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In this paper, we consider the problem of estimating a scalar field using a network of mobile sensors which can measure the value of the field at their instantaneous location. The scalar field to be estimated is assumed to be represented by positive definite radial basis kernels and we use techniques from adaptive control and Lyapunov analysis to prove the stability of the proposed estimation algorithm. The convergence of the estimated parameter values to the true values is guaranteed by planning the motion of the mobile sensors to satisfy persistence-like conditions.
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This paper considers the problem of simultaneous sensor fault detection, isolation, and networked estimation of linear full-rank dynamical systems. The proposed networked estimation is a variant of single time-scale protocol and is based on (i) consensus on textit{a-priori} estimates and (ii) measurement innovation. The necessary connectivity condition on the sensor network and stabilizing block-diagonal gain matrix is derived based on our previous works. Considering additive faults in the presence of system and measurement noise, the estimation error at sensors is derived and proper residuals are defined for fault detection. Unlike many works in the literature, no simplifying upper-bound condition on the noise is considered and we assume Gaussian system/measurement noise. A probabilistic threshold is then defined for fault detection based on the estimation error covariance norm. Finally, a graph-theoretic sensor replacement scenario is proposed to recover possible loss of networked observability due to removing the faulty sensor. We examine the proposed fault detection and isolation scheme on an illustrative academic example to verify the results and make a comparison study with related literature.
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) so they collectively meet the electric power demanded by a collection of loads, while minimizing the total generation cost and respecting the DER capacity limits. This problem can be cast as a convex optimization problem, where the global objective is to minimize a sum of convex functions corresponding to individual DER generation cost, while satisfying (i) linear inequality constraints corresponding to the DER capacity limits and (ii) a linear equality constraint corresponding to the total power generated by the DERs being equal to the total power demand. We develop distributed algorithms to solve the DER coordination problem over time-varying communication networks with either bidirectional or unidirectional communication links. The proposed algorithms can be seen as distribute
In this paper, a general nonlinear 1st-order consensus-based solution for distributed constrained convex optimization is considered for applications in network resource allocation. The proposed continuous-time solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected multi-agent networks. The solution is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of their limited actuation capabilities, e.g., quantization and saturation constraints among others. Moreover, different applications impose specific nonlinearities to the model, e.g., convergence in fixed/finite-time, robustness to uncertainties, and noise-tolerant dynamics. Our proposed distributed resource allocation protocol generalizes such nonlinear models. Putting convex set analysis together with the Lyapunov theorem, we provide a general technique to prove convergence (i) regardless of the particular type of nonlinearity (ii) with weak network-connectivity requirement (i.e., uniform-connectivity). We simulate the performance of the protocol in continuous-time coordination of generators, known as the economic dispatch problem (EDP).
While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy iteration algorithm for approximating the mean-field equilibrium in linear-quadratic MFGs with discounted cost. Given the mean-field, each agent faces a linear-quadratic tracking problem, the solution of which involves a dynamical system evolving in retrograde time. This makes the development of forward-in-time algorithm updates challenging. By identifying a structural property of the mean-field update operator, namely that it preserves sequences of a particular form, we develop a forward-in-time equilibrium computation algorithm. Bounds that quantify the accuracy of the computed mean-field equilibrium as a function of the algorithms stopping condition are provided. The optimality of the computed equilibrium is validated numerically. In contrast to the most recent/concurrent results, our algorithm appears to be the first to study infinite-horizon MFGs with non-stationary mean-field equilibria, though with focus on the linear quadratic setting.
Stochastic stability for centralized time-varying Kalman filtering over a wireles ssensor network with correlated fading channels is studied. On their route to the gateway, sensor packets, possibly aggregated with measurements from several nodes, may be dropped because of fading links. To study this situation, we introduce a network state process, which describes a finite set of configurations of the radio environment. The network state characterizes the channel gain distributions of the links, which are allowed to be correlated between each other. Temporal correlations of channel gains are modeled by allowing the network state process to form a (semi-)Markov chain. We establish sufficient conditions that ensure the Kalman filter to be exponentially bounded. In the one-sensor case, this new stability condition is shown to include previous results obtained in the literature as special cases. The results also hold when using power and bit-rate control policies, where the transmission power and bit-rate of each node are nonlinear mapping of the network state and channel gains.
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