Localized LQR optimal control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained ℋ2 optimal controller, but can be designed and implemented in a localized and distributed way.

[1]  Laurent Lessard,et al.  State-space solution to a minimum-entropy $\mathcal{H}_\infty$-optimal control problem with a nested information constraint , 2014 .

[2]  Laurent Lessard.  State-space solution to a minimum-entropy ℋ1-optimal control problem with a nested information constraint , 2014, 53rd IEEE Conference on Decision and Control.

[3]  Pablo A. Parrilo,et al.  An optimal controller architecture for poset-causal systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[4]  Sanjay Lall,et al.  Optimal controller synthesis for the decentralized two-player problem with output feedback , 2012, 2012 American Control Conference (ACC).

[5]  John C. Doyle,et al.  The H2 Control Problem for Quadratically Invariant Systems with Delays , 2013 .

[6]  Petros G. Voulgaris,et al.  A convex characterization of distributed control problems in spatially invariant systems with communication constraints , 2005, Syst. Control. Lett..

[7]  Fernando Paganini,et al.  Distributed control of spatially invariant systems , 2002, IEEE Trans. Autom. Control..

[8]  John Doyle,et al.  The $H_2$ Control Problem for Decentralized Systems with Delays , 2013, ArXiv.

[9]  Pablo A. Parrilo,et al.  ℋ2-optimal decentralized control over posets: A state space solution for state-feedback , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Carsten W. Scherer,et al.  Structured $H_\infty$-Optimal Control for Nested Interconnections: A State-Space Solution , 2013, 1305.1746.

[11]  Sanjay Lall,et al.  A Characterization of Convex Problems in Decentralized Control$^ast$ , 2005, IEEE Transactions on Automatic Control.

[12]  Nikolai Matni,et al.  Distributed Control Subject to Delays Satisfying an $\mathcal{H}_\infty$ Norm Bound , 2014 .

[13]  Pablo A. Parrilo,et al.  $ {\cal H}_{2}$-Optimal Decentralized Control Over Posets: A State-Space Solution for State-Feedback , 2010, IEEE Transactions on Automatic Control.

[14]  M. Fardad,et al.  Sparsity-promoting optimal control for a class of distributed systems , 2011, Proceedings of the 2011 American Control Conference.

[15]  Pablo A. Parrilo,et al.  Optimal output feedback architecture for triangular LQG problems , 2014, 2014 American Control Conference.

[16]  Nikolai Matni.  Distributed control subject to delays satisfying an ℋ1 norm bound , 2014, 53rd IEEE Conference on Decision and Control.

[17]  John Doyle,et al.  Output feedback ℌ2 model matching for decentralized systems with delays , 2012, 2013 American Control Conference.

[18]  Randy Cogill,et al.  Convexity of optimal control over networks with delays and arbitrary topology , 2010 .

[19]  Carsten W. Scherer,et al.  Structured H∞-optimal control for nested interconnections: A state-space solution , 2013, Syst. Control. Lett..

[20]  Nader Motee,et al.  Sparsity measures for spatially decaying systems , 2014, 2014 American Control Conference.

[21]  Nader Motee,et al.  Approximation methods and spatial interpolation in distributed control systems , 2009, 2009 American Control Conference.

[22]  Fu Lin,et al.  Design of Optimal Sparse Feedback Gains via the Alternating Direction Method of Multipliers , 2011, IEEE Transactions on Automatic Control.

[23]  Nikolai Matni,et al.  Localized distributed state feedback control with communication delays , 2014, 2014 American Control Conference.