Partial Stability Concept in Extremum Seeking Problems

The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the concept of partial asymptotic stability and analyzed by Lyapunov's direct method and averaging schemes. Sufficient conditions for the practical partial stability of a system with oscillating inputs are derived with the use of Lie bracket approximation techniques. These conditions are exploited to describe a broad class of extremum-seeking controllers ensuring the partial stability of the set of minima of a cost function. The obtained theoretical results are illustrated by the Brockett integrator and rotating rigid body.Comment: This is the author's version of the manuscript accepted for publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS & NOLCOS 2019

Control of an indoor autonomous mobile communications relay via antenna diversity

Presented in this thesis is a motion planning scheme for enabling a quadrotor unmanned aerial vehicle (UAV) to serve as an autonomous communications relay in indoor or GPS-denied environments. The goal of the algorithm is to maximize the throughput of the end-to-end communications channel. An extremum-seeking controller steers the quadrotor while collision avoidance is provided by artificial potential fields. Extremum-seeking is model-free adaptive control method; it\u27s applicable in situations where there is a nonlinearity in the control problem and the nonlinearity has a local minimum or maximum. The extremum-seeking controller presented here is driven by antenna diversity and attempts to optimize the inputs to an unknown, time-varying cost function characterized by the RF environment. Each of the multiple antennas onboard the quadrotor receives the same incoming packets and provides associated signal strength measurements. The extremum-seeking controller then uses these measurements to autonomously fly the quadrotor communications relay to an optimal location so as to maximize throughput, all without positioning data. This work is motivated by the need to extend the operating ranges of robots in complex urban and indoor environments. The algorithm and necessary technical background are presented in detail. Simulations results verify the validity of the proposed extremum-seeking approach. Experiments demonstrate the feasability of implementing the extremum-seeking controller with tangible hardware