A Continuous-Time Framework of Model-Free Adaptive Control for Nonlinear Plants

Continuous-time model-free adaptive control frame-works are proposed in this paper for solving tracking problems of unknown nonlinear plants described by high-order differential equations. To tackle situations where no form or structural information of plant models is present, the first step involves introducing continuous-time dynamic linearization techniques to create data models. Based on different ways for generating control inputs, two kinds of dynamic linearization processes for continuous-time nonlinear plants are established for the first time, where the nonlinear plants are parameterized by a time-varying linear data model. In the first dynamic linearization model (DLM), the control input is calculated by designating its derivative while the second one gives directly control inputs. Then, after acquiring different dynamic linearization models, based on traditional back-stepping methods, adaptive laws are proposed to learn the time-varying parameters in DLMs and the corresponding model-free adaptive controllers are designed. The conditions on designable parameters for the proposed controllers are provided to ensure semi-global practical stabilization and arbitrarily desirable ultimate tracking accuracy. Moreover, to eliminate the effects of unknown equilibrium points on tracking accuracy, a continuous-time model-free adaptive controller with pure integral terms is proposed under the second dynamic linearization model. Finally, several practical and numerical examples are simulated to illustrate the feasibility and efficiency of the proposed results.