Wireless Human-Machine Collaboration (WHMC) represents a critical advancement for Industry 5.0, enabling seamless interaction between humans and machines across geographically distributed systems. As the WHMC systems become increasingly important for achieving complex collaborative control tasks, ensuring their stability is essential for practical deployment and long-term operation. Stability analysis certifies how the closed-loop system will behave under model randomness, which is essential for systems operating with wireless communications. However, the fundamental stability analysis of the WHMC systems remains an unexplored challenge due to the intricate interplay between the stochastic nature of wireless communications, dynamic human operations, and the inherent complexities of control system dynamics. This paper establishes a fundamental WHMC model incorporating dual wireless loops for machine and human control. Our framework accounts for practical factors such as short-packet transmissions, fading channels, and advanced HARQ schemes. We model human control lag as a Markov process, which is crucial for capturing the stochastic nature of human interactions. Building on this model, we propose a stochastic cycle-cost-based approach to derive a stability condition for the WHMC system, expressed in terms of wireless channel statistics, human dynamics, and control parameters. Our findings are validated through extensive numerical simulations and a proof-of-concept experiment, where we developed and tested a novel wireless collaborative cart-pole control system. The results confirm the effectiveness of our approach and provide a robust framework for future research on WHMC systems in more complex environments.

We address fair sensor scheduling over bandwidth-constrained communication channels. While existing literature on fair scheduling overlooks overall system efficiency, we introduce a novel q-fairness framework to balance efficiency and fairness by adjusting the parameter q. Specifically, for two communication scenarios, we: (i) derive the optimal schedule under limited communication rates, and (ii) propose two suboptimal algorithms under limited simultaneous sensor transmissions and analyze their performance gaps relative to the optimal strategy. Simulations demonstrate that our algorithms effectively balance efficiency and fairness in both cases.

This article investigates a multileader Stackelberg game where leaders lack critical information about the follower’s objective function and face random disturbances with unknown distributions. Unlike conventional approaches requiring complete follower information, we consider leaders who manipulate physical plant states while observing the follower’s strategy through private tracking responders. To address distributional uncertainty in the follower’s best response, we reformulate the game as a distributionally robust equilibrium-seeking problem and develop a fully distributed FL algorithm. The proposed data-driven approach operates without prior knowledge of system models or disturbance distributions, enabling leaders to estimate states through neighbor communication and local gradient updates. We characterize equilibrium existence in nonconvex settings. The relationship between communication and gradient errors and the energy function of the dynamic system is established. The upper bound of the regret based on the proposed algorithm is rigorously analyzed. A case study demonstrates the framework’s effectiveness in achieving distributionally robust solutions against uncertain stochastic perturbations.

This paper considers the optimal power allocation of a jamming attacker against remote state estimation. The attacker is self-sustainable and can harvest energy from the environment to launch attacks. The objective is to carefully allocate its attack power to maximize the estimation error at the fusion center. Regarding the attacker's knowledge of the system, two cases are discussed: (i) perfect channel knowledge and (ii) unknown channel model. For both cases, we formulate the problem as a Markov decision process (MDP) and prove the existence of an optimal deterministic and stationary policy. Moreover, for both cases, we develop algorithms to compute the allocation policy and demonstrate that the proposed algorithms for both cases converge to the optimal policy as time goes to infinity. Additionally, the optimal policy exhibits certain structural properties that can be leveraged to accelerate both algorithms. Numerical examples are given to illustrate the main results.

Encrypted control has been extensively studied to ensure the confidentiality of system states and control inputs for networked control systems. This paper presents a computationally efficient encrypted control framework for networked systems enabled by quantum communication. A quantum channel between sensors and actuators is used to generate identical secret keys, whose security is further enhanced through quantum key distribution. These keys enable lightweight encryption and decryption while preserving confidentiality and control accuracy. We develop a novel encryption-decryption architecture for state-feedback control of linear systems based on quantum keys, and characterize the impact of quantum state errors on closed-loop stability. In particular, we establish the existence of a critical threshold on intrinsic quantum noise below which stability is guaranteed. In contrast to classical encrypted control schemes, which may collapse under a single key-bit error, the proposed quantum encrypted control exhibits strong robustness to key imperfections. We further adopt quantization techniques to address the scenarios with limited communication bits in practical situations, and implement privacy protection for quantum keys based on a stochastic quantizer. These results demonstrate that integrating quantum technologies into control systems in a nontrivial and principled manner, even at their current level of maturity, can yield substantial performance gains in reducing computational complexity and improving resilience to key errors while ensuring security against multiple eavesdropping sources.

