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We consider the problem of controlling a set of dynamically decoupled plants where the plants' subcontrollers communicate with each other according to a fixed and known network topology. We assume the communication to be instantaneous but there is a fixed processing delay associated with incoming transmissions. We provide explicit closed-form expressions for the optimal decentralized controller under these communication constraints and using standard LQG assumptions for the plants and cost function. Although this problem is convex, it is challenging due to the irrationality of continuous-time delays and the decentralized information-sharing pattern. We show that the optimal subcontrollers each have an observer-regulator architecture containing LTI and FIR blocks and we characterize the signals that subcontrollers should transmit to each other across the network.
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We consider a dynamically decoupled network of agents each with a local output-feedback controller. We assume each agent is a node in a directed acyclic graph and the controllers share information along the edges in order to cooperatively optimize a global objective. We develop explicit state-space formulations for the jointly optimal networked controllers that highlight the role of the graph structure. Specifically, we provide generically minimal agent-level implementations of the local controllers along with intuitive interpretations of their states and the information that should be transmitted between controllers.more » « less
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Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition, but expressed in terms of relations defined on a general semi-inner product space. This increased generality leads to a clean result that can be specialized in a variety of ways. First, we show how to recover both sufficient and necessary-and-sufficient versions of the afore-mentioned classical results. Second, we show that suitably choosing the semi-inner product space leads to a new necessary and sufficient condition for weighted stability, which is in turn sufficient for exponential stability.more » « less
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We consider a linear time-invariant system in discrete time where the state and input signals satisfy a set of integral quadratic constraints (IQCs). Analogous to the autonomous linear systems case, we define a new notion of spectral radius that exactly characterizes stability of this system. In particular, (i) when the spectral radius is less than one, we show that the system is asymptotically stable for all trajectories that satisfy the IQCs, and (ii) when the spectral radius is equal to one, we construct an unstable trajectory that satisfies the IQCs. Furthermore, we connect our new definition of the spectral radius to the existing literature on IQCs.more » « less
