Data‐Driven Control: Theory and Applications

Data-driven control refers to the use of artificial intelligence (AI) and advanced control techniques to accomplish the control objectives without resorting to an accurate system model. It collects information from actual data and experience and focuses on utilizing data generated during the operation of a system to learn its behavior and performance, enabling the formulation of more adaptive and intelligent control strategies. For multi-agent systems, especially for multiple unmanned systems, data-driven control algorithms exhibit significant advantages in the execution of complex tasks. This special issue is mainly dedicated to promoting the theory of data-driven control and its applications in multiple unmanned systems. Multiple unmanned systems are generally required to accomplish various complex tasks in challenging environments, such as collaborative path planning, formation-containment control, and air-ground coordination. Data-driven control has the advantages of effectively handling complex systems with multiple variables and nonlinear behavior, optimizing control strategies to achieve specific objectives, and continuously improving performance by learning from data and past experiences. Typical data-driven control includes machine learning, fuzzy logic control, reinforcement learning (RL), model predictive control, and genetic algorithms. In recent years, significant progress has been made in learning-based algorithms. RL algorithms can be combined with optimal control to realize data-driven optimal control and adaptive robust control, which play a role in the autonomous control of multiple unmanned systems. Additionally, complex characteristics, such as uncertainties, time delay, actuator faults, and constraints in multiple unmanned systems, cannot be ignored. There exist RL solutions to these problems. Nevertheless, data-driven control and its practical applications for multiple unmanned systems remain an open problem. The first theme of this special issue focuses on the theoretical foundations and methodological advances of data-driven control. At the single-system level, several papers investigate data-driven optimal control that lay the groundwork for intelligent control design. In [1], fundamental mechanisms behind indirect and direct policy iteration were systematically studied for unknown discrete-time linear time-invariant systems, offering a system-theoretic understanding of convergence and robustness under certain levels of excitation. In [2], by integrating the offline training of Gaussian process regression and the online high-accuracy tracking control, a data-driven predictive control method was proposed by exploiting probabilistic uncertainty in the predicted outputs. The controlled object was further considered as a discrete-time periodic system in [3], and a value iteration-based adaptive dynamic programming (ADP) algorithm was developed to achieve suboptimal control, without knowledge of system dynamics and without requiring prior stabilizing gains. In [4], a self-triggered actor-critic RL framework was developed for optimal regulation of nonlinear systems to reduce computation and communication loads. The critic weights were updated continuously while the actor weights were adjusted intermittently, achieving performance optimization and closed-loop stability without continuous signal measurement. Building upon this, the applications of data-driven control methods were also studied for multi-agent systems. In [5], a distributed data-driven consensus control approach was designed for unknown continuous-time multi-agent systems under both noiseless and noisy data scenarios. In the proposed framework, each agent computes feedback gains from locally sampled data, achieving leader-follower consensus by solving low-dimensional linear matrix inequalities. In [6], an event-triggered data-driven method was proposed for multi-agent systems achieving distributed optimal consensus. By incorporating the event-triggered mechanism and a goal-critic-actor neural network (NN) structure, the goal representation heuristic dynamic programming method was designed to ensure closed-loop stability while alleviating the communication and computation burden. The second theme of this special issue focuses on resilient and secure data-driven control in uncertain environments. In [7], the data-driven method was extended to systems under process and measurement noise, where semidefinite programming was used to construct a robust finite-horizon linear quadratic Gaussian controller from noisy data. In [8], the distributed optimal consensus problem was studied via proportional-integral regulation for high-order nonlinear agents with nonidentical unknown control directions, bounded disturbances, and input saturation over weight-unbalanced directed networks. A consensus algorithm was established based on adaptive proportional-integral variables, Nussbaum-type functions, and NNs. In [9], the distributed consensus problem under switching topology and external disturbances was formulated as a zero-sum game problem, and a single-critic NN-based integral RL algorithm combined with experience replay was employed to achieve optimal consensus performance while relaxing the traditional persistent excitation requirement. In [10], a model-free funnel control strategy was designed for multi-agent systems under denial-of-service (DoS) attacks to guarantee that tracking errors remained within prescribed bounds despite jamming signals. In [11], the resilient asymmetric bipartite consensus problem of multi-agent systems with both cooperative and antagonistic interactions under DoS attacks was studied. An attack compensation mechanism and an extended discrete state observer were designed to establish a resilient data-driven control method ensuring secure consensus. In [12], the communication links can be tampered with and blocked by distributed sequential link attacks, and a fully distributed adaptive secure consensus protocol was developed to counter distributed sequential link attacks on communication links under general directed topologies. The third theme of this special issue focuses on data-driven perception, optimization, and decision-making strategies in complex systems. In [13], the stateful time-series modeling problem was addressed through two state change detection methods, the first enhancing the discrepancy-based approach with temporal encoder-decoder modeling and the second