This paper investigates remote state estimation in cyber-physical systems (CPS) where direct and reliable communication between distributed sensors and the control center is unavailable due to the lack of infrastructure. In such scenarios, unmanned aerial vehicles (UAVs) can be deployed as mobile data collectors to facilitate information transfer. While joint UAV trajectory and resource allocation problems have been widely studied in various contexts, adapting these to minimize estimation error in remote state estimation of linear CPS—accounting for the nonlinear evolution of error covariances and spatio-temporal coupling—presents distinct challenges. To tackle this, we formulate a joint optimization problem and decompose it into UAV path planning and UAV-sensor resource allocation. The path planning problem is modeled as a Markov Decision Process, where we establish the existence and periodicity of the optimal policy, and the resource allocation is formulated as a many-to-one matching game. We jointly solve these sub-problems via an alternating optimization algorithm that combines dynamic programming with a deferred acceptance-based matching scheme, and we prove the stability of the resulting matching. Simulation results confirm the periodic structure of the optimal path and demonstrate the effectiveness of the proposed method in reducing estimation error compared with other representative matching-based schemes.

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 feedback learning 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.

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.

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 the 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. Note to Practitioners—With the increasing openness and anonymization of the networked estimation systems, privacy concerns require to be paid more attention. The essence of the privacy-preserving approaches is to seek certain tradeoffs among privacy budget and various performance metrics, such as utility and energy. Cryptographic methods are suitable for high-performance processors because they need sufficient computation resources to generate and operate complicated secret keys. By contrast, perturbation methods can be realized faster, but the adverse impact on the legitimate systems should be limited not to violently disrupt the desired operations. In conclusion, the choice of these encryption approaches depends on practical demands. Moreover, general state-space models, which can represent most real-world dynamics, are the basis of the reviewed methods. Thus these approaches can be easily deployed to practical engineering systems to effectively guarantee their privacy, providing significant application values.

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.

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 separate 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 article, 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 separate designs and some benchmark policies.

Remote state estimation of large-scale distributed dynamic processes plays an important role in Industry 4.0 applications. In this paper, we focus on the transmission scheduling problem of a remote estimation system. First, we derive some structural properties of the optimal sensor scheduling policy over fading channels. Then, building on these theoretical guidelines, we develop a structure-enhanced deep reinforcement learning (DRL) framework for optimal scheduling of the system to achieve the minimum overall estimation mean-square error (MSE). In particular, we propose a structure-enhanced action selection method, which tends to select actions that obey the policy structure. This explores the action space more effectively and enhances the learning efficiency of DRL agents. Furthermore, we introduce a structure-enhanced loss function to add penalties to actions that do not follow the policy structure. The new loss function guides the DRL to converge to the optimal policy structure quickly. Our numerical experiments illustrate that the proposed structure-enhanced DRL algorithms can save the training time by 50% and reduce the remote estimation MSE by 10% to 25%, when compared to benchmark DRL algorithms. In addition, we show that the derived structural properties exist in a wide range of dynamic scheduling problems that go beyond remote state estimation.

Remote state estimation of large-scale distributed dynamic processes plays an important role in Industry 4.0 applications. In this paper, by leveraging the theoretical results of structural properties of optimal scheduling policies, we develop a structure-enhanced deep reinforcement learning (DRL) framework for optimal scheduling of a multi-sensor remote estimation system to achieve the minimum overall estimation mean-square error (MSE). In particular, we propose a structure-enhanced action selection method, which tends to select actions that obey the policy structure. This explores the action space more effectively and enhances the learning efficiency of DRL agents. Furthermore, we introduce a structure-enhanced loss function to add penalty to actions that do not follow the policy structure. The new loss function guides the DRL to converge to the optimal policy structure quickly. Our numerical results show that the proposed structure-enhanced DRL algorithms can save the training time by 50% and reduce the remote estimation MSE by 10% to 25%, when compared to benchmark DRL algorithms.

Scheduling for multiple sensors to observe multiple systems is investigated. Only one sensor can transmit a measurement to the remote estimator over a Markovian fading channel at each time instant. A stochastic scheduling protocol is proposed, which first chooses the system to be observed via a probability distribution, and then chooses the sensor to transmit the measurement via another distribution. The stochastic sensor scheduling is modeled as a Markov decision process (MDP). A sufficient condition is derived to ensure the stability of remote estimation error covariance by a contraction mapping operator. In addition, the existence of an optimal deterministic and stationary policy is proved. To overcome the curse of dimensionality, the deep deterministic policy gradient, a recent deep reinforcement learning algorithm, is utilized to obtain an optimal policy for the MDP. Finally, a practical example is given to demonstrate that the developed scheduling algorithm significantly outperforms other policies.

