This paper addresses the problem of secure consensus tracking control for nonlinear leader-follower multi-agent systems, with a specific focus on safeguarding followers’ private information from external network eavesdroppers or internal untrusted neighbors. To tackle this problem, we first employ the dynamic linearization approximation technique to transform the nonlinear system models into equivalent linear forms that involve unknown time-varying pseudopartial derivatives. Then, a novel model-free secure distributed adaptive control (MFSDAC) framework is proposed using an encoding-decoding mechanism and Paillier encryption. Within this framework, we develop a secure distributed control scheme using a recursive form and design an adaptive updating law with a modified projection to estimate the time-varying pseudoparial derivatives. To enhance security, we introduce an adjustable parameter and a random integer into the distributed communication protocol, effectively preventing the disclosure of followers’ data during both network transmissions and controller evaluations. Additionally, parameter selection rules for the controller, quantizer, and adaptive updating law are provided, along with convergence analysis and guarantees against quantizer saturation. Finally, numerical simulations confirm that the proposed MFSDAC framework successfully achieves leader-following tracking and secure data transmission, even in the presence of external network eavesdroppers or internal untrusted neighbors. Note to Practitioners—Multi-agent systems (MASs) provide a versatile framework for modeling and understanding various real-world applications, including autonomous systems, traffic management, and distributed sensor networks. Designing effective control strategies for MASs is essential to enhance cooperation and coordination among agents, strengthen system-level resilience and adaptability, and tackle complex tasks that surpass the capabilities of individual agents. A key challenge in this area is ensuring network security and protecting individual privacy, especially in the presence of external eavesdroppers and untrusted internal neighbors. To tackle this challenge, we propose a model-free secure distributed adaptive control framework for nonlinear leader-follower MASs. This framework incorporates a confidential communication protocol that leverages homomorphic encryption to protect sensitive information. The proposed framework has undergone rigorous stability analysis and been validated through numerical simulations, demonstrating its feasibility and effectiveness in achieving secure consensus control of nonlinear MASs.

This correction addresses a citation oversight in the paper[1]. While[1]has cited recent publication about the model-free adaptive control (MFAC) theory, it omits foundational references that are critical to understanding the core principles underlying MFAC, such as dynamic linearization, generalized Lipschitz condition, and the time-varying pseudopartial derivative. To rectify this, the correction supplements[1]with citations to pioneering contributions in MFAC theory. This ensures proper attribution and provides readers with a deeper and more comprehensive understanding of the theoretical foundations of MFAC.

Homomorphic encryption enables secure control of networked systems with untrusted computing entities but greatly increases communication overhead compared with plaintext-based control. To address this, we propose a dynamic mode-switching secure control framework that alternates between plaintext and encrypted operations. In plaintext mode, sensor measurements are obfuscated using random dithered quantization, while in encrypted mode, measurements are fully encrypted to provide enhanced system security. To evaluate the framework, a worst-case eavesdropping scenario is introduced, where the adversary has complete knowledge of the system model and access to all plant-controller communications. Within this setting, we develop three switching strategies—periodic, random, and error-based—to govern the operational mode. Rigorous theoretical analysis establishes formal guarantees for both control performance and security, alongside deriving a critical parameter condition for decryption correctness. Ensuring the signal-to-noise ratio of the eavesdropper’s estimate remains below 10 dB, simulations show that periodic and random switching reduce communication by at least 30%. Error-based switching with an appropriate threshold (β = 1 × 10−4) achieves more than 70% reduction. These results confirm that the proposed framework effectively balances control performance, system security, and communication overhead, rendering it well-suited for resource-constrained networked systems.

