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Finite-horizon near optimal adaptive control of uncertain linear discrete-time systems

机译：不确定线性离散时间系统的有限水平近最优自适应控制

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In this paper, the finite-horizon near optimal adaptive regulation of linear discrete-time systems with unknown system dynamics is presented in a forward-in-time manner by using adaptive dynamic programming and Q-learning. An adaptive estimator (AE) is introduced to relax the requirement of system dynamics, and it is tuned by using Q-learning. The time-varying solution to the Bellman equation in adaptive dynamic programming is handled by utilizing a time-dependent basis function, while the terminal constraint is incorporated as part of the update law of the AE. The Kalman gain is obtained by using the AE parameters, while the control input is calculated by using AE and the system state vector. Next, to relax the need for state availability, an adaptive observer is proposed so that the linear quadratic regulator design uses the reconstructed states and outputs. For the time-invariant linear discrete-time systems, the closed-loop dynamics becomes non-autonomous and involved but verified by using standard Lyapunov and geometric sequence theory. Effectiveness of the proposed approach is verified by using simulation results. The proposed linear quadratic regulator design for the uncertain linear system requires an initial admissible control input and yields a forward-in-time and online solution without needing value and/or policy iterations. Copyright (C) 2014 John Wiley & Sons, Ltd.
机译：本文采用自适应动态规划和Q学习方法，以实时的方式提出了系统动力学未知的线性离散时间系统的有限水平近最优自适应调节。引入了一种自适应估计器（AE）来放松对系统动力学的要求，并使用Q学习对其进行调整。自适应动态规划中Bellman方程的时变解决方案通过利用时间相关的基函数来处理，而终端约束则作为AE更新定律的一部分纳入其中。卡尔曼增益通过使用AE参数获得，而控制输入通过使用AE和系统状态向量进行计算。接下来，为了放松对状态可用性的需求，提出了一种自适应观测器，以便线性二次调节器设计使用重构的状态和输出。对于时不变线性离散时间系统，闭环动力学变得非自治且涉及但通过使用标准Lyapunov和几何序列理论进行了验证。仿真结果验证了该方法的有效性。所提出的用于不确定线性系统的线性二次调节器设计需要初始可允许的控制输入，并能提供及时的在线解决方案，而无需进行值和/或策略迭代。版权所有（C）2014 John Wiley＆Sons，Ltd.

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