Graduation Year

2019

Document Type

Thesis

Degree

M.S.M.E.

Degree Name

MS in Mechanical Engineering (M.S.M.E.)

Degree Granting Department

Mechanical Engineering

Major Professor

Tansel Yucelen, Ph.D.

Committee Member

Kyle Reed, Ph.D.

Committee Member

Yasin Yilmaz, Ph.D.

Keywords

Adaptive control, Control under limited resources, Control with local information exchange, Stability analysis

Abstract

The objective of this thesis is (1) to show the experimental validation of recently proposed distributed adaptive control architecture for a class of heterogeneous uncertain multiagent systems as well as (2) to theoretically propose a proportional integral controller for multiagent systems having limited resources in the presence of a disturbance with stability analyses.

With regard to (1), the distributed adaptive control architecture used in the experiment utilizes a control input having a nominal part and an adaptive augmentation part for each agent to suppress the effect of uncertainties and disturbances effectively. This architecture is capable to provide uniform ultimate boundedness for the output tracking error between each heterogeneous uncertain agent and the leader with unknown dynamics. In addition, if the output of the leader converges to a constant, then the output of each agent asymptotically converges to the output of the leader by this architecture, where the system is subject to matched disturbances and time-invariant system uncertainties over fixed (i.e., time-invariant) and directed graph topology. The experimental setup for validating this architecture is a multiagent mechanical platform composed of two-cart inverted pendulums and a cart. In order to achieve heterogeneity, two carts are attached with different length of pendulums and a cart is used without pendulum. Our mechanical platform involves uncertainties due to friction between pinions of carts and the track. It is observed during the experimental process that the output of agents follow the output of the leader with huge amplitude of oscillations comparing to the control input with adaptive augmentation. This adaptive augmentation minimizes the effect of uncertainties and make the output of agents follow the output of the leader with considerably lower amplitude of oscillations. Several experimental plots are also given to show the efficacy of the proposed distributed adaptive control architecture.

We now summarize (2). In contrast to the control architecture used, for example (1), in some real-life scenarios it is not cost-effective to implement a controller into each agent. To address this problem, a proportional integral controller is proposed to implement only one control input into the multiagent system, which is composed of agents executing the distributed information based on the graph topology in the presence of a disturbance (i.e., cyber-attack or malfunction) through only an agent (i.e., driver agent) to robustify the overall closed-loop multiagent system. To this end, the trajectories of all agents in the multiagent system with a fixed, connected and undirected graph, where the system subject to a bounded disturbance through an agent (i.e., misbehaving agent), remain bounded with only one control input having a bounded command irrespective of which agent we apply the control input. After that, we introduce two methods to derive the steady-state value of each agent in the multiagent system whose graph topology for the first method is fixed, connected and undirected and for the second method is a fixed, connected, and undirected acyclic graph.

While the second method is applicable to only the acyclic graph, it does not require an inverse of a matrix dependent on the graph topology. The second approach also shows that the largest steady-state deviation from the desired command in the multiagent system is minimized if the driver agent is located as close as possible to the misbehaving agent. Several numerical examples are also presented to illustrate the implementation of the theoretical results.

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