Resilient control of cyber-physical systems (CPSs) against actuator and/or sensor attacks has been extensively researched. However, the existing research considers actuator attacks and sensor attacks separately and also designs resilient controllers based on complex nonlinear system models caused by unknown actuator and sensor attacks. This increases the difficulty in the analysis, computation, and control of CPSs under attacks. To address this issue, this article introduces an idea to deal with both actuator attacks and sensor attacks together with feedback linearization control. This simplifies the mathematical modeling of attacked CPSs, thus reducing the difficulty of resilient controller design. Then, from the simplified modeling, a composite controller is designed to enhance system resilience. It ensures the dynamic and steady-state performance of CPSs under attacks. Simulation studies are undertaken to demonstrate the effectiveness of the proposed method.

This paper considers a game-theoretic formulation of the covert communications problem with finite blocklength, where the transmitter (Alice) can randomly vary her transmit power in different blocks, while the warden (Willie) can randomly vary his detection threshold in different blocks. In this two-player game, the payoff for Alice is a combination of the coding rate to the receiver (Bob) and the detection error probability at Willie, while the payoff for Willie is the negative of his detection error probability. Nash equilibrium solutions to the game are obtained and shown to be efficiently computable using linear programming. For less covert requirements, our game-theoretic approach can achieve significantly higher coding rates than uniformly distributed transmit powers. We then consider the situation with an additional jammer, where Alice and the jammer can both vary their powers and jointly comprise one player, with Willie as the other player. The use of a jammer is shown in numerical simulations to lead to further significant performance improvements.

Recently, an efficient optimization strategy based on the sphere decoding algorithm (SDA) has been proposed to solve the optimal control problem underlying direct model predictive control (MPC) formulations with long horizons. However, as will be elucidated in this work, this optimization algorithm presents some limitations during transient operation of power converters, which increase the execution time required to obtain the optimal solution. To overcome this issue, the present work presents an improved version of the SDA for direct MPC that is not affected by transient operations of the power converter. The key novelty of the proposal is to reduce the execution time of the SDA when the system is in a transient by projecting the unconstrained optimal solution onto the envelope of the original finite control set. As evidenced by the simulation results, the proposed SDA is able to quickly compute the optimal solution for the long-horizon direct MPC during both steady-state and transient operation of the power converter.

This paper investigates an optimal energy allocation problem for multi sensor estimation of a random source where sensors communicate their measurements to a remote fusion centre (FC) over orthogonal fading wireless channels using uncoded analog transmissions. The FC reconstructs the source using the best linear unbiased estimator (BLUE). The sensors have limited batteries but can harvest energy and also transfer energy to other sensors in the network. A distortion minimization problem over a finite-time horizon with causal and non-causal information is studied and the optimal energy allocation policy for transmission and sharing is derived. Several structural necessary conditions for optimality are presented for the two sensor problem with non-causal information and a horizon of two time steps. Numerical simulations are included to illustrate the theoretical results.

This work presents a novel switched model predictive control (MPC) formulation for power converters. During transients, the proposed method uses horizon-one nonlinear finite control set (FCS) MPC to drive the system toward the desired reference. When the converter state is close to the reference, the controller switches to linear operation using an approximate converter model and a pulse-width modulation modulator. As an illustrative example, the proposed switched MPC is applied to a flying capacitor converter. As evidenced by experimental results, the proposed control strategy provides quick disturbance compensation, while giving excellent steady-state performance.

In this work, a cost function design based on Lyapunov stability concepts for finite control set model predictive control is proposed. This predictive controller design allows one to characterize the performance of the controlled converter, while providing sufficient conditions for local stability for a class of power converters. Simulation and experimental results on a buck dc-dc converter and a two-level dc-ac inverter are conducted to validate the effectiveness of our proposal.

In this paper, we consider robust source coding in closed-loop systems. In particular, we consider a (possibly) unstable LTI system, which is to be stabilized via a network. The network has random delays and erasures on the data-rate limited (digital) forward channel between the encoder (controller) and the decoder (plant). The feedback channel from the decoder to the encoder is assumed noiseless. Since the forward channel is digital, we need to employ quantization. We combine two techniques to enhance the reliability of the system. First, in order to guarantee that the system remains stable during packet dropouts and delays, we transmit quantized control vectors containing current control values for the decoder as well as future predicted control values. Second, we utilize multiple description coding based on forward error correction codes to further aid in the robustness towards packet erasures. In particular, we transmit M redundant packets, which are constructed such that when receiving any J packets, the current control signal as well as J-1 future control signals can be reliably reconstructed at the decoder. We prove stability subject to quantization constraints, random dropouts, and delays by showing that the system can be cast as a Markov jump linear system.

In this work, we propose a dual-stage control approach for a three-phase four-level Flying Capacitor Converter. The key idea of this proposal is to combine two control strategies to govern this converter. Thus, if the system state (output currents and floating voltages) is far from the desired reference, Finite-Control-Set Model Predictive Control is used to quickly lead the system towards the reference. Once the system state reaches a neighborhood of the reference, the propose control strategy switches to a PWM-based linear controller to finally achieve the desired reference in a gentle manner.

