未知饱和控制系统有穷域最优控制
Finite-horizon optimal control for unknown systems with saturating control inputs

针对带有饱和执行器且局部未知的非线性连续系统的有穷域最优控制问题, 设计了一种基于自适应动态 规划(ADP)的在线积分增强学习算法, 并给出算法的收敛性证明. 首先, 引入非二次型函数处理控制饱和问题. 其次, 设计一种由常量权重和时变激活函数构成的单一网络, 来逼近未知连续的值函数, 与传统双网络相比减少了计算 量. 同时, 综合考虑神经网络产生的残差和终端误差, 应用最小二乘法更新神经网络权重, 并且给出基于神经网络 的迭代值函数收敛到最优值的收敛性证明. 最后, 通过两个仿真例子验证了算法的有效性.
An adaptive dynamic programming (ADP)-based online integral reinforcement learning algorithm is designed for finite-horizon optimal control of nonlinear continuous-time systems with saturating control inputs and partially unknown dynamics. Moreover, the convergence of the algorithm is proved. Firstly, the control constraints are handled through nonquadratic function. Secondly, a single neural network (NN) with constant weights and time-dependent activation functions is designed in order to approximate the unknown and continuous value function. Compared with the traditional dual neural networks, the burden of computation by the single NN is lessened. Meanwhile, the NN weights are updated by the least square method with considering both the residual error and terminal error. Furthermore, the convergence of iterative value function on the base of NN is proved. Lastly, two simulation examples show the effectiveness of the proposed algorithm.