Abstract

Cooperative control has attracted a noticeable interest in control systems
community due to its numerous applications in areas such as formation flying
of unmanned aerial vehicles, cooperative attitude control of spacecraft, rendezvous
of mobile robots, unmanned underwater vehicles, traffic control, data
network congestion control and routing. Generally, in any cooperative control
of multi-agent systems one can find a set of locally sensed information, a
communication network with limited bandwidth, a decision making algorithm,
and a distributed computational capability. The ultimate goal of cooperative
systems is to achieve consensus or synchronization throughout the team members
while meeting all communication and computational constraints. The
consensus problem involves convergence of outputs or states of all agents to
a common value and it is more challenging when the agents are subjected to
disturbances, measurement noise, model uncertainties or they are faulty.
This dissertation deals with the above mentioned challenges and has developed
methods to design distributed cooperative control and fault recovery
strategies in multi-agent systems. Towards this end, we first proposed a
transformation for Linear Time Invariant (LTI) multi-agent systems that facilitates
a systematic control design procedure and make it possible to use
powerful Lyapunov stability analysis tool to guarantee its consensus achievement.
Moreover, Lyapunov stability analysis techniques for switched systems
are investigated and a novel method is introduced which is well suited for designing
consensus algorithms for switching topology multi-agent systems. This
method also makes it possible to deal with disturbances with limited root mean
square (RMS) intensities. In order to decrease controller design complexity, a
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method is presented which uses algebraic connectivity of the communication
network to decouple augmented dynamics of the team into lower dimensional
parts, which allows one to design the consensus algorithm based on the solution
to an algebraic Riccati equation with the same order as that of agent.
Although our proposed decoupling method is a powerful approach to reduce
the complexity of the controller design, it is possible to apply classical pole
placement methods to the transformed dynamics of the team to develop and
obtain controller gains.
The effects of actuator faults in consensus achievement of multi-agent systems
is investigated. We proposed a framework to quantitatively study actuator
loss-of-effectiveness effects in multi-agent systems. A fault index is defined
based on information on fault severities of agents and communication network
topology, and sufficient conditions for consensus achievement of the team are
derived. It is shown that the stability of the cooperative controller is linked to
the fault index. An optimization problem is formulated to minimize the team
fault index that leads to improvements in the performance of the team. A numerical
optimization algorithm is used to obtain the solutions to the optimal
problem and based on the solutions a fault recovery strategy is proposed for
both actuator saturation and loss-of-effectiveness fault types.
Finally, to make our proposed methodology more suitable for real life scenarios,
the consensus achievement of a multi-agent team in presence of measurement
noise and model uncertainties is investigated. Towards this end, first
a team of LTI agents with measurement noise is considered and an observer
based consensus algorithm is proposed and shown that the team can achieve
H∞ output consensus in presence of both bounded RMS disturbance input and
measurement noise. In the next step a multi-agent team with both linear and
Lipschitz nonlinearity uncertainties is studied and a cooperative control algorithm
is developed. An observer based approach is also developed to tackle
consensus achievement problem in presence of both measurement noise and
model uncertainties.