中文摘要：

非线性系统分析的核心归结为系统状态方程的求解问题,对于一般非线性控制系统,通过引入由状态量、控制量与自变量时间坐标构成的“广义状态空间”,在广义状态空间一点将方程的右端展开为时间的Taylor级数,进一步直接积分获得非线性控制系统状态方程关于自变量时间的级数解.以球型机器人这种存在耦合的非线性系统为例,设计一种自适应滑模控制器,利用本文提出的解法得出了控制量与输出量的解析解,并仿真验证了方法的正确性.

英文摘要：

The kernel of nonlinear system analysis is the solving of system state equation. Therefore, for a general nonlin- ear control system,the concept of general time-state space comprising of state variables,control variable,and time t is introduced. In order to solve the state equation of nonlinear control systems,at the operation point of general time-state space ,the fight side of the state equation can be expanded as Taylor series about time. Then the series solution of the nonlinear control state equation, for which the solution is expressed in time series ,can be obtained by using direct-integrating approach. Sliding mode controller is es- tablished to control the typical coupling nonlinear system model of the spherical robot. Then we obtain the analytical solution of control and controlled variable by the direct-integrating method. The validity of this method is verified by experiment.