Distributed LQR control of multi-agent systems

Tomic, Ivana (2016). Distributed LQR control of multi-agent systems. (Unpublished Doctoral thesis, City, University of London)

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The thesis develops optimal control methods for designing distributed cooperative control schemes in multi-agent networks. First, the model of a completely connected multi-agent network is presented, consisting of identical dynamically decoupled agents controlled by a centralized LQR (Linear Quadratic Regulator) based controller. The structure of the solution, as well as controller's spectral and robustness properties are presented. A special case of centralized control where the optimal solution for the whole network can be constructed from the solution of single agent LQR system is given. The problem is extended to distributed control where the special structure is imposed onto the information flow between agents and only local interaction is considered.

A systematic method is given for computing the performance loss of various distributed control configurations relative to the performance of the optimal centralized controller. Necessary and sufficient conditions are derived for which a distributed control configuration pattern arising from the optimal centralized solution does not entail loss of performance if the initial state vector lies is a certain subspace of state-space which is identified. It is shown that these conditions are always satisfied for systems with communication/control networks corresponding to complete graphs with a single link removed. The procedure is extended for the purposes of analysing the performance loss of an arbitrary distributed configuration. Cost increase due to decentralisation is quantified by introducing three cost measures corresponding to the worst-case, best-case and average directions in which the initial state of the system lies.

Finally, a cooperative scheme is presented for controlling arbitrary formations of low speed experimental UAVs (Unmanned Aerial Vehicles) based on a distributed LQR design methodology. Each UAV acts as an independent agent in the formation and its dynamics are described by a 6-DOF (six degrees-offreedom) nonlinear model. This is linearised for control design purposes around an operating point corresponding to straight flight conditions and simulated for longitudinal motion. It is shown that the proposed controller stabilises the overall formation and can control effectively the nonlinear multi-agent system. Also, it is illustrated via numerous simulations that the system provides reference tracking and that is robust to environmental disturbances such as nonuniform wind gusts acting on a formation of UAVs and to the loss of communication between two neighbouring UAVs.

Item Type: Thesis (Doctoral)
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/15883

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