In this article, a distributed optimization problem for minimizing a sum, n i=1 f i , of convex objective functions, f i , is addressed. Here each function f i is a function of n variables, private to agent i which defines the agent's objective. Agents can only communicate locally with neighbors defined by a communication network topology. These f i 's are assumed to be Lipschitz-differentiable convex functions. For solving this optimization problem, we develop a novel distributed algorithm, which we term as the gradient-consensus method. The gradient-consensus scheme uses a finite-time terminated consensus protocol called ρ-consensus, which allows each local estimate to be ρ-close to each other at every iteration. The parameter ρ is a fixed constant which can be determined independently of the network size or topology. It is shown that the estimate of the optimal solution at any local agent i converges geometrically to the optimal solution within O(ρ) where ρ can be chosen to be arbitrarily small.

Tailoring the properties of a material at the nanoscale holds the promise of achieving hitherto unparalleled specificity of the desired behavior of the material. Key to realizing this potential of tailoring materials at the nanoscale are methods for rapidly estimating physical properties of the material at the nanoscale. In this paper, we report a method for simultaneously determining the topography, stiffness and dissipative properties of materials at the nanoscale in a probe based dynamic mode operation. The method is particularly suited for investigating soft-matter such as polymers and bio-matter. We use perturbation analysis tools for mapping dissipative and stiffness properties of material into parameters of an equivalent linear time-invariant model. Parameters of the equivalent model are adaptively estimated, where, for robust estimation, a multi-frequency excitation of the probe is introduced. We demonstrate that the reported method of simultaneously determining multiple material properties can be implemented in real-time on existing probe based instruments. We further demonstrate the effectiveness of the method by investigating properties of a polymer blend in real-time.

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Consensus-based distributed algorithms are well suited for coordination among agents in a cyber-physical system. These distributed schemes, however, suffer from their vulnerability to cyber attacks that are aimed at manipulating data and control flow. In this article, we present a novel distributed method for detecting the presence of such intrusions for a distributed multi-agent system following ratio consensus. We employ a Max-Min protocol to develop low cost, easy to implement detection strategies where each participating node detects the intrusion independently, eliminating the need for a trusted certifying agent in the network. The effectiveness of the detection method is demonstrated by numerical simulations on a 1000 node network to demonstrate the efficacy and simplicity of implementation.