This paper proposes an encrypted control algorithm to the average consensus problem for agents whose communication topology is represented by a strongly connected digraph. Unlike many applications that use encryptions, encrypted control systems require encryptions and decryptions repeatedly at every sampling time. Thus, it is beneficial if the control algorithm allows us to balance the cipher strength and processing time. This property is acquired by constructing a finite-level uniform quantizer whose sensitivity changes with the evolution of the system, designing its associated control law, and then combining it with the Paillier cryptosystem. Numerical analysis of the quantized control law is also presented.
This paper proposes an encrypted control algorithm to the average consensus problem for agents whose communication topology is represented by a strongly connected digraph. Unlike many applications that use encryptions, encrypted control systems require encryptions and decryptions repeatedly at every sampling time. Thus, it is beneficial if the control algorithm allows us to balance the cipher strength and processing time. This property is acquired by constructing a finite-level uniform quantizer whose sensitivity changes with the evolution of the system, designing its associated control law, and then combining it with the Paillier cryptosystem. Numerical analysis of the quantized control law is also presented.
This paper proposes a quantum framework for the design of communication topologies in consensus-based multi-agent systems. The communication graph is selected online by solving a mixed-integer quadratic program (MIQP) that minimizes a cost combining communication and distance penalties with degree-regularization terms, while enforcing exact connectivity through a flow-based formulation. To cope with the combinatorial complexity of this NP-hard problem, we develop a three-block ADMM scheme that decomposes the MIQP into a convex quadratic program in relaxed edge and flow variables, a pure binary unconstrained subproblem, and a closed-form auxiliary update. The binary subproblem is mapped to a quadratic unconstrained binary optimization (QUBO) Hamiltonian and approximately solved via quantum imaginary time evolution (QITE). The resulting time-varying, optimizer-generated Laplacians are applied to linear first- and second-order consensus dynamics. Numerical simulations on networks demonstrate that the proposed method produces connected topologies that satisfy degree constraints, achieve consensus, and incur costs comparable to those of classical mixed-integer solvers, thereby illustrating how quantum algorithms can be embedded as topology optimizers within closed-loop distributed control architectures.
This paper proposes a novel event-driven encrypted control framework for linear networked control systems (NCSs), which relies on two modified uniform quantization policies, the Paillier cryptosystem, and an event-triggered strategy. Due to the fact that only integers can work in the Pailler cryptosystem, both the real-valued control gain and system state need to be first quantized before encryption. This is dramatically different from the existing quantized control methods, where only the quantization of a single value, e.g., the control input or the system state, is considered. To handle this issue, static and dynamic quantization policies are presented, which achieve the desired integer conversions and guarantee asymptotic convergence of the quantized system state to the equilibrium. Then, the quantized system state is encrypted and sent to the controller when the triggering condition, specified by a state-based event-triggered strategy, is satisfied. By doing so, not only the security and confidentiality of data transmitted over the communication network are protected, but also the ciphertext expansion phenomenon can be relieved. Additionally, by tactfully designing the quantization sensitivities and triggering error, the proposed event-driven encrypted control framework ensures the asymptotic stability of the overall closed-loop system. Finally, a simulation example of the secure motion control for an inverted pendulum cart system is presented to evaluate the effectiveness of the theoretical results.
In this article, the secure consensus control problem is investigated for discrete-time multiagent systems (DTMASs) subjected to denial-of-service (DoS) attacks, where a model-free controller is proposed based on the Q-learning (QL) method. In an attack-free case, a dynamic decaying encryption key is designed to enable secure state transmission over communication channels through quantization-based encryption to prevent unauthorized access. Under DoS attacks, the system switches to a safe mode that partially halts communication, where the key transforms into a local scaling parameter to prevent quantizer saturation through dynamic expansion. The QL-driven algorithm is introduced to autonomously synthesize control gain matrices, without requiring system dynamics models. Moreover, sufficient conditions on the frequency and duration of DoS attacks are derived to ensure that the model-free controller guarantees consensus in DTMASs. Finally, simulation studies involving highly maneuverable aircraft technology vehicles (HiMATVs) are conducted, demonstrating that DTMASs equipped with the proposed approach exhibit significantly enhanced attack resistance compared to conventional methods.
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.
This paper presents a control-theoretic survey of four representative quantum consensus algorithms, with a focus on their convergence properties and implementation feasibility. The selected algorithms—ranging from gossip-based method to measurement-based feedback method and geometric control methods—exhibit fundamentally different convergence targets, including symmetric state consensus and directional alignment of Bloch vectors. Each approach is analyzed in terms of its dynamical structure, physical requirements, and control complexity. To show their performance, numerical simulations are conducted on a 3-qubit network under a fully connected topology. The results imply the trade-offs between convergence strength, coherence preservation, and practical implementability, offering insights for the design of distributed control protocols in quantum networks.
The cyber-security of multi-agent control systems has become vital in practice. To protect the communication process between the individual agents over TCP/IP networks, one must encrypt the messages to be sent, which is costly in a large-scale network when high-level security is demanded. To lessen the burden of heavy encryption and decryption processes, we introduce the Homomorphic Encryption to reduce the number of encryption/decryption terminals that are supposed to equip with every agent. The security is enhanced by the quantum key distribution technology, which can generate secret keys that are theoretically absolutely secure even against quantum computation. We proposed a hybrid method that make good use of the randomness of quantum keys, one-time pad and symmetric encryption to make sure the overall security of homomorphic encryption algorithms. Numerical simulations are provided to illustrate how our scheme.