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Structural Sparsity in Networked Control Systems
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DOI：10.1109/TSMC.2018.2867187.png)
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Abstract
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A great deal of research is being conducted to define control strategies that involve a level of sparsity either in the communication network, number of sensors, or the number of active actuators during the control process. These sparse control strategies are typically formulated as an optimization problem that has a criterion with a component associated with the dynamics of the controlled system, and a component based on the l(1)-norm that induces sparsity on the optimization variables. Although this approach addresses the problem of obtaining sparse approximations, solving this optimization problem can be seen as a design process that is conducted simultaneously along with a variable selection process that does not take into account the inherent structural relationships between the components of the networked system to be controlled, such as spatial relations associated with the physics of the system or communication constraints. In this paper, we incorporate the concept of structural sparsity into the mathematical framework of control design in networked systems. Under this extended framework, it is possible to define control strategies that lead to sparse designs considering a prior knowledge on the structural relations between the variables of the system. This can potentially improve the system's performance, the consistency of the solution with physical constraints, and the interpretability of the design. First, we show how structural sparsity inducing norms can be constructed as a combination of l(1)- and l(2)-norms, encoding structures, such as overlapping groups, nonoverlapping groups, and hierarchies. Also, we show how these norms can induce both individual and group variable selection. Then, we present two different control design techniques, where structural sparsity is induced during the design process: linear feedback control design and dynamic resource allocation. We show through practical applications and simulation results the usefulness of structural sparsity in the control system design process.
Keywords:
Control systems
dynamic resource allocation
linear feedback control
networks
regularization
structural sparsity
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