Instability and Overshoots of Solutions For A Class of Homogeneous Hybrid Systems By Lyapunov-like Analysis

For a class of homogeneous hybrid systems we present a generalization to the hybrid systems framework of Chetaev's theorem and we propose a set of Lyapunov-like conditions for studying instability of the point x e = 0 and overshoots of solutions (namely when the norm of the solution vector x at some time instant exceeds the norm of the initial condition of x). Based on these results, we design a sum of squares algorithm that constructs a suitable Lyapunov-like function to fulfill such conditions.Peer reviewe

Stability For A Class of Homogeneous Hybrid Systems By Annular Lyapunov Analysis

For a class of homogeneous hybrid systems we present a set of annular Lyapunov-like conditions for inferring global pre-asymptotic stability of systems. Then, we prove that such conditions are mild, namely, that each globally pre-asymptotically stable system must satisfy them. Based on these results, we design a sum of squares algorithm that constructs a suitable Lyapunov-like function to fulfill such annular conditions. Finally, based on recent results on homogeneous approximations of hybrid systems, we point out that such conditions can also be used to deduce local pre-asymptotic stability for a wider class of hybrid systems.Peer reviewe

Lettuce modelling for growth control in precision agriculture

Improving the efficiency of agriculture is a growing priority due to food security issues, environmental concerns, and economics. Precision agriculture and variable rate application technology could enable increases in yield while maintaining or reducing fertiliser use. However, this requires the development of control algorithms which are suitable for the challenges of agriculture. In this paper, we propose a new mechanistic open model of lettuce growth for use in control of precision agriculture. We demonstrate that our model is cooperative and fits well to experimental data. We use the model to show, via simulations, that a simple proportional distributed control law increases crop uniformity and yield without increasing nitrogen use, even in the presence of sparse actuation and noisy observations.Comment: 8 pages, Submitted to ECC2

Follow the bouncing ball: global results on tracking and state estimation with impacts

peer reviewedIn this paper we formulate tracking and state- estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations