An effective scheme is presented to design the nearly optimal control for continuous-time (C-T) nonlinear systems. The generalized fuzzy hyperbolic model (GFHM) is used to approximate the solution of the Hamilton-Jacobi-Bellman (HJB) equation (i.e., the value function) for the first time. Further, the approximate solution is utilized to obtain the nearly optimal control. The value function is estimated by only using single GFHM, which captures the mapping between the state and value function. First, we illustrate the design process for the nearly optimal control involving nonlinear systems. Then stability conditions and conservatism analysis are given, and the approximate errors are proven to be uniformly ultimately bounded (UUB). Finally, a numerical example illustrates the effectiveness of our method and an example compared with the adaptive method based on dual neural-network models is used to demonstrate the advantages of our method.%为连续非线性系统提出了一种有效的最优控制设计方法.广义模糊双曲模型(Generalized fuzzy hyperbolic model,GFHM)首次作为逼近器用来估计HJB (Hamilton-Jacobi-Bellman)方程的解(值函数,即它是状态与代价函数之间的映射),然后,利用该近似解获得最优控制.本文方法只需要一个GFHM估计值函数.首先,阐述了对于连线非线性系统最优控制的设计过程；然后,证明了逼近误差是一致最终有界的(Uniformly ultimately bounded,UUB)；最后,一个数值例子验证了本文方法的有效性.另一个例子通过与神经网络自适应动态规划的方法作比较,演示了本文方法的优点.
展开▼
