SDP-based joint sensor and controller design for information-regularized optimal LQG control

We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that an optimal linear joint sensor-controller policy is comprised of a linear sensor, Kalman filter, and a certainty equivalence controller, and can be synthesized by a numerically efficient algorithm based on semidefinite programming (SDP).

[1]  Robin J. Evans,et al.  Topological feedback entropy and Nonlinear stabilization , 2004, IEEE Transactions on Automatic Control.

[2]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[3]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[4]  Pablo A. Parrilo,et al.  Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs , 2014, IEEE Transactions on Automatic Control.

[5]  João Pedro Hespanha,et al.  A Survey of Recent Results in Networked Control Systems , 2007, Proceedings of the IEEE.

[6]  Panos J. Antsaklis,et al.  Control and Communication Challenges in Networked Real-Time Systems , 2007, Proceedings of the IEEE.

[7]  A. D. Wyner,et al.  The wire-tap channel , 1975, The Bell System Technical Journal.

[8]  C. Sims.  Implications of rational inattention , 2003 .

[9]  James L. Massey,et al.  Conservation of mutual and directed information , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[10]  H. Vincent Poor,et al.  Utility-Privacy Tradeoffs in Databases: An Information-Theoretic Approach , 2011, IEEE Transactions on Information Forensics and Security.

[11]  H. Poor,et al.  Utility-Privacy Tradeoff in Databases : An Information-theoretic Approach , 2013 .

[12]  Muriel Médard,et al.  From the Information Bottleneck to the Privacy Funnel , 2014, 2014 IEEE Information Theory Workshop (ITW 2014).

[13]  John Baillieul,et al.  Data-rate requirements for nonlinear Feedback control , 2004 .

[14]  Tamer Basar,et al.  Simultaneous design of measurement and control strategies for stochastic systems with feedback , 1989, Autom..

[15]  Jan M. Maciejowski,et al.  Stabilizability of SISO control systems under constraints of channel capacities , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[16]  Mark L. Psiaki,et al.  Magnetic Torquer Attitude Control via Asymptotic Periodic Linear Quadratic Regulation , 2000 .

[17]  Charalambos D. Charalambous,et al.  LQG optimality and separation principle for general discrete time partially observed stochastic systems over finite capacity communication channels , 2008, Autom..

[18]  V. Borkar,et al.  LQG Control with Communication Constraints , 1997 .

[19]  Maxim Raginsky,et al.  Rational inattention in scalar LQG control , 2013, 52nd IEEE Conference on Decision and Control.

[20]  Tamás Linder,et al.  Optimization and convergence of observation channels in stochastic control , 2010, Proceedings of the 2011 American Control Conference.

[21]  W. Runggaldier,et al.  Optimization of Observations: a Stochastic Control Approach , 1997 .

[22]  Richard H. Middleton,et al.  Minimum Variance Control Over a Gaussian Communication Channel , 2008, IEEE Transactions on Automatic Control.

[23]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[24]  Tamer Basar,et al.  Stochastic Networked Control Systems , 2013 .

[25]  Anant Sahai,et al.  The Necessity and Sufficiency of Anytime Capacity for Stabilization of a Linear System Over a Noisy Communication Link—Part I: Scalar Systems , 2006, IEEE Transactions on Information Theory.

[26]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[27]  Dimitri P. Bertsekas,et al.  Stochastic optimal control : the discrete time case , 2007 .

[28]  Robin J. Evans,et al.  Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates , 2004, SIAM J. Control. Optim..

[29]  Takashi Tanaka,et al.  Semidefinite representation of sequential rate-distortion function for stationary Gauss-Markov processes , 2015, 2015 IEEE Conference on Control Applications (CCA).

[30]  D. Delchamps.  Stabilizing a linear system with quantized state feedback , 1990 .

[31]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[32]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[33]  George J. Pappas,et al.  Differentially Private Filtering , 2012, IEEE Transactions on Automatic Control.