For the first time, this paper addresses the problem of adaptive output-feedback control for a class of uncertain stochastic nonlinear strict-feedback systems with time-varying delays using neural networks (NNs). The circle criterion is applied to designing a nonlinear observer, and no linear growth condition is imposed on nonlinear functions depending on system states. Under the assumption that time-varying delays exist in the system output, only an NN is employed to compensate for all unknown nonlinear terms depending on the delayed output, and thus, the proposed control algorithm is more simple even than the existing NN backstepping control schemes for uncertain systems described by ordinary differential equations. Three examples are given to demonstrate the effectiveness of the control scheme proposed in this paper.

This brief addresses the problem of designing adaptive neural network tracking control for a class of strict-feedback systems with unknown time-varying disturbances of known periods which nonlinearly appear in unknown functions. Multilayer neural network (MNN) and Fourier series expansion (FSE) are combined into a novel approximator to model each uncertainty in systems. Dynamic surface control (DSC) approach and integral-type Lyapunov function (ILF) technique are combined to design the control algorithm. The ultimate uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. Two simulation examples are provided to illustrate the feasibility of control scheme proposed in this brief.

This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag–Leffler stable if there is a convex and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation.

A distributed algorithm is presented in this technical paper under directed communication networks, which is used to solve the economic dispatch problem in fixed time in smart grid systems. A new globally fixed-time stability theory (Lemma 3) is first given in this paper, which contains a new upper bound for the estimation of the settling time. Moreover, the fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization theory, the new lemma and Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, numerical simulations show the effectiveness and advantages of the distributed fixed-time optimization algorithm.

This paper proposes a nonlinear observer-based approach to address the robust cooperative tracking problem and application for heterogeneous spacecraft systems. By introducing appropriate assumptions, a weight average estimation is proposed to construct a class of distributed nonlinear observers for heterogeneous spacecraft systems with a target whose dynamics are available only to a few chasers. By synthesizing the observer dynamics among the neighbors, a novel cooperative tracking controller is developed to address nonidentical parameters both in model uncertainties and nonlinear dynamics. Then, the robust consensus tracking problem can be solved if the cooperative behaviors between the chasers and their observers can be achieved synchronically. A special case of the identical model uncertainty and nonlinear dynamics scenario is also discussed. As applications of the proposed nonlinear observer-based approaches, the controller and observer design of heterogeneous spacecraft attitude control and formation flying systems are revisited. Numerical simulations with a nonlinear dynamics model of spacecraft attitude control and formation flying system demonstrate the effectiveness of th

As unmanned aerial vehicles (UAVs) play an increasingly significant role in modern society, using reinforcement learning to build safe multi-UAV navigation algorithms has become a hot topic. One of the major issues is coordinating multi-UAV to navigate safely in complicated and unknown 3D environments. The current decentralized navigation systems suffer from the challenges of partially observable properties in unknown environments and unstable environments, resulting in poor learning effects. In this paper, we proposed a new multi-agent recurrent deterministic policy gradient (MARDPG) algorithm based on the depth deterministic policy gradient algorithm for controlling the navigation action of multi-UAV. Specifically, each critic network learns centrally so that each UAV can estimate the policies of other UAVs, thereby resolving the problem of slow convergence caused by the unstable environment. Decentralized execution eliminates the need for communication resources between UAVs. Sharing parameters in critics network accelerates training. The added LSTM network enables UAVs to use historical exploration information to improve the prediction of action values without being trapped by local traps. Finally, thorough simulation results in a realistic simulation environment were provided to demonstrate the superiority in terms of convergence and efficacy over the state-of-the-art DRL approach.