This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the feasible region is possibly unbounded. To address such problems, a unified DUal Consensus Algorithm (DUCA) and its proximal variant (Pro-DUCA) are proposed, which are unified frameworks that approximate the method of multipliers applied to the corresponding dual problem in no need of a closed-form dual objective. With varied parameter settings, DUCA and Pro-DUCA not only extend a collection of existing consensus optimization methods to solve the dual problem that they used to be inapplicable to, but also aid in offering new efficient algorithms to the literature. The proposed unified algorithms are shown to achieve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(1/k)$</tex-math></inline-formula> convergence rates in terms of optimality and feasibility, providing new or enhanced convergence results for a number of existing methods. Simulations demonstrate that these algorithms outperform several state-of-the-art alternatives in terms of objective and feasibility errors.

This paper studies the dynamics of a network of diffusively coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally to the set of equilibria for generic monotone (but not necessarily strictly monotone) regulatory functions. Sufficient conditions for global state synchronization are provided. Finally, by adopting a piecewise linear approximation of the vector field, we determine the existence, location and stability of the equilibria as a function of the coupling gain. The theoretical results are illustrated with numerical simulations.

Motivated by the swift global transmission of infectious diseases, we present a comprehensive framework for network-based epidemic control. Our aim is to curb epidemics using two different approaches. In the first approach, we introduce an optimization strategy that optimally reduces travel rates. We analyze the convergence of this strategy and show that it hinges on the network structure to minimize infection spread. In the second approach, we expand the classic SIR model by incorporating and optimizing quarantined states to strategically contain the epidemic. We show that this problem reduces to the problem of matrix balancing. We establish a link between optimization constraints and the epidemic's reproduction number, highlighting the relationship between network structure and disease dynamics. We demonstrate that applying augmented primal-dual gradient dynamics to the optimal quarantine problem ensures exponential convergence to a stationary point. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts.

In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller exhibits lower computational complexity compared to existing encrypted controllers implemented on LWE based schemes due to the polynomial structure of Ring-LWE. However, the structural difference introduces additional difficulties in analyzing the effect of error growth; Ring-LWE based schemes inject multiple error coefficients when encrypting a single message, which accumulate under recursive homomorphic multiplications. We show that their effect on the control performance can be arbitrarily bounded by the closed-loop stability, thus recovering the performance of the unencrypted controller. Furthermore, a novel method to “pack” a vector into a polynomial is presented, which enhances computational and memory efficiency when applied to the proposed encrypted controller. The effectiveness of the proposed design is demonstrated through numerical simulations.

This article studies the controllability of multiweighted directed dynamical networks, where the nodes are heterogeneous linear time-invariant dynamical systems and the connections are characterized by multiple weight attributes. For such multiweighted networks to be controllable, some necessary and sufficient conditions are established. To identify different weight attributes, a multiweighted network is decomposed into multiple single-weighted networks, and then their relationships are characterized with respect to their controllability. Furthermore, the controllability of multiweighted networks with some typical topologies is studied in detail, for which specific controllability conditions are derived. Simulations are presented to verify the theoretical results. This research reveals the impact of multiple weight attributes, node dynamics, and inner coupling structures on the controllability of the integrated multiweighted networks, demonstrating that the controllability of multiweighted networks is remarkably distinct from single-weighted networks.

Improving the controllability of power networks is crucial as they are highly complex networks operating in synchrony; even minor perturbations can cause desynchronization and instability. To that end, one needs to assess the criticality of key network components (buses and lines) in terms of their impact on system performance. Traditional methods to identify the key nodes/edges in power networks often rely on static centrality measures based on the network's topological structure ignoring the network's dynamic behavior. In this paper, using multimachine power network models and a new control-theoretic edge centrality matrix (ECM) approach, we: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> quantify the influence of edges (i.e., the line susceptances) in terms of controllability performance metrics, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> identify the most <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">influential</i> lines, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iii)</i> compute near-optimal edge modifications that improve the power network controllability. Employing various IEEE power network benchmarks, we validate the effectiveness of the ECM-based algorithm and demonstrate improvements in system reachability, control, and damping performance.

In this article, a distributed adaptive optimal control method is proposed to solve the bipartite consensus problem for heterogeneous multi-agent systems. First, with a change in coordinates, the optimal bipartite consensus can be transformed into the optimal consensus problem and the optimal control law is also established. Second, a distributed state observer is designed for each agent to estimate the leader's state under the cooperate/antagonistic interaction, which is used to replace the unavailable leader's signal. Then, to find the optimal control solution adaptively, two online integral reinforcement learning algorithms, i.e., on-policy and off-policy, are developed. Based on the policy iteration in learning process, the algorithms proposed here utilize the state data of systems without requiring the complete knowledge of the leader's and agents' dynamics. It is proven that the observer is exponentially convergent, which guarantees the accuracy of solution in algorithms. Finally, two examples are given to show the validity of the proposed method.

In this article, a novel approach toward addressing the filtering problem for a class of networked control systems (NCSs) with a mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> and passive (MHP) performance index is proposed. The underlying NCSs may manifest different characteristics (called quantization density herein) when subjected to channel switching. As such, it is possible to model the NCSs as a class of switched systems. A mode-dependent and quantization-error-dependent Lyapunov-like function is first adopted in order to conduct stability and MHP performance analysis with less conservatism. Based on the developed stability and MHP performance analysis, a set of MHP filters suitable for the controlled system is designed such that the filtering error system is globally uniformly asymptotically stable with a specified MHP performance index. The effectiveness and potential applications of the derived results are demonstrated via a numerical simulation.

In this paper, a formation-circumnavigation switching control problem is investigated for multiple heterogeneous omni-directional intelligent navigator (ODIN) systems over an intermittent communication network. First, a distributed finite-time hybrid observer is proposed for each ODIN system to estimate the state information of the target. Then a finite-time formation-circumnavigation controller is designed for each ODIN system. The controller uses the estimated state information of the target as the reference signal. A homogeneous technique is utilized to show that all ODINs can realize a switching formation-circumnavigation movement in finite time under the proposed formation-circumnavigation control strategy. Particularly, the formation-circumnavigation control strategy can ensure smooth switching between formation and circumnavigation for the ODIN systems by simply adjusting a control parameter, which is crucial for economic and security requirements in real applications. Finally, numerical simulations are conducted to illustrate the effectiveness of the proposed formation-circumnavigation switching control strategy.

This paper is concerned with output consensus of heterogeneous multi-agent systems under sparse attacks. The leader agent is only available to a small fraction nodes. To estimate the leader's signal, a distributed observer is proposed, which is of the integral type and possesses good robustness and high convergence rate. Unlike the existing literature on distributed observer, this paper introduces a novel event-triggered strategy that utilizes the agents' measurement error state instead of the norm of the state errors. It is theoretically and numerically demonstrated that the triggering times and communication loads between agents can be significantly reduced by using this strategy, and a positive lower bound on the triggering time interval is also computed. Furthermore, an adaptive scheme with pinning strategy is considered to ensure the output consensus with uniformly ultimately bounded in the presence of false data attacks. Finally, a numerical example is given to illustrate the effectiveness of the results.