Title: Convex Structured Controller Design
Abstract: We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations (H2,Hinf,LQR) and previous works have focused on characterizing classes of structural constraints that allow efﬁcient solution through convex optimization or dynamic programming techniques. In this work, we propose a new control objective and show that this formulation makes the problem of computing optimal linear feedback matrices convex under arbitrary convex constraints on the feedback matrix. This allows us to solve problems in decentralized control (sparsity in the feedback matrices), control with delays and variable impedance control. Although the control objective is nonstandard, we present theoretical and empirical evidence that it agrees well with standard notions of control. We also develop an extension of this approach to nonlinear control afﬁne systems. We present numerical experiments validating our approach.
Bio: Krishnamurthy Dvijotham (Dj) is a PhD candidate in the Department of Computer Science and Engineering at the University of Washington, Seattle. His research interests lie in computational aspects of optimal control and applications to movement control and power systems.