Compared with the existing neural network (NN) or fuzzy logic system (FLS) based adaptive consensus methods, the proposed approach can greatly alleviate the computation burden because it needs only to update a few adaptive parameters online. In the multiagent agreement control, the system uncertainties derive from the unknown nonlinear dynamics are counteracted by employing the adaptive NNs; the state delays are compensated by designing a Lyapunov-Krasovskii functional. Finally, based on Lyapunov stability theory, it is demonstrated that the proposed consensus scheme can steer a multiagent system synchronizing to the predefined reference signals. Two simulation examples, a numerical multiagent system and a practical multimanipulator system, are carried out to further verify and testify the effectiveness of the proposed agreement approach.

In this article, a control scheme based on optimized backstepping (OB) technique is developed for a class of nonlinear strict-feedback systems with unknown dynamic functions. Reinforcement learning (RL) is employed for achieving the optimized control, and it is designed on the basis of the neural-network (NN) approximations under identifier-critic-actor architecture, where the identifier, critic, and actor are utilized for estimating the unknown dynamic, evaluating the system performance, and implementing the control action, respectively. OB control is to design all virtual controls and the actual control of backstepping to be the optimized solutions of corresponding subsystems. If the control is developed by employing the existing RL-based optimal control methods, it will become very intricate because their critic and actor updating laws are derived by carrying out gradient descent algorithm to the square of Bellman residual error, which is equal to the approximation of the Hamilton-Jacobi-Bellman (HJB) equation that contains multiple nonlinear terms. In order to effectively accomplish the optimized control, a simplified RL algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function, which is generated from the partial derivative of the HJB equation. Meanwhile, the design can also release the condition of persistence excitation, which is required in most existing optimal controls. Finally, effectiveness is demonstrated by both theory and simulation.

In this paper, a control technique named optimized backstepping is first proposed by implementing tracking control for a class of strict-feedback systems, which considers optimization as a design philosophy of the high-order system control. The basic idea is that designing the actual and virtual controls of backstepping is the optimized solutions of the corresponding subsystems so that overall control of the high-order system is optimized. In general, optimization control is designed based on the solution of Hamilton-Jacobi-Bellman equation, but solving the equation is very difficult due to the inherent nonlinearity and intractability. In order to overcome the difficulty, the neural network (NN)-based reinforcement learning strategy of actor-critic architecture is used. In every backstepping step, the actor and critic NNs are constructed for executing control behavior and evaluating control performance, respectively. According to the Lyapunov stability theorem, it is proven that the desired control performance can be obtained. Finally, a simulation example is carried out to further demonstrate the effectiveness of the proposed control approach.

In this paper, a tracking control approach for surface vessel is developed based on the new control technique named optimized backstepping (OB), which considers optimization as a backstepping design principle. Since surface vessel systems are modeled by second-order dynamic in strict feedback form, backstepping is an ideal technique for finishing the tracking task. In the backstepping control of surface vessel, the virtual and actual controls are designed to be the optimized solutions of corresponding subsystems, therefore the overall control is optimized. In general, optimization control is designed based on the solution of Hamilton-Jacobi-Bellman equation. However, solving the equation is very difficult or even impossible due to the inherent nonlinearity and complexity. In order to overcome the difficulty, the reinforcement learning (RL) strategy of actor-critic architecture is usually considered, of which the critic and actor are utilized for evaluating the control performance and executing the control behavior, respectively. By employing the actor-critic RL algorithm for both virtual and actual controls of the vessel, it is proven that the desired optimizing and tracking performances can be arrived. Simulation results further demonstrate effectiveness of the proposed surface vessel control.

In this study, a novel adaptive neural network (NN)‐based leader‐following consensus approach is proposed for a class of non‐linear second‐order multi‐agent systems. For the existing NN consensus approaches, to obtain the desired approximation accuracy, the NN‐based adaptive consensus algorithms require the number of NN nodes to must be large enough, and thus the online computation burden often are very heavy. However, the proposed adaptive consensus scheme can greatly reduce the online computation burden, because the adaptive adjusting parameters are designed in scalar form, which is the norm of the estimation of the optimal NN weight matrix. According to Lyapunov stability theory, the proposed approach can guarantee the leader‐following consensus behaviour of non‐linear second‐order multi‐agent systems to be obtained. Finally, a numerical simulation and a multi‐manipulator simulation are carried out to further demonstrate the effectiveness of the proposed consensus approach.

This paper addresses formation control with obstacle avoidance problem for a class of second-order stochastic nonlinear multiagent systems under directed topology. Different with deterministic multiagent systems, stochastic cases are more practical and challenging because the exogenous disturbances depicted by the Wiener process are considered. In order to achieve control objective, both the leader-follower formation approach and the artificial potential field (APF) method are combined together, where the artificial potential is utilized to solve obstacle avoidance problem. For obtaining good system robustness to the undesired side effects of the artificial potential, H _∞ analysis is implemented. Based on the Lyapunov stability theory, it is proven that control objective can be achieved, of which obstacle avoidance is proven by finding an energy function satisfying that its time derivative is positive. Finally, a numerical simulation is carried out to further demonstrate the effectiveness of the proposed formation schemes.