A Model-Based Decoupling Method for Surge Speed and Heading Control in Vessel Path Following

In this paper, to solve the surge speed loss problem generated by sway-yaw motion in the path-following control, a model-based decoupling (MBD) method for surge speed and heading control in vessel path following is proposed. The guidance law is designed independently in the kinematic level. In the kinetic level, the surge model and sway-yaw model can be decoupled by assuming that the surge speed varies slowly, and the heading controller and surge speed controller are designed under the framework of the MBD method. Commonly, the surge speed controller is ignored in the path following or designed separately. In the MBD method, the heading controller is designed first through the MPC method, and the coupling terms between the surge model and sway-yaw model are treated as time-varying disturbances, which can be predicted through the outcomes of the heading controller. Then, the time-varying disturbances are compensating in the surge speed controller so that the surge speed can be feedforward compensated to achieve better performance. The simulation results compared the surge speed performance in path following of the MBD method and usual approaches to illustrate the effectiveness of the MBD method.

φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations

This paper is devoted to [Formula: see text]-entropies applied to Fokker–Planck and kinetic Fokker–Planck equations in the whole space, with confinement. The so-called [Formula: see text]-entropies are Lyapunov functionals which typically interpolate between Gibbs entropies and [Formula: see text] estimates. We review some of their properties in the case of diffusion equations of Fokker–Planck type, give new and simplified proofs, and then adapt these methods to a kinetic Fokker–Planck equation acting on a phase space with positions and velocities. At kinetic level, since the diffusion only acts on the velocity variable, the transport operator plays an essential role in the relaxation process. Here we adopt the [Formula: see text] point of view and establish a sharp decay rate. Rather than giving general but quantitatively vague estimates, our goal here is to consider simple cases, benchmark available methods and obtain sharp estimates on a key example. Some [Formula: see text]-entropies give rise to improved entropy–entropy production inequalities and, as a consequence, to faster decay rates for entropy estimates of solutions to non-degenerate diffusion equations. We prove that faster entropy decay also holds at kinetic level away from equilibrium and that optimal decay rates are achieved only in asymptotic regimes.

Theory of Time-Resolved Somatic Complementation and Its Use to Explore the Sporulation Control Network in Physarum polycephalum

Mutants of Physarum polycephalum can be complemented by fusion of plasmodial cells followed by cytoplasmic mixing. Complementation between strains carrying different mutational defects in the sporulation control network may depend on the signaling state of the network components. We have previously suggested that time-resolved somatic complementation (TRSC) analysis with such mutants may be used to probe network architecture and dynamics. By computer simulation it is now shown how and under which conditions the regulatory hierarchy of genes can be determined experimentally. A kinetic model of the sporulation control network is developed, which is then used to demonstrate how the mechanisms of TRSC can be understood and simulated at the kinetic level. On the basis of theoretical considerations, experimental parameters that determine whether functional complementation of two mutations will occur are identified. It is also shown how gene dosage-effect relationships can be employed for network analysis. The theoretical framework provided may be used to systematically analyze network structure and dynamics through time-resolved somatic complementation studies. The conclusions drawn are of general relevance in that they do not depend on the validity of the model from which they were derived.