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- 주제어 : two-player zero-sum game. (검색결과 3 건)
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Sholeh Yasini,Mohammad Bagher Naghibi Sistani,Ali Karimpour 제어·로봇·시스템학회 2015 International Journal of Control, Automation, and Vol.13 No.1
This paper develops a concurrent learning-based approximate dynamic programming (ADP) algorithm for solving the two-player zero-sum (ZS) game arising in H∞ control of continuous-time (CT) systems with unknown nonlinear dynamics. First, the H∞ control is formulated as a ZS game and then, an online algorithm is developed that learns the solution to the Hamilton-Jacobi-Isaacs (HJI) equation without using any knowledge on the system dynamics. This is achieved by using a neural network (NN) identifier to approximate the uncertain system dynamics. The algorithm is implemented on actor-critic-disturbance NN structure along with the NN identifier to approximate the optimal value function and the corresponding Nash solution of the game. All NNs are tuned at the same time. By using the idea of concurrent learning the need to check for the persistency of excitation condition is re-laxed to simplified condition. The stability of the overall system is guaranteed and the convergence to the Nash solution of the game is shown. Simulation results show the effectiveness of the algorithm.
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H∞ Suboptimal Tracking Controller Design for a Class of Nonlinear Systems
Yazdan Batmani 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.5
In this paper, a new technique is proposed to solve the H∞ tracking problem for a broad class of nonlinearsystems. Towards this end, based on a discounted cost function, a nonlinear two-player zero-sum differential(NTPZSD) game is defined. Then, the problem is converted to another NTPZSD game without any discount factorin its corresponding cost function. A state-dependent Riccati equation (SDRE) technique is applied to the latterNTPZSD game in order to find its approximate solution which leads to obtain a feedback-feedforward controllaw for the original game. It is proved that the tracking error between the system state and its desired trajectoryconverges asymptotically to zero under mild conditions on the discount factor. The proposed H∞ tracking controlleris applied to two nonlinear systems (the Vander Pol’s oscillator and the insulin-glucose regulatory system of type Idiabetic patients). Simulation results demonstrate that the proposed H∞ tracking controller is so effective to solvethe problem of tracking time-varying desired trajectories in nonlinear dynamical systems.
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Xiangquan Li,Zhengguang Xu,Yanrong Lu,Jiarui Cui,Lixin Zhang 제어·로봇·시스템학회 2021 International Journal of Control, Automation, and Vol.19 No.10
This paper addresses a pattern-moving-based modified model free adaptive control (PMFAC) scheme and illustrates the convergence of its tracking error for a class of nonlinear systems with unknown model and multi-threshold quantized observations. The basic idea is to consider the system’s quantization error as an external disturbance and an improved performance index function of control law is proposed from the perspective of twoplayer zero-sum game (TP-ZSG) based on the existed MFAC algorithms. The PMFAC scheme is established which mainly includes an improved tracking control law and a pseudo-partial derivative (PPD) estimation algorithm. Under certain conditions, the bounded convergence of system tracking error and the stability of PMFAC system with quantization errors can be guaranteed. The theoretical results are demonstrated by two numerical examples.
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