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•We show how Recurrent Neural Networks (RNN) can be used to design an Internal Model Control architecture for unknown dynamical systems•A first RNN is used to identify the plant’s model, and then another RNN is trained to approximate the model’s inverse•Recent stability results are leveraged to ensure the closed loop stability, while also satisfying input saturation constraints•The proposed architecture is suitable to the deployment to low power controllers, since no online computation is required Owing to their superior modeling capabilities, gated Recurrent Neural Networks, such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to discuss how these networks can be adopted for the synthesis of Internal Model Control (IMC) architectures. To this end, first a gated recurrent network is used to learn a model of the unknown input-output stable plant. Then, a controller gated recurrent network is trained to approximate the model inverse. The stability of these networks, ensured by means of a suitable training procedure, allows to guarantee the input-output closed-loop stability. The proposed scheme is able to cope with the saturation of the control variables, and can be deployed on low-power embedded controllers, as it requires limited online computations. The approach is then tested on the Quadruple Tank benchmark system and compared to alternative control laws, resulting in remarkable closed-loop performances.

Trained deep reinforcement learning (DRL) based controllers can effectively control dynamic systems where classical controllers can be ineffective and difficult to tune. However, the lack of closed‐loop stability guarantees of systems controlled by trained DRL agents hinders their adoption in practical applications. This research study investigates the closed‐loop stability of dynamic systems controlled by trained DRL agents using Lyapunov analysis based on a linear‐quadratic polynomial approximation of the trained agent. In addition, this work develops an understanding of the system's stability margin to determine operational boundaries and critical thresholds of the system's physical parameters for effective operation. The proposed analysis is verified on a DRL‐controlled system for several simulated and experimental scenarios. The DRL agent is trained using a detailed dynamic model of a non‐linear system and then tested on the corresponding real‐world hardware platform without any fine‐tuning. Experiments are conducted on a wide range of system states and physical parameters and the results have confirmed the validity of the proposed stability analysis (https://youtu.be/QlpeD5sTlPU). This research investigates the closed‐loop stability of dynamic systems controlled by deep reinforcement learning agents through Lyapunov analysis and a linear‐quadratic polynomial approximation of the trained agent. The study validates its approach with simulations and experiments on real‐world hardware, confirming the deep reinforcement learning's effectiveness and identifying critical operational thresholds and stability margins for practical applications.

In this work, an adaptive learning robust controller is proposed to suppress the vibration of offshore platforms, which are subject to waves, winds, varying control delays and parametric perturbations. To realize nonlinear uncertainty approximation under the bounded H∞ $H_\\infty$performance, the H∞ $H_\\infty$controller incorporates both an online adaptive part and an offline fixed part. The adaptive part constructed by neural networks adjusts online, while the fixed part is obtained by regulating the H∞ $H_\\infty$performance. Importantly, adaptive updating strategy does not require accurate values or upper bounds for real‐time control delay or uncertainty. Several comparable experiments demonstrate the feasibility and effectiveness in vibration‐suppression of the designed adaptive controller in shallow/deep water. This scheme significantly reduces system response variations due to structural and hydrodynamic uncertainty, as well as additional random environmental forces caused by winds. To realize nonlinear uncertainty approximation during vibration‐attenuation under the bounded H∞ $H_\\infty$performance, the proposed H∞ $H_\\infty$controller incorporates with the online adaptive part and the offline fixed part, respectively. The adaptive part is self‐adjusting based on neural network, and the fixed part is derived through minimizing the generalized H∞ $H_\\infty$disturbance‐rejection index.

This article addresses the challenge of adaptive neural‐based asynchronous control for nonhomogeneous Markov jumping systems with input dead zones. Time‐varying transition probabilities are precisely characterized using a two‐layer nonhomogeneous Markov process. A hidden Markov model is employed to detect system modes and resolve the asynchronous issues of controllers. Based on the detected modes and a neural network strategy, an adaptive asynchronous control strategy is proposed. The Lyapunov stability theory is used to prove that the system remains probabilistically bounded under this control law. Finally, the effectiveness of the control strategy is demonstrated through a simulation example. Time‐varying transition probabilities are precisely characterized using a two‐layer nonhomogeneous Markov process. A hidden Markov model is employed to detect system modes and resolve the asynchronous issues of controllers. Based on the detected modes and a neural network strategy, an adaptive asynchronous control strategy is proposed.

