Showing papers on "Convergence (routing) published in 2022"

Prescribed-Time Robust Differentiator Design Using Finite Varying Gains

Abstract: A novel hybrid differentiator is proposed for any time-varying signal, whose second derivative is uniformly bounded. The exact real-time differentiation is obtained in prescribed time, and it is based on the robust observer design for the perturbed double integrator. The proposed observer strategy is in successive applications of rescaled and standard supertwisting observers with finite (time-varying and respectively constant) gains. The former observer aims to nullify the observation error dynamics in prescribed time whereas the latter observer is to extend desired robustness features to the infinite horizon. The resulting real-time differentiator uses the current signal measurement only and inherits the observer features of robust convergence to the estimated signal derivative in prescribed time regardless of the initial differentiator state. Tuning conditions to achieve the exact signal differentiation in prescribed time are explicitly derived. Theoretical results are supported by an experimental study of the exact prescribed-time velocity estimation of an oscillating pendulum, operating under uniformly bounded disturbances. The developed approach is additionally discussed to admit an extension to the sequential arbitrary order differentiation.

Learning Distributed Stabilizing Controllers for Multi-Agent Systems

Abstract: We address model-free distributed stabilization of heterogeneous continuous-time linear multi-agent systems using reinforcement learning (RL). Two algorithms are developed. The first algorithm solves a centralized linear quadratic regulator (LQR) problem without knowing any initial stabilizing gain in advance. The second algorithm builds upon the results of the first algorithm, and extends it to distributed stabilization of multi-agent systems with predefined interaction graphs. Rigorous proofs are provided to show that the proposed algorithms achieve guaranteed convergence if specific conditions hold. A simulation example is presented to demonstrate the theoretical results.

Learning-Accelerated ADMM for Distributed DC Optimal Power Flow

Abstract: We propose a novel data-driven method to accelerate the convergence of Alternating Direction Method of Multipliers (ADMM) for solving distributed DC optimal power flow (DC-OPF) where lines are shared between independent network partitions. Using previous observations of ADMM trajectories for a given system under varying load, the method trains a recurrent neural network (RNN) to predict the converged values of dual and consensus variables. Given a new realization of system load, a small number of initial ADMM iterations is taken as input to infer the converged values and directly inject them into the iteration. We empirically demonstrate that the online injection of these values into the ADMM iteration accelerates convergence by a significant factor for partitioned 14-, 118- and 2848-bus test systems under differing load scenarios. The proposed method has several advantages: it maintains the security of private decision variables inherent in consensus ADMM; inference is fast and so may be used in online settings; RNN-generated predictions can dramatically improve time to convergence but, by construction, can never result in infeasible ADMM subproblems; it can be easily integrated into existing software implementations. While we focus on the ADMM formulation of distributed DC-OPF in this letter, the ideas presented are naturally extended to other distributed optimization problems.

Push-SAGA: A Decentralized Stochastic Algorithm With Variance Reduction Over Directed Graphs

Abstract: In this letter, we propose Push-SAGA, a decentralized stochastic first-order method for finite-sum minimization over a directed network of nodes. Push-SAGA combines node-level variance reduction to remove the uncertainty caused by stochastic gradients, network-level gradient tracking to address the distributed nature of the data, and push-sum consensus to tackle directed information exchange. We show that Push-SAGA achieves linear convergence to the exact solution for smooth and strongly convex problems and is thus the first linearly-convergent stochastic algorithm over arbitrary strongly connected directed graphs. We also characterize the regime in which Push-SAGA achieves a linear speed-up compared to its centralized counterpart and achieves a network-independent convergence rate. We illustrate the behavior and convergence properties of Push-SAGA with the help of numerical experiments on strongly convex and non-convex problems.

