This article studies a class of distributed nonsmooth convex optimization problems subject to local set constraints and coupled nonlinear inequality constraints. In particular, each local objective function consists of one differentiable convex function and multiple nonsmooth convex functions. By applying multiple proximal splittings and derivative feedback techniques, a new distributed continuous-time multiproximal algorithm is developed, whose dynamics satisfies Lipschitz continuity even if the considered problem is nonsmooth. Compared with previous results that rely on either the differentiability or strong convexity of local objective functions, the proposed algorithm can be applied to more general functions, which are only convex and not necessarily smooth. Moreover, in contrast to some results that require some specific initial conditions, the developed algorithm is free of initialization. The convergence analysis of the proposed algorithm is conducted by applying Lyapunov stability theory. It is shown that the states of all the agents achieve consensus at an optimal solution. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed algorithm.
A working predictive schedule can be useless because of the various external or internal disruptions in a job shop. Total rescheduling may cause problems such as shop floor nervousness. Thus, the job shop scheduling repair (recovery) approach aims at generating a solution satisfying the updated constraints and making deviations minimized. We propose an incremental temporal reasoning approach in this paper to solve job shop scheduling repair problems. Specifically, such a problem is formulated as a disjunctive temporal problem (DTP), framed as an optimal constraint satisfaction problem (OCSP) formally, and finally solved by performing an algorithm integrating incremental temporal consistency and efficient candidate generation. Through involving human interactive mechanism, domain experts can make higher quality decisions by balancing makespan and deviations.
This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than the complete row or column in the existing literatures. Firstly, we focus on the case of a homogeneous partition of linear equations. A distributed algorithm is proposed via a single-layered grid network, in which each agent only needs to control three scalar states. Secondly, we consider the case of heterogeneous partitions of linear equations. Two distributed algorithms with doubled-layered network are developed, which allows each agent's states to have different dimensions and can be applied to heterogeneous agents with different storage and computation capability. Rigorous proofs show that the proposed distributed algorithms collaboratively obtain a least square solution with exponential convergence, and also own a solvability verification property, i.e., a criterion to verify whether the obtained solution is an exact solution. Finally, some simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.
With the continuous deepening of research and development in the field of aerospace, the requirements for aerospace payloads are also increasing. The stray light received by the spaceborne telescope in the space environment will be one of the most important factors affecting its performance. The optical mechanical surface of spaceborne telescope will deviate from the original design due to various objective factors during the whole link process, and the actual optical mechanical surface is not ideal. In order to ensure that it can work normally, it is necessary to simulate and analyze the stray light situation of the whole link. This paper mainly introduces the complex environment and complex characteristics experienced from the ground section to the orbit section, analyzes and summarizes the sources of stray light, and finally proposes a framework for establishing a digital twin model of stray light for spaceborne telescopes. Through data-driven and model-driven methods, finally build a complete set of ground, launch, and in-orbit digital twin models.
In this paper, an inherent property of uncertain systems is revealed and the concept of the Self-Stable Region ( SSR ) is put forward. A novel constructive synthesis method for nonlinear uncertain systems is then proposed. The feedback law is determined by the recursively constructed functions according to the suggested inequalities. The convergence of the trajectories is guaranteed by the convergence to the designed SSR. So this approach is robust and dynamic characteristics can be designed. Finally, various properties of the SSR approach are discussed.
For large-scale symmetric discrete ill-posed problems, MR-II, a minimal residual method, is a competitive alternative to LSQR and CGLS. In this paper, we establish bounds for the distance between an underlying $k$-dimensional Krylov subspace and the subspace spanned by the $k$ dominant eigenvectors. They show that the $k$-step MR-II captures the $k$ dominant spectral components better for severely and moderately ill-posed problems than for mildly ill-posed problems, so that MR-II has better regularizing effects for the first two kinds of problems than for the third kind. By the bounds, we derive an estimate for the accuracy of the rank $k$ approximation generated by the symmetric Lanczos process. We analyze the regularization of MINRES and compare it with MR-II, showing why it is generally not enough to compute a best possible regularized solution and when it is better than MR-II. Our general conclusions are that MINRES and MR-II have only the partial regularization for general symmetric ill-posed problems and mildly ill-posed problems, respectively. Numerical experiments confirm our assertions. Furthermore, they illustrate that MR-II has the full regularization for severely and moderately ill-posed problems and MINRES has only the partial regularization independent of the degree of ill-posedness. The experiments also indicate that MR-II is as equally effective as and more efficient than LSQR for symmetric ill-posed problems.
Abstract：Aimed at the problem that the synchronous error would accumulate with time in mechanical vibration acquisition using wireless sensor networks, according to the mechanism analysis of accumulated synchronous error, an accumulated synchronous error control method based on synchronous information tracking method is presented.Hardware layer of acquisition node is employed to capture the synchronous information to avoid hysteresis caused by task preemption; Crystal oscillator frequency offset estimate method based on Kalman filter is researched to improve the estimate accuracy.A feedback control system is built to feedback and compensate the synchronous error dynamically to avoid synchronous error accumulation.An embedded multitask priority management firmware is designed to guarantee the real-time performance of sampling task and accumulate synchronous error control task in mechanical vibration acquisition with high sampling rate.Experiments show that the synchronous error is kept within 0.6 us in 30 s with the sampling rate up to 51.2 kHz, and the maximum synchronous error does not exceed 3% of the sampling period, which can meet the requirement of synchronous acquisition in mechanical vibration monitoring. Key words：mechanical vibration
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