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.

The paper “Structural results and explicit solution for two-player LQG systems on a finite time horizon” by me and Ashutosh Nayyar was submitted to CDC’13 in Florence, Italy! This paper explores the two-player problem (see ALLER’11 and ACC’12 papers) but this time in discrete-time with a finite time horizon. The paper develops sufficient statistics and provides an efficient recursive implementation of the optimal controller. The optimal controller can be computed with complexity proportional to the length of the time horizon, as in the centralized case. Our paper is also available on arXiv.

The paper “On Structured Realizability and Stabilizability of Linear Systems” by me, Maxim Kristalny, and Anders Rantzer was accepted for publication at ACC’13 in Washington DC! This paper reveals the relationship between structured realizability and structured stabilizability for linear systems defined over graphs.

I attended the 51st IEEE Conference on Decision and Control at the Grand Wailea hotel in Maui, Hawaii. The venue was beautiful, and provided a welcome escape from the cold and rain we’ve been getting in the bay area. At the conference, I presented a paper entitled “Decentralized LQG Control of Systems with a Broadcast Architecture”. The paper shows how to extend the method from my ACC’12 paper on the two-player problem to more general star-shaped graph topologies. Slides can be downloaded here.  

I have moved back to California! On November 1st, I started as a new postdoc in Mechanical Engineering at UC Berkeley, co-supervised by Andrew Packard and Kameshwar Poolla. I had a wonderful time in Lund, and am very thankful for the opportunity to have met and collaborated with so many great people. At Berkeley, I plan to work on robust analysis and safety validation tools for complex systems, as well as power systems applications.

I attended the LCCC Workshop on Information and Control in Networks, hosted by the Department of Automatic Control at Lund. I gave a talk, which was entitled “Optimal Collaborative Control in the Absence of Communication”. The talk presented the work from my recent Allerton paper, along with some newer results. Slides for my talk are available here.

I attended the 50th annual Allerton Conference on Communication, Control, and Computing in Monticello, Illinois. I presented a new paper, “Optimal Control of a Fully Decentralized Quadratic Regulator”, which shows the optimal way for two dynamic agents to collaborate in the absence of any explicit or implicit communication. It’s not as simple as it sounds!

The paper “On Structured Realizability and Stabilizability of Linear Systems” by me, Maxim Kristalny, and Anders Rantzer was submitted to ACC’13 in Washington DC! This paper reveals the relationship between structured realizability and structured stabilizability for linear systems defined over graphs.

The paper “Optimal State-Feedback Control Under Sparsity and Delay Constraints” by Andrew Lamperski and me was presented at NecSys’12 in Santa Barbara! The paper solves a general decentralized control problem under both sparsity and delay constraints using a dynamic programming approach. Our poster is available here.

My paper “Decentralized LQG Control of Systems with a Broadcast Architecture” was accepted for publication at CDC’12 in Maui! This paper generalizes the method of our recent ACC’12 paper to systems with a broadcast architecture.