Link prediction by deep non-negative matrix factorization

Abstract: Link prediction aims to predict missing links or eliminate spurious links and new links in future network by known network structure information. Most existing link prediction methods are shallow models and did not consider network noise. To address these issues, in this paper, we propose a novel link prediction model based on deep non-negative matrix factorization, which elegantly fuses topology and sparsity-constrained to perform link prediction tasks. Specifically, our model fully exploits the observed link information for each hidden layer by deep non-negative matrix factorization. Then, we utilize the common neighbor method to calculate the similarity scores and map it to multi-layer low-dimensional latent space to obtain the topological information of each hidden layer. Simultaneously, we employ the l 2 , 1 -norm constrained factor matrix at each hidden layer to remove the random noise. Besides, we provide an effective the multiplicative updating rules to learn the parameter of this model with the convergence guarantees. Extensive experiments results on eight real-world datasets demonstrate that our proposed model significantly outperforms the state-of-the-art methods.

A Novel Fixed-Time Sliding Mode Control of Quadrotor With Experiments and Comparisons

Abstract: In this letter, a practical fixed-time sliding mode controller is designed for quadrotors. A novel fixed-time stable system is derived, which has a faster convergence rate than existing methods. The proof of the fixed-time convergence is presented. Meanwhile, the faster convergence rate compared with the other two methods is detailed using simulations. Based on this derivation, a fixed-time sliding mode controller with bounded convergence time independent of initial conditions is developed. The comparative simulation and flight experiment results are presented, showing that the proposed control scheme is practical to an actual quadrotor and can achieve good control performance.

A Learning-based Innovized Progress Operator for Faster Convergence in Evolutionary Multi-objective Optimization

Abstract: Learning effective problem information from already explored search space in an optimization run, and utilizing it to improve the convergence of subsequent solutions, have represented important dir...

Maximizing Convergence Speed for Second Order Consensus in Leaderless Multi-Agent Systems

Abstract: The paper deals with the consensus problem in a leaderless network of agents that have to reach a common velocity while forming a uniformly spaced string. Moreover, the final common velocity (reference velocity) is determined by the agents in a distributed and leaderless way. Then, the consensus protocol parameters are optimized for networks characterized by a communication topology described by a class of directed graphs having a directed spanning tree, in order to maximize the convergence rate and avoid oscillations. The advantages of the optimized consensus protocol are enlightened by some simulation results and comparison with a protocol proposed in the related literature. The presented protocol can be applied to coordinate agents such as mobile robots, automated guided vehicles (AGVs) and autonomous vehicles that have to move with the same velocity and a common inter-space gap.

High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

Abstract: In this paper, the space-time fractional advection-diffusion equation (STFADE) is considered in the finite domain that the time and space derivatives are the Caputo fractional derivative. At first, a quadratic interpolation with convergence order O ( τ 3 - α ) is applied to obtain the semi-discrete in time variable. Then, the Chebyshev collocation method of the fourth kind has been used to approximate the spatial fractional derivative. In addition, the energy method has been employed to show the unconditional stability and gained convergence order of the time-discrete scheme. Finally, the accuracy of the numerical method is analyzed and showed that our method is much more accurate than existing techniques.

A General Regularized Distributed Solution for System State Estimation From Relative Measurements

Abstract: This work presents a novel general regularized distributed solution for the state estimation problem in networked systems. Resting on the graph-based representation of sensor networks and adopting a multivariate least-squares approach, the designed solution exploits the set of the available inter-sensor relative measurements and leverages a general regularization framework, whose parameter selection is shown to control the estimation procedure convergence performance. As confirmed by the numerical results, this new estimation scheme allows ( $i$ ) the extension of other approaches investigated in the literature and ( $ii$ ) the convergence optimization in correspondence to any (undirected) graph modeling the given sensor network.

Finding Optimal Results in the Homotopy Analysis Method to Solve Fuzzy Integral Equations

Abstract: The goal of this work is to apply the discrete stochastic arithmetic (DSA) and the fuzzy CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method to validate the results of solving fuzzy Fredholm or Volterra integral equations (IEs) by the homotopy analysis method (HAM). The CADNA (Control of Accuracy and Debugging for Numerical Applications) library is applied to implement the fuzzy CESTAC method. Furthermore, the optimal convergence control parameter of the HAM is obtained. A theorem is proved to show the accuracy of the HAM based on the concept of common significant digits and two algorithms are proposed by applying the fuzzy CESTAC method to compute the optimal results. The results of the sample examples illustrate the efficiency of using the DSA in place of the usual computer arithmetic.