This paper presents a stochastic sampling framework for privacy-aware data sharing, where a sensor observes a process correlated with private information. A sampler determines whether to retain or discard sensor observations, balancing the tradeoff between data utility and privacy. Retained samples are shared with an adversary who may attempt to infer the private process, with privacy leakage quantified using mutual information. The sampler design is formulated as an optimization problem with two objectives: (i) minimizing the reconstruction error of the observed process using the sampler’s output, (ii) reducing the privacy leakages. For a general class of processes, we show that the optimal reconstruction policy is deterministic and derive the optimality conditions for the sampling policy using a dynamic decomposition method, which enables the sampler to control the adversary’s belief about private inputs. For linear Gaussian processes, we propose a simplified design by restricting the sampling policy to a specific collection, providing analytical expressions for the reconstruction error, belief state, and sampling objectives based on conditional means and covariances. Additionally, we develop a numerical optimization algorithm to optimize the sampling and reconstruction policies, wherein the policy gradient theorem for the optimal sampling design is derived based on the implicit function theorem. Simulations demonstrate the effectiveness of the proposed method in achieving accurate state reconstruction, privacy protection, and data size reduction.

This paper addresses the secure control problem of uncertain networked control systems (NCSs) with an untrusted controller, such as a cloud-based controller. Using the Paillier cryptosystem, we propose a model-based adaptive encrypted networked control framework that incorporates joint static and dynamic quantization policies, and an encrypted controller. Within this framework, a novel adaptive updating law is designed to compensate for the nonlinearities caused by quantization and parameter estimation, contributing to the asymptotic convergence of the system state. Moreover, since no raw information is transmitted over the communication network or utilized inside the controller device, the security of NCSs is effectively ensured. Further, to tackle the issue of ciphertext expansion, we develop an event-based adaptive encrypted control scheme. This scheme employs two distinct triggering functions, which significantly reduces frequent information transmission and skillfully eliminates the comprehensive nonlinearities arising from quantization, estimation, and triggering. It is worth noting that, due to the integer-based nature of the Paillier cryptosystem, both the system state and the estimated controller gain should be quantized. This differs significantly from existing works on quantized-based adaptive control methods, where only a single variable, either the system state or the control input, is quantized. Finally, simulation results validate the effectiveness of the proposed encrypted control frameworks.

This paper studies the optimal hub-based platoon formation at hubs along a highway under decentralized, distributed, and centralized policies. Hubs are locations along highways where trucks can wait for other trucks to form platoons. A coordinator at each hub decides the departure time of trucks, and the released trucks from the hub will form platoons. The problem is cast as an optimization problem where the objective is to maximize the platooning reward. We first show that the optimal release policy in the decentralized case, where the hubs do not exchange information, is to release all trucks at the hub when the number of trucks exceeds a threshold computed by dynamic programming. We develop efficient approximate release policies for the dependent arrival case using this result. To study the value of information exchange among hubs on platoon formation, we next study the distributed and centralized platoon formation policies which require information exchange among hubs. To this end, we develop receding horizon solutions for the distributed and centralized platoon formation at hubs using the dynamic programming technique. Finally, we perform a simulation study over three hubs in northern Sweden. The profits of the decentralized policies are shown to be approximately$3.5\%$lower than the distributed policy and$8\%$lower than the centralized release policy. This observation suggests that decentralized policies are prominent solutions for hub-based platooning as they do not require information exchange among hubs and can achieve a similar performance compared with distributed and centralized policies.

In this paper, we develop a framework against inference attacks aimed at inferring the values of the controller gains of an active steering control system (ASCS). We first show that an adversary with access to the shared information by a vehicle, via a vehicular ad hoc network (VANET), can reliably infer the values of the controller gains of an ASCS. This vulnerability may expose the driver as well as the manufacturer of the ASCS to severe financial and safety risks. To protect controller gains of an ASCS against inference attacks, we propose a randomized filtering framework wherein the lateral velocity and yaw rate states of a vehicle are processed by a filter consisting of two components: a nonlinear mapping and a randomizer. The randomizer randomly generates a pair of pseudo gains which are different from the true gains of the ASCS. The nonlinear mapping performs a nonlinear transformation on the lateral velocity and yaw rate states. The nonlinear transformation is in the form of a dynamical system with a feedforward-feedback structure which allows real-time and causal implementation of the proposed privacy filter. The output of the filter is then shared via the VANET. The optimal design of randomizer is studied under a privacy constraint that determines the protection level of controller gains against inference attacks, and is in terms of mutual information. It is shown that the optimal randomizer is the solution of a convex optimization problem. By characterizing the distribution of the output of the filter, it is shown that the statistical distribution of the filter’s output depends on the pseudo gains rather than the true gains. Using information-theoretic inequalities, we analyze the inference ability of an adversary in estimating the control gains based on the output of the filter. Our analysis shows that the performance of any estimator in recovering the controller gains of an ASCS based on the output of the filter is limited by the privacy constraint. The performance of the proposed privacy filter is compared with that of an additive noise privacy mechanism. Our numerical results show that the proposed privacy filter significantly outperforms the additive noise mechanism, especially in the low distortion regime.

