We propose a distributed online optimization al-gorithm with continuously learning ability. In this algorithm, we first perform one-step gradient descent with fixed step size to ensure the ability of tracking the optimal solutions, and then use multi-step consensus to ensure the collaboration between neighboring nodes. For strongly convex and smooth objective functions, we provide a dynamic regret analysis of the proposed algorithm and show that the dynamic regret is upper bounded by the initial values, the path variation of the optimal solution, and a linear growth term. The coefficient of the linear growth term can be made arbitrarily small by adjusting the step size of gradient descent. We also demonstrate the performance of the proposed algorithm by numerical simulations.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

In the paper, the problem of multiple controlled synchronization of a pair of unbalanced rotors is considered. To ensure the desired system behavior in the face of uncertainty and variations of the system parameters a novel adaptive control law based on the Implicit Reference Model (IRM) approach taking into account the discrete-time implementation is proposed and studied both by the computer simulations and experiments on the Multiresonance Mechatronic Laboratory Setup (MMLS) SV-2M of the IPME RAS, demonstrating the efficiency of the proposed approach and revealing its application scope.

We analyze the convergence of decentralized regularized linear regression algorithm. At each time step, every node over the random time-varying graphs runs an online estimation algorithm consisting of an innovation term processing its own new measurement, a consensus term taking a weighted sum of estimations of its own and its neighbors with additive and multiplicative communication noises and a regularization term preventing over-fitting. The sample path spatio-temporal persistence of excitation condition is established for the almost sure convergence. Especially, it is shown that this condition holds if the graphs are uniformly conditionally jointly connected and conditionally balanced, and the regression models of all nodes are uniformly conditionally spatio-temporally jointly observable, under which the algorithm converges in mean square and almost surely.

We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly time-varying observation matrices. The underlying communication network is modeled by a sequence of random digraphs and is subjected to nonuniform random time-varying delays in channels. Each node runs an online estimation algorithm consisting of a consensus term taking a weighted sum of its own estimate and neighbours' delayed estimates, and an innovation term processing its own new measurement at each time step. By stochastic time-varying system, martingale convergence theories and the binomial expansion of random matrix products, we transform the convergence analysis of the algorithm into that of the mathematical expectation of random matrix products. Firstly, for the delay-free case, we show that the algorithm gains can be designed properly such that all nodes' estimates converge to the true parameter in mean square and almost surely if the observation matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition. Secondly, for the case with time delays, we introduce delay matrices to model the random time-varying communication delays between nodes. It is shown that under the stochastic spatio-temporal persistence of excitation condition, for any given bounded delays, proper algorithm gains can be designed to guarantee mean square convergence for the case with conditionally balanced digraphs.

We consider a discrete-time distributed averaging algorithm over multi-agent networks with measurement noises and time-varying random graphs. Each agent updates its state by a weighted sum of pairwise state differences between its neighbors and itself with both additive and multiplicative measurement noises. The network structure is modeled by a sequence of time-varying random digraphs, which may be spatially and temporally dependent. By stochastic Lyapunov method and the combination of algebraic graph theory and martingale convergence theory, we obtain sufficient conditions for stochastic approximation type algorithms to achieve mean square and almost sure average consensus. We prove that all states of the agents converge to a common random variable, whose mathematical expectation is the average of initial values, in mean square and almost surely if the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected. An upper bound of the variance of the limit random variable, that is, the mean square steady-state error for stochastic average consensus is given quantitatively related to the weights, the algorithm gain and the energy level of the noises.

In this paper, we analyze the performance limit of sensor localization from a novel perspective. We consider distance-based single-hop sensor localization with noisy distance measurements by time of arrival (TOA). Differently from the existing studies, the anchors are assumed to be randomly deployed, with the result that the trace of the associated Cramer-Rao Lower Bound (CRLB) matrix becomes a random variable. We adopt this random variable as a scalar metric for the performance limit and then focus on its statistical attributes. By the Central Limit Theorems for U-statistics, we show that as the number of anchors goes to infinity, this scalar metric converges to a random variable which is an affine transformation of a chi-square random variable of degree 2. In addition, we provide the quantitative relationship among the mean, the standard deviation, the number of anchors, parameters of communication channels and the distribution of the anchors. Extensive simulations are carried out to confirm the theoretical results. On the one hand, our study reveals some fundamental features of sensor localization; on the other hand, the conclusions we draw can in turn guide us in the design of wireless sensor networks.