Finite-control-set model predictive control (FCS-MPC) is a novel and promising control scheme for power converters and drives. Many practical and theoretical issues have been presented in the literature, showing good performance of this technique. The present work deals with one of the most relevant aspects of any controller, namely, the steady-state operation. As will be shown, basic FCS-MPC formulations can be enhanced to achieve a reduced average steady-state error. As an illustrative example, we apply our proposal to a simple H-Bridge power converter. Experimental results were carried out to verify the performance obtained by the proposed predictive strategies.

We investigate the use of compressive sampling for networked feedback control systems. The method proposed serves to compress the control vectors which are transmitted through rate-limited channels without much deterioration of control performance. The control vectors are obtained by an ℒ1-ℒ2optimization, which can be solved very efficiently by FISTA (Fast Iterative Shrinkage-Thresholding Algorithm). Simulation results show that the proposed sparsity-promoting control scheme gives a better control performance than a conventional energy-limiting L2-optimal control.

We study state estimation via wireless sensor networks over fading channels affected by random packet loss. In the configuration examined, the sensors send their measurements to a single gateway, which decides upon the source coding scheme and the sensor transmitter power levels. The decision process is carried out on-line and adapts to changing channel conditions to achieve an optimal trade-off between estimation quality and sensor energy expenditure. In particular, if some channel conditions are poor, then the gateway commands the corresponding sensors to increase power levels and use multiple-description coding. Simulations based on measured channel data illustrate that the proposed scheme gives excellent results.

In this work, we construct a novel scheme for efficient perceptual coding of audio for robust communication between encoders and wireless hearing aids. To limit the physical size of the hearing aids and to reduce power consumption and thereby increase the lifetime expectancy of the batteries, the hearing aids are constrained to be of low complexity. We therefore provide an asymmetric strategy where most of the computational load is placed at the encoding side. We make use of multiple-description coding. This combats possible erasures on the wireless link between the encoder and the hearing aids without introducing significant delay. Furthermore, we employ psychoacoustically optimized noise-shaping quantizers based on the moving-horizon principle, which exploits a finite prediction horizon.

This paper presents novel results on scalar feedback quantization (SFQ) with uniform quantizers. We focus on general SFQ configurations where reconstruction is via a linear combination of frame vectors. Using a deterministic approach, we derive two necessary and sufficient conditions for SFQ to be optimal, i.e., to produce, for every input, a quantized sequence that is a global minimizer of the 2-norm of the reconstruction error. The first optimality condition is related to the design of the feedback quantizer, and can always be achieved. The second condition depends only on the reconstruction vectors, and is given explicitly in terms of the Gram matrix of the reconstruction frame. As a by-product, we also show that the the first condition alone characterizes scalar feedback quantizers that yield the smallest MSE, when one models quantization noise as uncorrelated, identically distributed random variables.

This paper describes a novel control strategy aimed at achieving good performance over an unreliable communication network affected by packet loss and variable transmission delays. The key ingredient in the method described here is to use the large data packet frame size of typical modern communication protocols to transmit control sequences which cover multiple data-dropout and delay scenarios. Stability and performance of the resultant scheme are addressed under nominal networked conditions. Simulations verify that the strategy performs exceptionally well under realistic conditions with noise and unmeasured disturbances.

Orthogonal frequency division multiple access (OFDMA) has been widely recognized as a promising solution for broadband wireless networks. Unfortunately, in OFDMA uplink scenarios, high peak-to-average power ratios (PARs) dramatically degrade the power efficiency of the mobile users. This turns out to be one of the most critical problems when implementing OFDMA systems. In this paper, we propose efficient PAR reduction schemes based upon tone reservation. We show by simulation that the PAR can be significantly reduced without incurring multiple- access interference and with a very small loss in bandwidth.

This paper formulates the channel equalization problem in the framework of constrained maximum-likelihood estimation. This allows us to highlight key issues including the need to summarize past data and to apply a finite alphabet constraint over a sliding optimization window. The approach adopted here leads to embellishments of the usual (nonadaptive) decision-feedback equalizer and its multistep extensions. It includes a provision for degrees of belief in past estimates, which addresses the problem of error propagation.

We consider joint data detection and channel estimation for multiple-input multiple-output orthogonal frequency division multiplexing systems. The expectation maximization algorithm is employed to capture the dynamics of a time-varying fading channel and also to recover the channel input. This is done iteratively: channel estimates are updated in the E-step, whilst the sphere decoding algorithm is used in the M-step to realize data recovery. Initial channel estimates are obtained through the use of a small number of pilot symbols. We show by simulation that the performance of the proposed algorithm can approach coherent detection with reasonable computational complexity.

This paper presents novel results on the joint problem of sampling and quantization of non bandlimited signals. Existing literature typically focuses either on sampling in the absence of quantization, or, conversely, studies quantization for already sampled signals. Our emphasis here is on the issues that arise al the intersection of these two design problems. We argue that the joint problem can be formulated and solved to any desired level of accuracy, using moving horizon optimization methods. We present several examples which show that consideration of the combined sampling and quantization problem gives important performance gains, relative to strategies which don't specifically address the interaction between these two problems