Tracking Control of Marine Craft in the port-Hamiltonian Framework: A Virtual Differential Passivity Approach

Abstract

In this work we propose a family of trajectory tracking controllers for marine craft in the port-Hamiltonian (pH) framework using virtual differential passivity based control (v-dPBC). Two pH models of marine craft are considered, one in a body frame and another in an inertial frame. The structure and workless forces of pH models are exploited to design two virtual control systems which are related to the original marine craft's pH models. These virtual systems are rendered differentially passive with an imposed steady-state trajectory, both by means of a control scheme. Finally, the original marine craft pH models in closed-loop with above controllers solve the trajectory tracking problem. The performance of the closedloop system is evaluated on numerical simulations.R. Reyes-Báez, B. Jayawardhana and A.J. van der Schaft are with the Jan C.

Passivity based distributed tracking control of networked Euler-Lagrange systems

“…Remarkably, such virtual system inherits the passivity of the actual one and it has been shown recently that this virtual system has contraction properties in Jouffroy and Fossen (2010). This observation was recently exploited for differential passivity based control design in Reyes- Báez et al (2018b), Reyes Báez et al (2017) and Reyes-Báez et al (2018a). Recently, the passivity approach has been extended to solve the distributed control problem for networked EL systems.…”

“…The term passivity-based control was introduced in Ortega and Spong (1988). Recent results on PBC for a single EL system are the works of Reyes- Báez et al (2018b), Reyes Báez et al (2017), Reyes-Báez et al (2018a) which incorporate recent advances in contraction theory and incremental stability, such as, Jouffroy and Fossen (2010) and Andrieu et al (2016).…”

Optimal Damping Concept Implementation for Marine Vessels’ Tracking Control

“…Various issues associated with the design of tracking controllers for marine surface vessels have already been extensively researched and presented in numerous publications (for example, [1,2,[6][7][8][9][10][11][12][13][14][15][16]). To evaluate the state of the art in marine tracking control, let us address some modern works presenting this direction of research.…”

“…Currently, it is possible to use various ideas to design nonlinear tracking control laws that are reflected in numerous publications, for example, [7,8,[13][14][15][16]. However, let us note that the mentioned works are not directly oriented to the application of the optimization technique.…”

“…At present time, numerous approaches are used for a practical solution of these problems [1][2][3][4][5][6][7][8][9][10][11][12]17,18]. Usually, they are based on Pontryagin's maximum principle, on Bellman's dynamic programming principle, on finite-dimensional approximation in the range of model predictive control (MPC) technique, etc.…”