improve the performance of an ultrasonic transducer [28]. For the control of DP systems, authors in [21] have deployed the PSO method to optimize the fuzzy function/parameters to enhance the quality and performance of the DP system of the ship. In this paper, we propose a dynamic IDA-PBC controller that stabilizes the ship/vessel. It introduces a modified version of the IDA-PBC controller which was proposed in [27] by adopting the state-transformation to obtain a dynamical feedback controller with robustness capability due to the incorporation of the integral action controller. In addition, damping is injected in both the position and momenta states to ensure asymptotic stability. Furthermore, the design and selection of parameters/gains of nonlinear controllers are generally obtained using trial and error which relies mainly on experience, and usually requires tedious computations.