We consider a joint uplink and downlink scheduling problem of a fully distributed wireless networked control system (WNCS) with a limited number of frequency channels. Using elements of stochastic systems theory, we derive a sufficient stability condition of the WNCS, which is stated in terms of both the control and communication system parameters. Once the condition is satisfied, there exists a stationary and deterministic scheduling policy that can stabilize all plants of the WNCS. By analyzing and representing the per-step cost function of the WNCS in terms of a finite-length countable vector state, we formulate the optimal transmission scheduling problem into a Markov decision process and develop a deep reinforcement learning (DRL)-based framework for solving it. To tackle the challenges of a large action space in DRL, we propose novel action space reduction and action embedding methods for the DRL framework that can be applied to various algorithms, including deep Q-network (DQN), deep deterministic policy gradient (DDPG), and twin delayed DDPG (TD3). Numerical results show that the proposed algorithm significantly outperforms benchmark policies.

This manuscript focuses on mitigating the effect of deception attacks on control signals, that is, in the presence of an adversary that tampers with data coming from the controller to the system actuators in order to degrade the plant performance. We propose adding Multiple-Inputs Multiple-Outputs (MIMO) filters to the loop, between the received control actions (which are potentially corrupted by attacks) and the plant actuators. These filters are designed to dynamically steer the reachable set induced by the attack signals to a known safe region of the state space. We provide a synthesis framework (built in terms of the solution of a collection of semidefinite programs) to design the filters so that attack-free control signals are distorted as little as possible-in terms of H infinity$$ {H}_{\infty } $$ and H2$$ {H}_2 $$ norms of the difference between original and filtered control signals-and the trajectories are guaranteed to be contained in a predefined safe set. The results are illustrated through a simulation case focusing on the stability augmentation system of an airplane.

This letter addresses the problem of optimal channel selection for remote state estimation in cyber-physical systems, where a sensor transmits measurements over multiple time-varying wireless channels. We model the packet arrival probability of each channel as a non-stationary Bernoulli process and adapt two discounted Multi-Armed Bandit (MAB) algorithms, Discounted Upper Confidence Bound (D-UCB) and Discounted Thompson Sampling (D-TS), to select channels with the highest expected packet arrival rates adaptively. The estimation error covariance is analyzed using Kalman filtering, and the cumulative estimation regret is defined as the excess trace of the estimation error covariance compared to an optimal policy. Theoretical analysis shows the algorithms achieve a regret that grows gradually over time, and numerical simulations validate their effectiveness under non-stationary conditions.

We study the problem of remote state estimation in the presence of a passive eavesdropper, under the challenging network environment of no packet receipt acknowledgments. A remote legitimate user estimates the state of a linear plant from the state information received from a sensor via an insecure and unreliable network. The transmission from the sensor may be intercepted by the eavesdropper. To maintain state confidentiality, we propose an encoding scheme. Our scheme transmits noise based on a pseudo-random indicator, pre-arranged at the legitimate user and sensor. The transmission of noise harms the eavesdropper's performance, more than that of the legitimate user. Using the proposed encoding scheme, we impair the eavesdropper's expected estimation performance, whilst minimising expected performance degradation at the legitimate user. We explore the trade-off between state confidentiality and legitimate user performance degradation.

Although classical model predictive control with finite control sets (FCS-MPC) is quite a popular control method, particularly in the realm of power electronics systems, its direct data-driven predictive control (FCS-DPC) counterpart has received relatively limited attention. In this paper, we introduce a novel reformulation of a commonly used DPC scheme that allows for the application of a modified sphere decoding algorithm, known for its efficiency and prominence in FCS-MPC applications. We test the reformulation on a popular electrical drive example and compare the computation times of sphere decoding FCS-DPC with an enumeration-based and a MIQP method.

