Centralized Versus Decentralized Team Games of Distributed Stochastic Differential Decision Systems with Noiseless Information Structures-Part II: Applications

In this second part of our two-part paper, we invoke the stochastic maximum principle, conditional Hamiltonian and the coupled backward-forward stochastic differential equations of the first part [1] to derive team optimal decentralized strategies for distributed stochastic differential systems with noiseless information structures. We present examples of such team games of nonlinear as well as linear quadratic forms. In some cases we obtain closed form expressions of the optimal decentralized strategies. Through the examples, we illustrate the effect of information signaling among the decision makers in reducing the computational complexity of optimal decentralized decision strategies.Comment: 39 pages Submitted to IEEE Transaction on Automatic Contro

Optimal Distributed Controller Design with Communication Delays: Application to Vehicle Formations

This paper develops a controller synthesis algorithm for distributed LQG control problems under output feedback. We consider a system consisting of three interconnected linear subsystems with a delayed information sharing structure. While the state-feedback case of this problem has previously been solved, the extension to output-feedback is nontrivial, as the classical separation principle fails. To find the optimal solution, the controller is decomposed into two independent components. One is delayed centralized LQR, and the other is the sum of correction terms based on additional local information. Explicit discrete-time equations are derived whose solutions are the gains of the optimal controller.Comment: Submitted to the 51nd IEEE Conference on Decision and Control, 201

Optimal Control for LQG Systems on Graphs---Part I: Structural Results

In this two-part paper, we identify a broad class of decentralized output-feedback LQG systems for which the optimal control strategies have a simple intuitive estimation structure and can be computed efficiently. Roughly, we consider the class of systems for which the coupling of dynamics among subsystems and the inter-controller communication is characterized by the same directed graph. Furthermore, this graph is assumed to be a multitree, that is, its transitive reduction can have at most one directed path connecting each pair of nodes. In this first part, we derive sufficient statistics that may be used to aggregate each controller's growing available information. Each controller must estimate the states of the subsystems that it affects (its descendants) as well as the subsystems that it observes (its ancestors). The optimal control action for a controller is a linear function of the estimate it computes as well as the estimates computed by all of its ancestors. Moreover, these state estimates may be updated recursively, much like a Kalman filter

Unified Approach to Convex Robust Distributed Control given Arbitrary Information Structures

We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this technical note, we focus on the requirement that the control policy is distributed, in the sense that it can only be based on partial information about the history of the outputs. It is well-known that when a condition denoted as Quadratic Invariance (QI) holds, the optimal distributed control policy can be computed in a tractable way. Our goal is to unify and generalize the class of information structures over which quadratic invariance is equivalent to a test over finitely many binary matrices. The test we propose certifies convexity of the output-feedback distributed control problem in finite-horizon given any arbitrarily defined information structure, including the case of time varying communication networks and forgetting mechanisms. Furthermore, the framework we consider allows for including polytopic constraints on the states and the inputs in a natural way, without affecting convexity