针对时变轨迹的非线性仿射系统的鲁棒近似最优跟踪控制

Robust approximate optimal tracking control of time-varying trajectory for nonlinear affine systems

针对非线性连续系统难以跟踪时变轨迹的问题,本文首先通过系统变换引入新的状态变量从而将非线性系统的最优跟踪问题转化为一般非线性时不变系统的最优控制问题,并基于近似动态规划算法(ADP)获得近似最优值函数与最优控制策略.为有效地实现该算法,本文利用评价网与执行网来估计值函数及相应的控制策略,并且在线更新二者.为了消除神经网络近似过程中产生的误差,本文在设计控制器时增加一个鲁棒项;并且通过Lyapunov稳定性定理来证明本文提出的控制策略可保证系统跟踪误差渐近收敛到零,同时也验证在较小的误差范围内,该控制策略能够接近于最优控制策略.最后给出两个时变跟踪轨迹实例来证明该方法的可行性与有效性.

For continuous time nonlinear systems, it is difficult to track their time-varying trajectory. To deal with this problem, we use a system transformation to introduce a new state variable for converting the optimal tracking problem of nonlinear systems into optimal control problem of general nonlinear time-invariant systems. For this system, we obtain the approximate optimal value function and the approximate optimal control policy based on approximate dynamic program- ming （ADP）. Then, we use the critic network and the actor network to estimate the value function and the corresponding control strategy, and update both of them online. Besides, a robust control term is added to the controller to eliminate the residual errors generated in the process of neural network approximation. By using the Lyapunov stability theorem, we prove that the proposed control strategy can guarantee the tracking error to converge asymptotically to zero, and the control strategy is close to the optimal control strategy when the error is in a small bound. Finally, simulations of two time-varying trajectory tracking examples show the feasibility and effectiveness of the proposed method.