A Characterization of Convex Problems in Decentralized Control$^ast$

By Michael C. Rotkowitz, Sanjay Lall. IEEE Transactions on Automatic Control, 2005

766 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1b5599d29671074256398830bcb5b0f85a323d27

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Citations in the corpus

Distributed LQR Design for Identical Dynamically Decoupled Systems (2008, background): “One of the most notable recent result in characterizing the complexity of optimal distributed controller design subject to constraints on the controller structure was presented in [12].”
A Survey of Distributed Optimization and Control Algorithms for Electric Power Systems (2017, methodology): “This has been carried out in the seminal work [171] by deriving a sufficient condition named quadratic invariance, which has been generalized in [172] by deploying the concept of partially ordered sets.”
Feedback controller parameterizations for Reinforcement Learning (2011, background): “Recently, very interesting results have emerged describing conditions under which the search for an optimal linear decentralized control is convex in the Youla parameter [22], [15].”
Decentralized Stochastic Control with Partial History Sharing: A Common Information Approach (2012, background): “Conditions under which the problem of determining optimal control strategies within the class of affine control strategies becomes a convex optimization problem were identified in [32], [33].”
Convexity of optimal control over networks with delays and arbitrary topology (2010, background): “It has been shown for general decentralised control that a property called quadratic invariance allows the optimal control problem to be recast as a convex optimisation problem (Rotkowitz and Lall, 2006).”
Graph Neural Networks for Decentralized Multi-Robot Path Planning (2019, background): “, problem convexity and invariance of communication graph [15], [16]) that can generally not be guaranteed in real robot systems.”
Decentralized control: An overview (2008, background): “Rotkowitz and Lall (2006) consider the problem of constructing decentralized control minimizing a norm of the closed-loop subject to a subspace constraint by using the concept of quadratic invariance.”
Distributed optimal control of multiple systems (2010, methodology): “(2) The quadratic invariance property in Rotkowitz and Lall (2006) is not required.”
A Framework to Describe, Analyze and Generate Interactive Motor Behaviors (2012, background): “In the case of cooperation or collaboration, when there is perfect knowledge of the state, then the problem can be transformed into an optimal control problem for each player [82],”
Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers (2011, background): “A similar but more general algebraic characterization of the constraint set was introduced and convexity was established under the condition of quadratic invariance in [7].”