We study the strategic interaction among vehicles in a non-cooperative platoon coordination game. Vehicles have predefined routes in a transportation network with a set of hubs where vehicles can wait for other vehicles to form platoons. Vehicles decide on their waiting times at hubs and the utility function of each vehicle includes both the benefit from platooning and the cost of waiting. We show that the platoon coordination game is a potential game when the travel times are either deterministic or stochastic, and the vehicles decide on their waiting times at the beginning of their journeys. We also propose two feedback solutions for the coordination problem when the travel times are stochastic and vehicles are allowed to update their strategies along their routes. The solutions are evaluated in a simulation study over the Swedish road network. It is shown that uncertainty in travel times affects the total benefit of platooning drastically and the benefit from platooning in the system increases significantly when utilizing feedback solutions.

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner, in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with ∈ accuracy. First, we consider the class G of all N-player non-cooperative games with a continuous action space that admit at least one NE. Using information-theoretic inequalities, a lower bound on the complexity of solving G is derived which depends on the Kolmogorov 2∈-capacity of the constraint set and the total capacity of the communication channels. Our results indicate that the game class G can be solved at most exponentially fast. We next consider the class of all N-player non-cooperative games with at least one NE such that the players' utility functions satisfy a certain (differential) constraint. We derive lower bounds on the complexity of solving this game class under both Gaussian and non-Gaussian noise models. Finally, we derive upper and lower bounds on the sample complexity of a class of quadratic games. It is shown that the complexity of solving this game class scales according to Θ (1/∈2) where € is the accuracy parameter.

This paper studies the achievable throughput performance of the cognitive uplink under a limited primary cooperation scenario wherein the primary base station cannot feed back all interference channel gains to the secondary base station. To cope with the limited primary cooperation, we propose a feedback protocol called K-out-of-N feedback protocol, in which the primary base station feeds back only the KN smallest interference channel gains, out of N of them, to the secondary base station. We characterize the throughput performance under the K-out-of-N feedback protocol by analyzing the achievable multiuser diversity gains (MDGs) in cognitive uplinks for three different network types. Our results show that the proposed feedback mechanism is asymptotically optimum for interference-limited (IL) and individual-power-and-interference-limited (IPIL) networks for a fixed positive KN. It is further shown that the secondary network throughput in the IL and IPIL networks (under both the full and limited cooperation scenarios) logarithmically scales with the number of users in the network. In total-power-and-interference-limited (TPIL) networks, on the other hand, the K-out-of-N feedback protocol is asymptotically optimum for KN= Nδ, where δ ∈ (0, 1). We also show that, in TPIL networks, the secondary network throughput under both the limited and full cooperation scales logarithmically double with the number of users in the network. These results indicate that the cognitive uplink can achieve the optimum MDG even with limited cooperation from the primary network. They also establish the dependence of pre-log throughput scaling factors on the distribution of fading channel gains for different network types.

