Abstract-We study the finite-time average-consensus problem for arbitrary connected networks. Viewing this consensus problem as a factorization of 1 n 11T by suitable families of matrices, we prove the existence of a finite factorization and provide tight bounds on the size of the minimal factorization by exhibiting finite-time average-consensus algorithms and bounding their runtimes. We also show that basic matrix theory yields insights into the structure of finite-time consensus algorithms.

Abstract-Two approaches, extended Kalman filter (EKF) and moving horizon estimation (MHE), are discussed for state estimation for nonlinear dynamical systems over packetdropping networks. For EKF, we provide sufficient conditions that guarantee a bounded EKF error covariance. For MHE, a natural scheme on organizing the finite horizon window is proposed to handle intermittent observations. A nonlinear programming software package, SNOPT, is employed in MHE and the formulation for constraints is discussed in detail. Examples and simulation results are presented.

Abstract-We study the problem of link scheduling for discrete-time agents to achieve average consensus in finite time under communication constraints. We provide necessary and sufficient conditions under which finite time consensus is possible. Furthermore, we prove bounds on the consensus time and exhibit provably optimal communication policies. We also discuss the dual problem of designing communication schedules given a fixed consensus-time requirement.

We study the LQG control of scalar systems under communication constraints by naturally extending the LQG cost to include a quadratic penalty for communication. We show that the resulting optimization problem is quasiconvex in the communications parameter so that it can be solved in a computationally efficient manner.