Control of Nonlinear Systems with Partially Unknown Parameters

Professor Liu Jinkun's sliding mode control methodology provides an effective solution for controlling nonlinear systems with partially unknown parameters. The core concept of sliding mode control involves designing a sliding surface (hyperplane) where system states are forced to reach and maintain within this surface in finite time through control laws, thereby achieving robustness against uncertainties and external disturbances.

For nonlinear systems with partially unknown parameters, this approach handles uncertainties through adaptive mechanisms or boundary estimation techniques without requiring precise mathematical models. The disturbance rejection capability stems from the variable structure nature of sliding mode control - when system states deviate from the sliding surface, the control input instantly switches direction to forcefully pull the states back, effectively suppressing matched disturbances. In implementation, this typically involves designing switching functions using sign() or sat() functions to manage control discontinuities.

Practical applications require attention to chattering issues, which can be optimized through boundary layer methods or higher-order sliding mode techniques. This control strategy demonstrates outstanding performance in strongly nonlinear scenarios such as robotics and motor drives, effectively balancing performance and robustness. Code implementation often includes adaptive update laws for parameter estimation and saturation functions to smooth control signals.