30th Congress of the International Council of the Aeronautical Sciences

05.1 - Flight Dynamics and Control (Control & Modelling)

ON STABILITY MARGIN OF A LQR-BASED VEHICLE NETWORK

Y. Kim¹, G. Seo¹; ¹Gyeongsang National University, South Korea

A classical controller can be designed for a single vehicle to guarantee a certain stability margin. For instance, a LQR (linear quadratic regulator) control-based vehicle has a guaranteed stability margin of 6 dB (gain margin) and 60 degrees (phase margin); the LQR control u is given as u = Fx, where F is a LQR gain and x is the state vector. But then, what will happen to the guaranteed stability margin if multiple LQR control-based vehicles are connected according to a certain network topology for some purpose such as formation flight? For the purpose of formation flight, the same LQR control gain as for a single aircraft can be used but multiplied with the relative state vector being calculated based on each aircraft’s neighbours; the LQR control u this time is given as u = FL(x-h), where F is the same LQR gain as before, L is an expanded version of the Laplacian matrix Lg corresponding to the network topology, and h is a desired state vector. In this case, it can be shown that (1) the gain margin of the networked system is at least 6 dB if the second smallest eigenvalue of Lg is greater than or equal to 1; and (2) the phase margin of the networked system stays the same if the network topology is undirected (or, directed and symmetric) and connected. In addition, a generalized Laplacian matrix (instead of L) can be designed for a (not necessarily symmetric) directed network, in a way to maximize the phase margin of the networked system via a LMI (linear matrix inequality) technique.


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