Adaptive hybird control of nonlinear systems

In the paper, a novel global control strategy to deal with nonlinear system with unknown function is presented. Firstly, a group of variable coefficient nonlinear differential equations, namely HX equations, were derived from the acquired sampled-data. And then the coresponding piecewise constant coefficient linear differential equations were deduced by using the marginal linearization method. Subsequently, the linear optimal regulator for each subsystem is designed to minimize a quadratic performance index. These controllers are melted together to realize the global control of original nonlinear system. To improve the performance, an adaptive control gain is appended. We apply the proposed approach to the output tracking control of Van der Pol equation. Step response test indicates that the proposed controller exhibits a prominent performance with shorter settling time, smaller overshoot and stronger robustness, compared with standard LQR.