The vulnerability analysis of remote state estimation with batch-data detectors is investigated in this article. The considered scenario is that sensors measure the process state and transmit measurements to the remote end via wireless networks, where the yielded innovation may be altered by an adversary in an affine form. At the remote end, a detector utilizing batch statistics is deployed to detect anomalies. In this setup, finding the worst-case estimation performance degradation during a detection interval is formulated as a nonconvex optimization problem on the Stiefel manifold with linear equation constraints, which is generally hard to tackle. Such a problem is addressed by introducing new optimization variables, and structural expressions of attack strategies in worst-case are proposed. Then, by means of Riemannian optimization tools, we provide additional properties for such attack strategies in a scalar sensor by solving a boundary trust region subproblem. Furthermore, analytical attack strategies in worst-case are derived under the case where a sequence of contaminated innovation covariances has been determined. A necessary condition of the existence of attack strategies in worst-case for the attacker with symmetric attack parameter matrices is also presented. Finally, two numerical examples in multisensor and a scalar sensor are conducted to demonstrate the validity of results developed.

We consider a networked control system where information is transmitted over lossy communication channels on both the uplink (sensor to controller) and downlink (controller to actuator). At each time instant, only one out of M different channels can be chosen for transmission. The statistics of the channels are unknown and must be learnt by observing transmission outcomes. We model this scenario as a multi-armed bandit type problem and investigate the use of Thompson sampling for carrying out this learning while simultaneously controlling the system. We derive necessary and sufficient conditions for stability of the controlled system. In addition, the notion of (accumulated) control regret is introduced and shown to scale logarithmically with time. Numerical comparisons show that Thompson sampling outperforms other channel selection methods such as periodic sampling and decaying ɛ-greedy.

In this paper, we consider the security of remote state estimation in cyber-physical systems, where a wireless sensor sends the measurement of the considered system to a remote state estimator using a wireless channel. In this scenario, time-stamp technology is commonly used to record the time characteristic of the data for different objectives, such as realizing time synchronization and dealing with time delays. We consider a potential threat to this mechanism, and investigate a time-stamp attack, where a malicious adversary manipulates data packets to degrade the estimation performance of the remote estimator. In particular, we assume that the attacker can alter the time-stamps of any two packets. We consider two types of sensor transmission, namely innovation and local estimate, respectively, and analyze the evolution of the remote estimation error covariance for both cases. Furthermore, we characterize the optimal attack strategy that maximizes the estimation error covariance from the attacker's point of view. Finally, we present numerical simulations to demonstrate the effectiveness of our results.

Wireless networked control system (WNCS) connecting sensors, controllers, and actuators via wireless communications is a key enabling technology for highly scalable and low-cost deployment of control systems in the Industry 4.0 era. Despite the tight interaction of control and communications in WNCSs, most existing works adopt separative design approaches. This is mainly because the co-design of control-communication policies requires large and hybrid state and action spaces, making the optimal problem mathematically intractable and difficult to be solved effectively by classic algorithms. In this paper, we systematically investigate deep learning (DL)-based estimator-control-scheduler co-design for a model-unknown nonlinear WNCS over wireless fading channels. In particular, we propose a co-design framework with the awareness of the sensor's age-of-information (AoI) states and dynamic channel states. We propose a novel deep reinforcement learning (DRL)-based algorithm for controller and scheduler optimization utilizing both model-free and model-based data. An AoI-based importance sampling algorithm that takes into account the data accuracy is proposed for enhancing learning efficiency. We also develop novel schemes for enhancing the stability of joint training. Extensive experiments demonstrate that the proposed joint training algorithm can effectively solve the estimation-control-scheduling co-design problem in various scenarios and provide significant performance gain compared to separative design and some benchmark policies.

