arXiv subjects

Min Meng

Publications and source records attributed to Min Meng.

22 records · Page 2Linked to original sources

arXiv2021

Decentralized Online Learning for Noncooperative Games in Dynamic Environments

Decentralized online learning for seeking generalized Nash equilibrium (GNE) of noncooperative games in dynamic environments is studied in this paper. Each player aims at selfishly minimizing its own time-varying cost function subject to time-varying coupled constraints and local feasible set constraints. Only local cost functions and local constraints are available to individual players, who can receive their neighbors' information through a fixed and connected graph. In addition, players have no prior knowledge of cost functions and local constraint functions in the future time. In this setting, a novel distributed online learning algorithm for seeking GNE of the studied game is devised based on mirror descent and a primal-dual strategy. It is shown that the presented algorithm can achieve sublinearly bounded dynamic regrets and constraint violation by appropriately choosing decreasing stepsizes. Finally, the obtained theoretical result is corroborated by a numerical simulation.

math.OC↗

arXiv2020

Aug-PDG: Linear Convergence of Convex Optimization with Inequality Constraints

This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It is shown that Aug-PDG can converge semi-globally to the optimizer at a linear rate under some mild assumptions, such as the quadratic gradient growth condition for the objective function, which is strictly weaker than strong convexity. To our best knowledge, this paper is the first to establish a linear convergence for the studied problem in the discrete-time setting, where an explicit bound is provided for the stepsize. Finally, a numerical example is presented to illustrate the efficacy of the theoretical finding.

math.OC↗

arXiv2020

Self-Triggered Scheduling for Boolean Control Networks

It has been shown that self-triggered control has the ability to reduce computational loads and deal with the cases with constrained resources by properly setting up the rules for updating the system control when necessary. In this paper, self-triggered stabilization of Boolean control networks (BCNs), including deterministic BCNs, probabilistic BCNs and Markovian switching BCNs, is first investigated via semi-tensor product of matrices and Lyapunov theory of Boolean networks. The self-triggered mechanism with the aim to determine when the controller should be updated is given based on the decrease of the corresponding Lyapunov functions between two successive sampling times. We show that the self-triggered controllers can be chosen as the conventional controllers without sampling, and also can be optimally constructed based on the triggering conditions.

eess.SY↗

arXiv2017

A Unified Hamiltonian Solution to Maxwell-Schrodinger Equations for Modeling Electromagnetic Field-Particle Interaction

A novel unified Hamiltonian approach is proposed to solve Maxwell-Schrodinger equation for modeling the interaction between classical electromagnetic (EM) fields and particles. Based on the Hamiltonian of electromagnetics and quantum mechanics, a unified Maxwell-Schrodinger system is derived by the variational principle. The coupled system is well-posed and symplectic, which ensures energy conserving property during the time evolution. However, due to the disparity of wavelengths of EM waves and that of electron waves, a numerical implementation of the finite-difference time-domain (FDTD) method to the multiscale coupled system is extremely challenging. To overcome this difficulty, a reduced eigenmode expansion technique is first applied to represent the wave function of the particle. Then, a set of ordinary differential equations (ODEs) governing the time evolution of the slowly-varying expansion coefficients are derived to replace the original Schrodinger equation. Finally, Maxwell's equations represented by the vector potential with a Coulomb gauge, together with the ODEs, are solved self-consistently. For numerical examples, the interaction between EM fields and a particle is investigated for both the closed, open and inhomogeneous electromagnetic systems. The proposed approach not only captures the Rabi oscillation phenomenon in the closed cavity but also captures the effects of radiative decay and shift in the open free space. After comparing with the existing theoretical approximate models, it is found that the approximate models break down in certain cases where a rigorous self-consistent approach is needed. This work is helpful for the EM simulation of emerging nanodevices or next-generation quantum electrodynamic systems.

physics.optics↗