This paper investigates the learning and control problem of sampled‐data systems with only output measurements. A unified approach is presented by integrating the sampled‐data observer and deterministic learning. First, an adaptive radial basis function network (RBFN) learning controller with a sampled‐data observer is designed to track a recurrent reference model. Along the trajectory estimated by the observer, it is proven that the RBFN weights can exponentially converge to their ideal values with the satisfaction of a persistent excitation (PE) condition and the closed‐loop dynamics can be accurately learned during the output‐feedback process. Second, by using the learning results, a knowledge‐based output‐feedback controller is developed to improve the tracking performance. Further research shows that choosing appropriate parameters for the observer and RBFN can guarantee learning and control performance. The significance of the proposed approach is that the closed‐loop dynamics of the output‐feedback process can be accurately learned and further utilized to improve control performance. Simulation studies indicate the effectiveness and advantages of the learning control approach. By combining deterministic learning and sampled‐data observer, an adaptive radial basis function network (RBFN) controller is designed to achieve the tracking of a recurrent reference model, which leads to the satisfaction of the PE condition. During the stable tracking process, closed‐loop dynamics can be accurately identified/learned by the RBFN under the PE condition. Based on the learned dynamics, a new knowledge‐based controller is developed for another output feedback task, which reduces computational complexity and improves tracking performance.

The control problem for a class of stochastic nonlinear systems with both unknown control directions and unmodelled dynamics is investigated here for the first time. The technique of dynamics signal is adopted to cope with the unmodelled dynamics in the considered system. The unknown control directions problem are addressed by Nussbaum function. RBF neural networks are employed to approximate the lumped unknown functions, and regardless of the number of neural networks used and the order of the system, only one adaptive parameter requires to be adjusted. Dynamic surface control(DSC) is utilized to cope with the complexity explosion of the backstepping design. Hence, a novel neural control scheme is proposed by means of dynamics signal method, DSC technique and Nussbaum function. Stability analysis proves all closed‐loop signals are SGUUB by choosing the parameters appropriately, and the simulation results demonstrate the correctness and effectiveness of the proposed scheme.

In this study, an online adaptive optimal control scheme is developed for solving the infinite-horizon optimal control problem of uncertain non-linear continuous-time systems with the control policy having saturation constraints. A novel identifier-critic architecture is presented to approximate the Hamilton–Jacobi–Bellman equation using two neural networks (NNs): an identifier NN is used to estimate the uncertain system dynamics and a critic NN is utilised to derive the optimal control instead of typical action–critic dual networks employed in reinforcement learning. Based on the developed architecture, the identifier NN and the critic NN are tuned simultaneously. Meanwhile, unlike initial stabilising control indispensable in policy iteration, there is no special requirement imposed on the initial control. Moreover, by using Lyapunov's direct method, the weights of the identifier NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. Finally, an example is provided to demonstrate the effectiveness of the present approach.

In this study, a novel online adaptive dynamic programming (ADP)-based algorithm is developed for solving the optimal control problem of affine non-linear continuous-time systems with unknown internal dynamics. The present algorithm employs an observer–critic architecture to approximate the Hamilton–Jacobi–Bellman equation. Two neural networks (NNs) are used in this architecture: an NN state observer is constructed to estimate the unknown system dynamics and a critic NN is designed to derive the optimal control instead of typical action–critic dual networks employed in traditional ADP algorithms. Based on the developed architecture, the observer NN and the critic NN are tuned simultaneously. Meanwhile, unlike existing tuning laws for the critic, the newly developed critic update rule not only ensures convergence of the critic to the optimal control but also guarantees stability of the closed-loop system. No initial stabilising control is required, and by using recorded and instantaneous data simultaneously for the adaptation of the critic, the restrictive persistence of excitation condition is relaxed. In addition, Lyapunov direct method is utilised to demonstrate the uniform ultimate boundedness of the weights of the observer NN and the critic NN. Finally, an example is provided to verify the effectiveness of the present approach.

To solve the joint-angle and joint-velocity drift problems in cyclic motion of redundant robot manipulators, an acceleration-level drift-free (ALDF) scheme subject to a linear equality constraint is proposed, of which the effectiveness is analysed and proved via the theory of second-order system. The scheme is then reformulated into a quadratic program (QP). Furthermore, two recurrent neural networks (RNNs) are developed for solving the resultant QP problem. The first RNN solver is based on Zhang et al's neural-dynamic method and called Zhang neural network (ZNN), whereas the other is based on the gradient-descent method and called gradient neural network (GNN). Comparison results based on computer simulations between the ZNN and GNN solvers with a circular-path tracking task demonstrate that the ZNN solver has faster convergence and fewer errors. In addition, the hardware experiments of tracking a straight-line path and a rhombic path based on a six degrees of freedom manipulator validate the physical realisability and efficacy of the proposed ALDF scheme and the two RNN QP-solvers. Moreover, the position, velocity and acceleration error analyses indicate the accuracy of the proposed ALDF scheme and the corresponding RNN QP-solvers.

In this study, a theoretical framework for reconfigurable flight control is developed and applied to near space vehicle (NSV) attitude dynamics. First, NSV reentry mode is described. Second, an adaptive neural network observer is proposed, which ensures asymptotic convergence of the state observer error to zero under control effector damage and uncertainty. Next, a reconfigurable command-filter backstepping controller is designed based on the adaptive neural network observer. The authors focus is on the accommodation of the control effector damage, uncertainty and resulting disturbances. It is shown that the presented new control design results in asymptotic convergence of the attitude tracking error to zero. Finally, simulation results are given to demonstrate the effectiveness and potential of the proposed fault tolerant control scheme.