Networked systems are increasingly the target of cyberattacks that exploit vulnerabilities within digital communications, embedded hardware, and software. Arguably, the simplest class of attacks -- and often the first type before launching destructive integrity attacks -- are eavesdropping attacks, which aim to infer information by collecting system data and exploiting it for malicious purposes. A key technology of networked systems is state estimation, which leverages sensing and actuation data and first-principles models to enable trajectory planning, real-time monitoring, and control. However, state estimation can also be exploited by eavesdroppers to identify models and reconstruct states with the aim of, e.g., launching integrity (stealthy) attacks and inferring sensitive information. It is therefore crucial to protect disclosed system data to avoid an accurate state estimation by eavesdroppers. This survey presents a comprehensive review of existing literature on privacy-preserving state estimation methods, while also identifying potential limitations and research gaps. Our primary focus revolves around three types of methods: cryptography, data perturbation, and transmission scheduling, with particular emphasis on Kalman-like filters. Within these categories, we delve into the concepts of homomorphic encryption and differential privacy, which have been extensively investigated in recent years in the context of privacy-preserving state estimation. Finally, we shed light on several technical and fundamental challenges surrounding current methods and propose potential directions for future research.

Secrecy encoding for remote state estimation in the presence of adversarial eavesdroppers is a well studied problem. Typical existing secrecy encoding schemes rely on the transmitter's knowledge of the remote estimator's current performance. This performance measure is often shared via packet receipt acknowledgments. However, in practical situations the acknowledgment channel may be susceptible to interference from an active adversary, resulting in the secrecy encoding scheme failing. Aiming to achieve a reliable state estimate for a legitimate estimator while ensuring secrecy, we propose a secrecy encoding scheme without the need for packet receipt acknowledgments. Our encoding scheme uses a pre-arranged scheduling sequence established at the transmitter and legitimate receiver. We transmit a packet containing either the state measurement or encoded information for the legitimate user. The encoding makes the packet appear to be the state but is designed to damage an eavesdropper's estimate. The pre-arranged scheduling sequence and encoding is chosen psuedo-random. We analyze the performance of our encoding scheme against a class of eavesdropper, and show conditions to force the eavesdropper to have an unbounded estimation performance. Further, we provide a numerical illustration and apply our encoding scheme to an application in power systems.

For cyber-physical systems in the 6G era, semantic communications connecting distributed devices for dynamic control and remote state estimation are required to guarantee application-level performance, not merely focus on communication-centric performance. Semantics here is a measure of the usefulness of information transmissions. Semantic-aware transmission scheduling of a large system often involves a large decision-making space, and the optimal policy cannot be obtained by existing algorithms effectively. In this letter, we first establish the monotonicity of the Q function of the optimal semantic-aware scheduling policy and then develop advanced deep reinforcement learning (DRL) algorithms by leveraging the theoretical guideline. Our numerical results show a 30% performance improvement compared to benchmark algorithms.

We consider the joint design of control and scheduling under stochastic Denial-of-Service (DoS) attacks in the context of networked control systems. A sensor takes measurements of the system output and forwards its dynamic state estimates to a remote controller over a packet-dropping link. The controller determines the optimal control law for the process using the estimates it receives. An attacker aims at degrading the control performance by increasing the packet-dropout rate with a DoS attack on the sensor-controller channel. We assume both the controller and the attacker are rational in a game-theoretic sense and establish a partially observable stochastic game to derive the optimal joint design of scheduling and control. Using dynamic programming we prove that the control and scheduling policies can be designed separately without sacrificing optimality, making the problem equivalent to a complete information game. We employ Nash Q-learning to solve the problem and prove that the solution is guaranteed to constitute an ϵ-Nash equilibrium. Numerical examples are provided to illustrate the interactions between the controller and the attacker.

We study the maximum information gain that an adversary may obtain through hacking without being detected. Consider a dynamical process observed by a sensor that transmits a local estimate of the system state to a remote estimator according to some reference transmission policy across a packet-dropping wireless channel equipped with acknowledgments (ACK). An adversary overhears the transmissions and proactively hijacks the sensor to reprogram its transmission policy. We define perfect secrecy as keeping the averaged expected error covariance bounded at the legitimate estimator and unbounded at the adversary. By analyzing the stationary distribution of the expected error covariance, we show that perfect secrecy can be attained for unstable systems only if the ACK channel has no packet dropouts. In other situations, we prove that independent of the reference policy and the detection methods, perfect secrecy is not attainable. For this scenario, we devise a Stackelberg game to derive the optimal defensive reference policy for the legitimate estimator and present a branch-and-bound algorithm with global optimality to solve the proposed game.