基于零和博弈的级联非线性系统的跟踪控制

Tracking control of cascaded nonlinear systems based on the zero-sum game

针对带有不确定干扰的级联非线性系统的跟踪控制问题,将控制和干扰视为博弈的双方,在跟踪过程中将跟踪轨迹的最优性考虑在内,利用反推技术设计前馈控制器,将严格反馈系统的跟踪控制问题转化成等价的仿射系统的零和微分博弈问题;采用自适应动态规划(adaptive dynamic programming,ADP)技术,构建评价网络、控制网络和干扰网络实时在线学习,近似求解非线性零和微分博弈产生的HJI(hamilton-jacobi-isaacs)方程,进而得到值函数、控制策略和干扰策略。利用Lyapunov理论,证明了基于反推技术的零和微分博弈的收敛性和闭环系统的稳定性。仿真实例验证了该方法的有效性。

The tracking control problem of cascaded nonlinear systems with an uncertain interference is investigated.The control and interference are regarded as the two sides of the game,and the optimality of the tracking trajectory is taken into account in the tracking process.The feedforward controller is designed by using backstepping technique to convert the tracking problem of the strict feedback system into the zero-sum differential game problem of the equivalent affine system.Adaptive dynamic programming(ADP)technology is used to construct the evaluation network,control network and interference network in real-time online learning,and to solve approximately the Hamilton-Jacobi-Isaacs(HJI)equations generated by the nonlinear zero-sum differential games.Then value functions,control strategies and interference strategies are obtained.By using Lyapunov theory,the convergence of the zero-sum differential game based on the backstepping and the stability of the closed-loop system are proved.A simulation experiment is carried out to illustrate the effectiveness of the proposed method.