I attended the 52nd IEEE Conference on Decision and Control in Florence, Italy. On the right is a photo of the Duomo as viewed from the top of the neighboring Campanile bell tower. At the conference, I presented a paper entitled “Structural results and explicit solution for two-player LQG systems on a finite time horizon”. The paper, co-authored with Ashutosh Nayyar, solves a two-player decentralized control problem on a finite horizon by first determining the optimal structure and then computing the associated gains. Key features of this work are that: the structural result has a particularly simple derivation, and the gains can be computed as efficiently as if the problem had been centralized. We are currently working on generalizing these results so that they could apply to problems with more than two players. Slides are available here.

I attended the 51st annual Allerton Conference on Communication, Control, and Computing in Monticello, IL. On the right is a photo of fellow Berkeley students and postdocs in front of the Allerton house. At the conference, I presented a paper entitled “A separation principle for decentralized state-feedback optimal control”. The paper describes a new separation principle for a class of fully decentralized LQR problems. The class considered have a curious property that is not present in centralized problems: the optimal controller has a state dimension that increases as the exogenous disturbances become more correlated. Slides are available here.

The paper “Performance certification of interconnected systems using decomposition techniques” by Chris Meissen, me, and Andrew Packard was submitted to ACC’14 in Portland, Oregon! This paper proposes a framework by which one may certify the performance of an interconnected system. The main idea is to certify something about each component in such a way that we can deduce the desired property for the interconnected system. We also show that the Alternating Direction Method of Multipliers (ADMM) is a potentially viable algorithm for solving our optimization formulation. Scalability is a key feature; all difficult computations are done locally and possibly in parallel. The goal is to eventually apply our technique to interconnected systems consisting of a large number of nonlinear components, a task that is computationally intractable when the interconnected system is treated as a single large system.

The paper “An Algebraic Approach to the Control of Decentralized Systems” by me and Sanjay Lall was submitted to the inaugural issue of the Transactions on Control of Network Systems. The paper is a follow-up to our ACC’10 paper and my doctoral thesis. It gives an algebraic treatment of the notion of quadratic invariance, which can be used to analyze decentralized control problems. This new viewpoint is powerful because it allows one to work with rational transfer functions, for example, without needing to define an underlying topology or norm. Indeed, we only rely on the basic operations of addition and multiplication. Our paper is also available on arXiv.

The paper “Structural results and explicit solution for two-player LQG systems on a finite time horizon” by me and Ashutosh Nayyar was accepted for publication at CDC’13! (see previous post here) I am excited to have the opportunity to travel to Florence this December to present our work. Final versions of the paper are available via the link above or on arXiv.

It was a great honor to receive the O. Hugo Schuck Best Paper Award for 2013. The award is given annually by the American Automatic Control Council (AACC) to recognize the best two papers (one for theory and the other for applications) presented at the previous American Control Conference. Our winning paper (in the theory category) was “Optimal Controller Synthesis for the Decentralized Two-Player Problem with Output Feedback” by me and Sanjay Lall, and it was presented at ACC’12 in Montréal. The award itself was presented at this year’s ACC’13 in Washington, D.C. on June 18, 2013. A description of the award may be found on the AACC website.

I attended the 2013 American Control Conference at the Renaissance Hotel in downtown DC. The venue is in the heart of the city, and walking distance from countless museums, art galleries, and historical monuments. At the conference, I presented a paper entitled “On Structured Realizability and Stabilizability of Linear Systems”. The paper shows that structured stabilizability implies structured realizability. This observation is important, because S-realizations are difficult to establish/construct whereas S-stabilizability is easy to verify (a complete characterization is given in the paper). Slides are available here. This ACC was also a special occasion for me because I was awarded the O. Hugo Schuck Best Paper Award together with Sanjay Lall for our contribution to last year’s ACC.

The paper “Optimal Decentralized State-Feedback Control with Sparsity and Delays” by Andrew Lamperski and me was submitted to Automatica. This paper concerns optimal decentralized controller synthesis for systems that satisfy a nested information structured. That is, for any two decision-makers, one must know strictly more than the other at every instant. Two ways in which this can happen are delays (information doesn’t propagate to everyone simultaneously) or sparsity (not all information reaches everybody). These two cases were studied independently by other researchers. In this work, we unify both bodies of work and show how to solve problems containing a mixture of both types of constraints. A preliminary version of this work appeared at the NecSys’12 Workshop. In this much-expanded journal submission, we include a new distributed implementation of the optimal controller, as well as new illustrative examples and in-depth discussions. Our paper is also available on arXiv.

The paper “Convexity of Decentralized Controller Synthesis” by me and Sanjay Lall was submitted to Transactions on Automatic Control. This paper concerns the general problem of optimal structured controller synthesis. Such problems are hard in general, but can sometimes be expressed as convex optimization problems, which makes them much more tractable. This paper shows that under suitable assumptions, the simple algebraic condition of quadratic invariance is necessary and sufficient for the set of achievable closed-loop maps to be convex. This work is a generalization of some results that first appeared in my thesis and applied only to bounded linear operators. The new results also cover extended spaces, which means that they can be applied in cases when the plant or controller is unstable. Our paper is also available on arXiv.

The paper “Optimal control of two-player systems with output feedback” by me and Sanjay Lall was submitted to Transactions on Automatic Control. This paper was a long time in the making, and represents the culmination of several years of work. The paper explores a very fundamental control problem, which we call the two-player problem. Two decision-making agents must cooperatively control a system. Roughly speaking, one agent is more informed, while the other is more influential. In this paper, we give a complete characterization of when stabilization is possible, and parameterize all stabilizing controllers. We also show how to efficiently construct the optimal controller and quantify the cost due to the information constraint (as compared to a scenario where both agents are equally informed and influential). Two major facts come to light in this work. First, the optimal two-player controller has a separation structure that bears resemblance to the observer-controller structure present in classical (centralized) control theory. The difference here is that the associated estimation and controller gains turn out to be coupled in an intricate way. Second, finding these coupled gains can be reduced to solving a set of linear equations, and thus can be done in an efficient manner. Our paper is also available on arXiv.