Sanjay Lall

Output-Feedback Decentralized Control

March 14, 2013

• The paper Optimal Control of Two-Player Systems with Output Feedback by Laurent Lessard and me addresses a long-standing problem in optimal control theory. For the class of two-player systems considered, it has long been known that the optimal control policy is linear, but little more was known. In this paper we give a state-space realization for the optimal controller, which hence shows its explicit separation structure and order.

State-Space Decentralized Control

November 10, 2009

• The paper An Explicit State-Space Solution for a Decentralized Two-Player Optimal Linear-Quadratic Regulator addresses the decentralized linear-quadratic control problem. Here we show that the optimal policy is not as might be expected; each player has to do more than simply estimate the states that they cannot observe. In other words, the simplest separation principle does not hold for decentralized control.

Presidential Award

December 19, 2008

• It is a great honor to receive the Presidential Early Career Awards for Scientists and Engineers (PECASE). I was nominated by the National Science Foundation, and the award was presented at the White House on December 19, 2008. Press releases describing the award were issued by the White House and the National Science Foundation. There is also a Stanford News article.

Adaptive Optics

May 14, 2008

• The image on the right shows a single star observed using adaptive optics, and that on the left shows the same star observed without it. The experiment is presented in the paper Experimental Validation of Single-Iteration Multigrid Wavefront Reconstruction at the Palomar Observatory. The paper Warm-started Wavefront Reconstruction for Adaptive Optics analyzes the achievable error for warm-started multigrid algorithms in large adaptive-optics systems for telescopes. We address the underlying linear estimation problem, which must be solved at very high rates.

George S. Axelby Award

December 15, 2007

• The paper A Characterization of Convex Problems in Decentralized Control was awarded the George S. Axelby Outstanding Paper Award by the IEEE Control Systems Society. The award is given annually to recognize outstanding papers published in the IEEE Transactions on Automatic Control during the preceding two years. The paper gives conditions under which one can use convex optimization to synthesize minimum-norm decentralized controllers.

Networked Markov Decision Processes

September 17, 2007

• The paper Optimal Control of Distributed Markov Decision Processes with Network Delays shows that for certain networked problems there are easily computable finite memory optimal controllers.

Systems with Delays

July 1, 2007

• The paper Positive Forms and Stability of Linear Time-Delay Systems gives a simple way to construct polynomial Lyapunov functions for systems with delays.

Event-Based Sampling

October 5, 2006

• The paper A Constant Factor Approximation Algorithm for Event-Based Sampling gives a simple bound on the performance of an event-based sampling method. The idea here is that when communication is constrained to be infrequent, event-based sampling can achieve better estimator performance than periodic sampling.

Workshop Photos

October 5, 2006

• Some photos from the workshop SDP Relaxations and Algebraic Optimization in Control which Pablo Parrilo and I presented at MTNS in July 2006.

Symmetries

October 5, 2006

• Here is the latest version of the paper On Structured Semidefinite Programs for the Control of Symmetric Systems. It shows how symmetries in linear systems may be exploited when using convex programming for controller synthesis.

Control Performance Bounds without Solving the Hamilton-Jacobi Equation

March 20, 2006

• The latest paper, Suboptimality Bounds in Stochastic Control: A Queueing Example gives a simple way to compute upper and lower bounds on the performance of stochastic control systems. A particularly interesting aspect of this work is that any function may be used as an approximate Hamilton-Jacobi solution; better choices give better bounds.