This paper presents a novel adaptive dynamic programming (ADP) method to solve the optimal consensus problem for a class of discrete‐time multi‐agent systems with completely unknown dynamics. Different from the classical RL‐based optimal control algorithms based on one‐step temporal difference method, a multi‐step‐based (also call n‐step) policy gradient ADP (MS‐PGADP) algorithm, which have been proved to be more efficient owing to its faster propagation of the reward, is proposed to obtain the iterative control policies. Moreover, a novel Q‐function is defined, which estimates the performance of performing an action in the current state. Then, through the Lyapunov stability theorem and functional analysis, the proof of optimality of the performance index function is given and the stability of the error system is also proved. Furthermore, the actor‐critic neural networks are used to implement the proposed method. Inspired by deep Q network, the target network is also introduced to guarantee the stability of NNs in the process of training. Finally, two simulations are conducted to verify the effectiveness of the proposed algorithm.
On the base of traditional robust optimal design in statics, in this paper, by considering the system under the incentive force of the arbitrary time function, the dynamic response robust optimal design problem, when system dynamic response can only be calculated using numerical integration. Considering the environmental interference factors in a system, derived the expression of response with a small parameter perturbation finite element method. Through the tiny fluctuation frame system in a post and beam’s elastic modulus, realize the robust optimal design of the structural dynamic response, and using New-mark method for dynamic analysis, robust optimal design is applied in dynamic response optimization. Compared to the traditional optimal design’s result in a frame system, robust optimal design of the frame displayed a significant improvement in performance.
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