This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also includes two possible steering mechanisms: a conventional rudder and a simple moving mass system. Starting from this model, we then design, for both steering mechanisms, a nonlinear heading controller using the integrator backstepping method, which exponentially stabilizes the heading/yaw dynamics. By computing the equilibrium points of the system, the course is related to the heading angle, and course control is also achieved. A few simulation results are presented to illustrate the behavior of our control designs.

This paper presents a simulation model environment for the popular and low-cost remotely operated vehicle (ROV) BlueROV2 implemented in Simulink™ which has been designed and experimentally validated for benchmark control algorithms for underwater vehicles. The BlueROV2 model is based on Fossen’s equations and includes a kinematic model of the vehicle, the hydrodynamics of vehicle and water interaction, a dynamic model of the thrusters, and, lastly, the gravitational/buoyant forces. The hydrodynamic parameters and thruster model have been validated in a test facility. The benchmark model also includes the ocean current, modeled as constant velocity. The tether connecting the ROV to the top-site facility has been modeled using the lumped mass method and is implemented as a force input to the ROV model. At last, to show the usefulness of the benchmark model, a case study is presented where a BlueROV2 is deployed to inspect an offshore monopile structure. The case study uses a sliding mode controller designed for the BlueROV2. The controller fulfills the design criteria defined for the case study by following the provided trajectory with a low error. It is concluded that the simulator establishes a benchmark for future control schemes for position control and trajectory tracking under the influence of environmental disturbances.

This paper introduces a methodology for differential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the observer in the case of observer convergence analysis, the plant and the controller in the case of tracking controller analysis), the definition of an abstract system common to the two systems and denoted as the 'virtual system', and the convergence study of the virtual system using its virtual dynamics representation. The approach is illustrated on several simple examples

Because contraction analysis stems from a differential and incremental framework, the nature and methodology of contraction-based proofs are significantly different from those of their Lyapunov-based counterparts. This paper specifically studies this issue, and illustrates it by revisiting some classical examples traditionally addressed using Lyapunov theory. Even in these cases, contraction tools can often yield significantly simplified analysis. The examples include adaptive control, robotics, and a proof of convergence of the deterministic extended Kalman filter.

This paper discusses the use of techniques related to the modulating function method for performing joint parameter and state estimation. After a short review of other methods related to modulating functions, we look at observability issues and the so-called Least-Squares observers to extend currently existing results on joint parameter and state estimation using modulating functions. An example is given as illustration.

Contraction analysis is a recent tool for analyzing the convergence behavior of nonlinear systems in state-space form (see Lohmiller and Slotine [16] for the main reference). However, it seems that earlier results derived by mathematicians in the 1950s closely match some of the results of contraction analysis. In this paper, we review and place into perspective some references of this era, and relate them with contraction.