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UBC Theses and Dissertations

Stability of switched systems with switching delay : application to remote operation of aircraft under distributed control Matni, Nikolai


Unmanned aerial vehicles are becoming more and more useful tools for not only the military, but law enforcement, search and rescue and scientific data collection. With the advent of inexpensive and reliable wireless communication, remote operators are now able to control fleets of UAVs cooperating towards the accomplishment of their tasks. As the complexity and size of these fleets increase, distributed control methods are needed -- large fleet sizes will lead to intractable centralized problems. Furthermore, UAVs, like most aircraft, are inherently hybrid systems, combining both discrete and continuous dynamics. This thesis attempts to combine hybrid and distributed control theories in a way useful for the operation of UAVs, while taking communication delays inherent to a remote operator into account. Specifically, we consider the stability of block upper-triangular switched linear systems with switching delay, when switching between stable modes. We show that the problem of proving globally uniformly asymptotic stability (GUAS) of a block upper-triangular switched linear system can be reduced to proving GUAS for each of its block diagonal subsystems. This allows for a scalable LMI-based computational test for GUAS under arbitrary switching whose complexity depends linearly on the number of block diagonal elements of the system. In cases for which the system is not GUAS under arbitrary switching, we partition the state space into regions in which switching will preserve GUAS despite a delay between the state measurements and switching time. This is accomplished by adding a delay buffer to standard Piecewise Lyapunov based partitions. Additionally, we show that the effect of the delay buffer on the standard Piecewise Lyapunov based partitions asymptotically approaches zero. Although we tailor these results to block upper-triangular switched linear systems, they are applicable to any switched linear system with switching delay. These results are then extended to nonlinear switched systems. We apply our results to the control of a formation of vehicles under supervisory discrete control, and to switched systems under remote control. We then finish by addressing the issue of interface design for continuous systems under shared control, motivated by applications to pilot-automation interactions.

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