integrating Bayesian inference to balance between detection accuracy and efficiency. In [14], a hierarchical interactive graph variational inference model was developed for data-driven information perception in complex industrial networks. By organizing multi-layer latent structures to represent influencing factors and applying hierarchical attention learning to capture entity interactions, the framework enables generative self-supervised perception for downstream tasks. At the decision-making level, in [15], reciprocal decision-making in multi-player pursuit-evasion games was studied by modeling altruistic behavior through a modified performance function. The Nash policy under irrationality was derived with the maximum principle and approximated via RL, and conditions for altruism and reciprocity were established. In [16], a game-theoretic optimal control design was proposed for building's heating, ventilation, and air conditioning (HVAC) systems, where a model-free Q-learning algorithm solves a two-player non-zero-sum cooperative game using mass flow rate and supply air temperature as decision variables, achieving effective temperature tracking under unknown dynamics and disturbances. In [17], a multiplayer hierarchical decision-making problem in discrete-time nonlinear networks was addressed from the perspective of Nash-Stackelberg-Nash game. A two-level value iteration ADP algorithm was designed to solve the coupled Hamilton-Jacobi-Bellman equations without requiring known dynamics. In [18], transformer-based large models were applied to trajectory decision-making in complex multiagent systems with topological structures. By integrating transformer architectures into model-free control, the approach enhanced decision-making efficiency, safety, and reliability in dynamic environments. A significant theme of this special issue concerns the application of data-driven control methods in unmanned systems. In [19], a suboptimal tracking controller was developed for hypersonic flight vehicles under input delay, amplitude, and rate constraints. The constraints were transformed into inequalities, and the NN-based integral RL algorithm was used for data-driven control of the unconstrained augmented system. In [20], an anti-saturation optimization algorithm based on dynamic self-triggered ADP framework was proposed for bounded acceleration guidance interception. A nonlinear input-constrained guidance system with dynamic self-triggered control was designed to improve communication efficiency. In [21], a path planning method for unmanned surface vessels (USVs) in complex environments was developed using a dynamic artificial potential field to uniformly represent dynamic and static obstacles. Considering USV state constraints and international collision avoidance rules, an obstacle avoidance strategy was formulated, and the optimal path was obtained via a genetic algorithm. In [22], a passive defensive strategy was proposed for a target-attacker-defenders game, where defenders form around an optimal formation point instead of actively intercepting the attacker. The optimal point was determined through an evaluation model and optimized using an improved pigeon-inspired algorithm with a backbone exchange mechanism, enabling effective defense against fast attackers. In [23], a distributed formation control protocol for multiple quadrotors was developed by decoupling the outer position-velocity and inner attitude loops. Self-feedback and formation registration terms were introduced to regulate formation errors and motion trajectories. Flight experiments with an optical motion capture system verified the effectiveness of the proposed method. The final theme highlights the cross-domain and engineering applications of data-driven control. The data-driven methods in [14, 16, 17] were applied to industrial networks and energy management, showing their versatility in addressing large-scale, multi-objective, and information-intensive applications. Several studies further demonstrate the engineering potential of data-driven control. In [24], a robust inverse control strategy based on disturbance boundary estimation was proposed for dissolved oxygen regulation in wastewater treatment processes. A nonlinear disturbance observer and inverse controller were designed to handle internal and external disturbances, and experiments on the BSM1 benchmark verified the effectiveness and robustness of the developed control scheme. In [25], a hybrid energy storage control strategy combining Q-learning and fuzzy logic was developed for mitigating wind power fluctuations in grid-connected microgrids. By adaptively tuning the time constants of a two-stage low-pass filter, the approach improved power quality while accounting for practical constraints of energy storage systems. In [26], deep reinforcement learning was applied to tracking control in real-time hybrid simulation of structural systems, where physical and numerical components are coupled through boundary conditions. Three DRL-based controllers integrating time-delay compensation, feedback control, and complex neural architectures were developed and validated on a virtual benchmark, showing improved synchronization and model-free adaptability. This special issue demonstrates the broad scope and practical maturity of data-driven control, spanning from theoretical developments to real-world validation. The work in [23] conducted flight experiments of multiple quadrotors with an optical motion capture system to validate the effectiveness of the developed distributed formation control approach. The work in [2] performed physical experiments on a four-wheel-mecanum mobile robot platform to validate the applicability of the proposed data-driven control method. This special issue demonstrates the broad scope and practical maturity of data-driven control, spanning from theoretical developments to real-world validation. The work in [23] conducted flight experiments of multiple quadrotors with an optical motion capture system, and the work in [2] performed experiments on a four-wheel-mecanum mobile robot platform, showing the effectiveness and applicability of the developed data-driven control methods. Collectively, the abovementioned studies highlight the transition of data-driven control from theoretical frameworks to practical implementations, underscoring its growing role in advancing autonomous and intelligent control across diverse engineering domains. The authors declare no conflicts of interest.