This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control. Each secondary user executes the derived power control policy in a distributed fashion by using local knowledge of its direct and interference channel gains such that the resulting aggregate (average) interference does not disrupt primary's communication. Then, the tight sum-rate scaling laws are derived as a function of the number of secondary users N under the optimum distributed power control policy. The fading models considered to derive sum-rate scaling laws are general enough to include Rayleigh, Rician and Nakagami fading models as special cases. When transmissions of secondary users are limited by both transmission and interference power constraints, it is shown that the secondary network sum-rate scales according to 1/enhlog log (N), where n_h is a parameter obtained from the distribution of direct channel power gains. For the case of transmissions limited only by interference constraints, on the other hand, the secondary network sum-rate scales according to 1/eγglog (N), where γgis a parameter obtained from the distribution of interference channel power gains. These results indicate that the distributed cognitive uplink is able to achieve throughput scaling behavior similar to that of the centralized cognitive uplink up to a pre-log multiplier 1/e, whilst primary's quality-of-service requirements are met. The factor 1/e can be interpreted as the cost of distributed implementation of the cognitive uplink.

This paper studies optimal distributed power allocation and scheduling policies (DPASPs) for distributed total power and interference limited (DTPIL) cognitive multiple access networks in which secondary users (SU) independently perform power allocation and scheduling tasks using their local knowledge of secondary transmitter secondary base-station (STSB) and secondary transmitter primary base-station (STPB) channel gains. In such networks, transmission powers of SUs are limited by an average total transmission power constraint and by a constraint on the average interference power that SUs cause to the primary base-station. We first establish the joint optimality of water-filling power allocation and threshold-based scheduling policies for DTPIL networks. We then show that the secondary network throughput under the optimal DPASP scales according to 1/enhlog log (N), where nhis a parameter obtained from the distribution of STSB channel power gains and N is the total number of SUs. From a practical point of view, our results signify the fact that distributed cognitive multiple access networks are capable of harvesting multiuser diversity gains without employing centralized schedulers and feedback links as well as without disrupting primary's quality-of-service (QoS).

In cognitive multiple access networks, primary-secondary feedback links are needed to convey secondary transmitter primary base station (STPB) channel gains from the primary base station (PBS) to the secondary base station (SBS). To reduce the amount of feedback exchange between PBS and SBS, this paper proposes a feedback control protocol called K-smallest channel gains (K-SCG) feedback protocol in which the PBS feeds back the KNsmallest STPB channel gains, out of N of them, to the SBS. We study the performance of K-SCG feedback protocol for total power and interference limited (TPIL) networks when transmit powers of secondary users (SUs) are optimally allocated. In TPIL networks, transmit powers of SUs are limited by an average total power constraint as well as a constraint on the average total interference power that they cause to the PBS. It is shown that for KN= Nδwith δ ∈ (0, 1), K-SCG feedback protocol is asymptotically optimal, i.e., secondary network throughput under K-SCG and full feedback protocols scales according to 1/nhlog log (N) where nhis a parameter obtained from the distribution of secondary transmitter secondary base station (STSB) channel power gains, and N is the number of SUs. It is also shown that for KN= o(N), the interference power at the PBS converges to zero almost surely and in mean as N becomes large. This result implies that for N large enough, the secondary network just requires the indices of SUs corresponding to the KNsmallest STPB channel gains for performing jointly optimal user scheduling and power allocation rather than the actual realizations of STPB channel gains.

Abstract-This paper focuses on the secondary network throughput scaling in cognitive radio networks when secondary users' transmission powers are optimally allocated. Throughput scaling laws are obtained for two different cognitive radio networks under two different communication scenarios. In the first network type called power-interference limited networks, secondary users' transmission powers are limited by both average total power constraint and the constraint on the average interference that they cause to primary users. In the second network type called interference limited networks, secondary users' transmission powers are only limited by average interference constraint. For both network types, an asymmetric communication scenario, in which the channels between secondary users and the secondary base station experience Rayleigh fading and those between secondary users and the primary base station experience Rician fading, and a symmetric communication scenario, in which both types of channels experience Rayleigh fading, are considered. It is shown that the secondary network throughput scales like log log ((K+1/eK)N) and log ((K+1/eK)N) for power-interference limited and interference limited networks, respectively, under the asymmetric communication scenario, where N is the number of secondary users and K >; 0 is the Rician factor. For the symmetric communication scenario, these scaling laws are given by log log (N) and log(N) for power-interference limited and interference limited networks, respectively.