Abstract
AbstractThe problem of stabilizing networked dynamical systems (NDS) in a scalable fashion is addressed. As a first contribution, an example is provided to demonstrate that the standard NDS stabilization methods can fail even for simple linear time-invariant systems. Then, a solution to this issue is proposed, in which the controller synthesis is decentralized via a set of parameterized local functions. The corresponding stability conditions allow for max-type construction of a Lyapunov function (LF) for the full closed-loop system, while neither of the local functions is required to be a local LF. It is shown that the provided approach is non-conservative in the sense that it is able to find a stabilizing control law for the motivating example network, whereas state-of-the-art non-centralized Lyapunov techniques fail. For input-affine NDS and quadratic parameterized local functions, the combined LF synthesis and control scheme can be formulated as a set of low-complexity semi-definite programs that are solved on-line, in a receding horizon manner.
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