We consider the decentralized bisimilarity control problem for nondeterministic discrete event systems with nondeterministic specifications. This problem requires us to synthesize a decentralized supervisor that consists of multiple local supervisors so that the supervised system is bisimilar to the specification. In this paper, to solve it, we restrict local supervisors to deterministic ones. We synthesize deterministic local supervisors based on the specification model, and show that the decentralized bisimilarity control problem is solvable by deterministic local supervisors if and only if it is solved by the synthesized local supervisors.
This paper proposes a theory of angle rigidity for frameworks with nodes embedded in non-Euclidean space $\mathbb {S}^{1}$, which is then applied to solve the problem of single-anchor cooperative localization. Different from angle rigidity in Euclidean space, only rotational infinitesimal motions remain in $\mathbb {S}^{1}$. To address the $2\pi$ wrap-around effect which makes existing Euclidean angle rigidity inapplicable, we introduce a branched angle function and prove its almost-everywhere differentiability on the complement of a measure-zero singular set, upon which a coordinate-independent angle rigidity matrix is derived for chamber-wise frameworks in $\mathbb {S}^{1}$. Inspired by the Henneberg construction, we propose sequential construction methods that exhaustively characterize minimally angle rigid frameworks. By analyzing the rank of the angle rigidity matrix and the structure of infinitesimal motions, we establish necessary and sufficient algebraic conditions. The equivalence among angle rigidity, infinitesimal angle rigidity, and global angle rigidity is established via the connectivity of an auxiliary edge graph in a chamber. Moreover, we obtain topological conditions via an associated trigraph. Based on these results, we establish single-anchor localizability in contrast to Euclidean schemes that require at least two anchors, and design estimation algorithms that achieve global exponential convergence in chamber-wise $\mathbb {S}^{1}$. Simulations validate the theoretical results.
We study the finite-time convergence of the well-known Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm for stochastic gradient optimization. Experimental results have shown that convergence is faster if the two step-size sequences used in this algorithm are well separated. We show this formally. In the two-timescale SPSA algorithm, the slower time scale corresponds to the gradient search and the faster scale to the function measurement. We show in this paper that, if the slower scale is propositional to $1/n^{a}$ and the faster to $1/n^{b}$, the convergence rate is $O(1/n^{(a-b)})$ for convex functions and $O(1/n^{2(a-b)})$ for strongly convex functions. Finally, we give some experimental results which validate our theory.
Limited communication bandwidth poses a major challenge for networked iterative learning control (ILC). When only a few quantization bits are available, conventional deterministic quantizers become inadequate because quantization errors may be unbounded and saturation effects are likely to occur. To overcome these difficulties, this paper proposes a finite-level probabilistic quantization framework for networked ILC under severe bandwidth constraints. The scheme integrates a cyclic quantizer with a stochastic encoding–decoding strategy, enabling any prescribed number of quantization levels to cover the entire real axis while inherently avoiding saturation. Instead of using a sector-bounded error description, the framework derives an exact codeword-consistency probability and provides analytical approximations of the reconstruction-error and tracking-error distributions. This probabilistic model is then incorporated into P-type learning controllers with both constant and decreasing gains. Rigorous convergence analysis establishes mean-square and almost-sure convergence of the tracking error despite extremely coarse quantization. The stability conditions do not explicitly depend on the number of quantization levels, so the proposed framework remains applicable even under one-bit communication. Simulation studies show that the proposed method achieves faster convergence and higher steady-state accuracy than conventional uniform and differential quantizers, without increasing the communication burden. The developed framework offers rigorous performance guarantees for ILC under arbitrarily coarse yet saturation-free quantization, and thus opens new possibilities for bandwidth-constrained networked control systems.
This paper considers a distributed nonconvex optimization problem, where the objective is to minimize a global cost function formed as the sum of local cost functions across agents in an unbalanced directed communication network. Solving this problem typically requires information exchange among agents and access to gradient information. However, communication bandwidth is often limited, and gradient information may be unavailable or expensive to compute. To address these challenges, we propose a zeroth-order compressed push-pull algorithm that reduces communication overhead and removes the reliance on explicit gradient information. We design a novel Lyapunov function to establish that the proposed algorithm converges sublinearly to a stationary point when each local cost function is smooth. Under the additional assumption that the global cost function satisfies the Polyak–Łojasiewicz condition, we establish that the algorithm achieves linear convergence to the global optimum. Finally, numerical simulations demonstrate the effectiveness of the proposed algorithm.
