A. Stephen Morse

Stability of switched systems: a Lie-algebraic condition (

We present a sucient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We also discuss the implications of this result for switched nonlinear systems. c 1999 Elsevier Science B.V. All rights reserved.

Control Using Logic-Based Switching

Between the well-studied areas of discontinuous control [1], [2] on the one hand and sampled data control [3] on the other lies the largely unexplored area of logic-based switching control systems. By a logic-based switching controller is meant a controller whose subsystems include not only familiar dynamical components {integrators, summers, gains, etc.} but logic-driven elements as well {e.g., [4]}. More often than not the predominately logical component within such a system is called a supervisor [5], a mode changer [6], a gain scheduler, or something similar. Within the last decade a number of analytical studies of such systems have emerged, mainly in the area of self-adjusting control [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. These studies and others have shown that much can be gained by using logic-based switching together with more familiar techniques in the synthesis of feedback controls. The overall models of systems composed of such logics together with the processes they are intended to control are concrete examples of hybrid dynamical systems [17, 18, 19]. The aim of this paper is to give a brief tutorial review of four different classes of hybrid systems of this type — each consists of a continuous-time process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic.

Switching between stabilizing controllers

This paper deals with the problem of switching between several linear time-invariant (LTI) controllers-all of them capable of stabilizing a specific LTI process-in such a way that the stability of the closed-loop system is guaranteed for any switching sequence. We show that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system remains stable, no matter how we switch among the controller. The motivation for this problem is the control of complex systems where conflicting requirements make a single LTI controller unsuitable.

Towards mobility as a network control primitive

In the near future, the advent of large-scale networks of mobile agents autonomously performing long-term sensing and communication tasks will be upon us. However, using controlled node mobility to improve communication performance is a capability that the mobile networking community has not yet investigated. In this paper, we study mobility as a network control primitive. More specifically, we present the first mobility control scheme for improving communication performance in such networks. Our scheme is completely distributed, requiring each node to possess only local information. Our scheme is self-adaptive, being able to transparently encompass several modes of operation, each respectively improving power efficiency for one unicast flow, multiple unicast flows, and many-to-one concast flows. We provide extensive evaluations on the feasibility of mobility control, showing that controlled mobility can improve network performance in many scenarios. This work constitutes a novel application of distributed control to networking in which underlying network communication serves as input to local control rules that guide the system toward a global objective.

Overcoming the limitations of adaptive control by means of logic-based switching

In this paper we describe a framework for deterministic adaptive control which involves logic-based switching among a family of candidate controllers. We compare it with more conventional adaptive control techniques that rely on continuous tuning, emphasizing how switching and logic can be used to overcome some of the limitations of traditional adaptive control. The issues are discussed in a tutorial, non-technical manner and illustrated with specific examples.

Brief Hysteresis-based switching algorithms for supervisory control of uncertain systems

We address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers. We present a new hysteresis-based switching logic, designed specifically for this purpose, and derive a bound on the number of switches produced by this logic on an arbitrary time interval. The resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

Localization in sparse networks using sweeps

Determining node positions is essential for many next-generation network functionalities. Previous localization algorithms lack correctness guarantees or require network density higher than required for unique localizability. In this paper, we describe a class of algorithms for fine-grained localization called Sweeps. Sweeps correctly finitely localizes all nodes in bilateration networks. Sweeps also handles angle measurements and noisy measurements. We demonstrate the practicality of our algorithm through extensive simulations on a large number of networks, upon which it consistently localizes one-thousand-node networks of average degree less than five in less than two minutes on a consumer PC.

Fundamental limits to force detection using quartz tuning forks

This paper explores the fundamental limits of the use of quartz tuning forks as force detectors in scanned probe microscopy. It is demonstrated that at room temperature, pressure, and atmosphere these force sensors have a noise floor of 0.62 pN/Hz and exhibit a root mean square Brownian motion of only 0.32 pm. When operated as a shear force sensor both dissipative and reactive forces are detected on approach to the sample. These forces are sufficient to reduce the amplitude of motion of the probe nearly to zero without physically contacting the surface. It is also demonstrated that conventional proportional-integral feedback control yields closed loop responses at least 40 times faster than their open loop response.

A FRAMEWORK FOR MAINTAINING FORMATIONS BASED ON RIGIDITY

In this paper, a framework for maintaining formations of large number of mobile autonomous vehicles based on rigidity is proposed. The aim of this paper is to explore strategies for maintaining formations with more limited communi- cation/sensing requirements. An inductive construction method for provably rigid formations is proposed, and a method for optimum angle measures between vehicles is developed. The method scales with the number of vehicles and is ∞exible to support many rigid formation shapes. Copyright c ∞2002 IFAC

Control of a three-coleader formation in the plane

This paper considers a formation of three point agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour; further, each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour, and the current and desired distance from its neighbour. The motion of the formation is studied when distances are initially incorrect. A convergence result is established, to the effect that provided agents never become collinear, the correct distances will be approached exponentially fast, and the formation as a whole will rotate by a finite angle and translate by a finite distance.