Discrete-Time Local Value Iteration Adaptive Dynamic Programming: Convergence Analysis
研究了离散时间局部值迭代自适应动态规划算法的收敛性，允许任意半正定函数初始化，通过状态依赖学习率在状态子集更新，降低计算负担，证明在温和条件下迭代值函数收敛到最优。
In this paper, convergence properties are established for the newly developed discrete-time local value iteration adaptive dynamic programming (ADP) algorithm. The present local iterative ADP algorithm permits an arbitrary positive semidefinite function to initialize the algorithm. Employing a state-dependent learning rate function, for the first time, the iterative value function and iterative control law can be updated in a subset of the state space instead of the whole state space, which effectively relaxes the computational burden. A new analysis method for the convergence property is developed to prove that the iterative value functions will converge to the optimum under some mild constraints. Monotonicity of the local value iteration ADP algorithm is presented, which shows that under some special conditions of the initial value function and the learning rate function, the iterative value function can monotonically converge to the optimum. Finally, three simulation examples and comparisons are given to illustrate the performance of the developed algorithm.