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This work proposes a control algorithm to stabilize a circular formation of AUVs tracking a time-varying center. We also consider the problem of uniform distribution of all the agents along the circle from two approaches: all-to-all and limited communication. We tackle with this communication constraint using a cooperative control strategy which includes the Laplacian matrix of the communication graph...
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
In this paper we combine an invariant-set approach to fault detection and identification (FDI), recently proposed by the authors, with the virtual actuator approach to controller reconfiguration of Steffen, Lunze and co-authors. The FDI approach is based on the separation of invariant sets that characterise healthy system operation from invariant sets that characterise faulty operation. The derivation...
This paper is concerned with the theory of quasivelocities and its applications to control. The equations of motion of a mechanical system are derived using the Lagrange-d'Alembert principle written in an arbitrary configuration-dependent frame. The structure of the equations of motion written in quasivelocities is utilized in the design of a nonlinear feedback stabilizing controller for an example...
In this work we investigate the stability of bimodal and bistable (both modes are stable) continuous time linear systems in ??3. Under certain conditions, we first show that all the trajectories which start on the plane separating the two modes are bound to hit the plane again in finite time and go into the other mode. This property yields fixed directions on the separating plane. Eventually, all...
Stabilization for a collection of feedback linearizable systems with uncertain parameter is dealt with in this paper. Necessary and sufficient conditions for a quadratic control Lyapunov function to be a common control Lyapunov function for these systems are obtained. A continuous state feedback control is designed based on the common control Lyapunov function. It can simultaneously stabilize these...
In this paper, we develop a method to realize an autonomous periodic motion of a small blimp system in a horizontal plane. The idea behind the method is to make the dynamics of a small blimp system approach asymptotically to that of the van der Pol equation that has a limit cycle. The method consists of the following two steps: First, we introduce two constraints. One has a role to connect the motion...
An adaptive friction compensator is proposed using the generalized Maxwell-slip (GMS) friction model, with a new, linearly-parameterized Stribeck function. It employs a polynomial equation that is linear-in-the-parameter to describe the nonlinear Stribeck effect in the GMS model, and simplifies the design of an adaptive friction compensator. The proposed compensator has a switching structure to accommodate...
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