Convergence and synthesis issues in extremum seeking control

Convergence and synthesis issues in an extremum seeking control scheme are addressed. The goal of an extremum seeking controller is to operate at a setpoint that represents the optimal value of a function being optimized in the feedback loop. The results presented here are based solely on assumptions on the curvature of the function being optimized in the loop. We present a class of generalized PI compensators and a set of strictly proper and stable compensators. Copyright © 2003 John Wiley & Sons, Ltd.     

Vision-based obstacle detection for rotorcraft flight

The ability of rotorcraft to fly at low altitude is hindered by the high pilot workload required to avoid obstacles. The development of automation tools that can detect obstacles in the rotorcraft flight path, warn the crew, and interact with the guidance system to avoid detected obstacles would significantly reduce pilot workload and increase safety. This article describes an obstacle detection approach based on feature tracking and recursive range estimation that takes into account the characteristics of rotorcraft flight. The merits and weaknesses of the approach are discussed using image sequences from the laboratory and from flight. © 1992 John Wiley & Sons, Inc.     

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the partial differential equation (PDE) associated to the kinetic energy which is nonlinear and inhomogeneous and the solution, that defines the desired inertia matrix, must be positive-definite. In this note, we prove that we can eliminate or simplify the forcing term in this PDE by modifying the target dynamics and introducing a change of coordinates in the original system. Furthermore, it is shown that, in the particular case of transformation to the Lagrangian coordinates, the possibility of simplifying the PDEs is determined by the interaction between the Coriolis and centrifugal forces and the actuation structure. The examples of pendulum on a cart and Furuta's pendulum are used to illustrate the results.