Observer-Based Sampled-Data Model-Free Adaptive Control for Continuous-Time Nonlinear Nonaffine Systems With Input Rate Constraints

A sampled-data model-free adaptive control (SMFAC) strategy is proposed for continuous-time nonlinear nonaffine systems with input rate constraints. By using differential and integral mean value theorems as two basic mathematic tools, a sampled-data local dynamic linearization method is proposed at first to transform the continuous-time nonlinear nonaffine model into a sampled-data nonlinear affine I/O model, including a linear parametric term affined to the control input and a nonlinear uncertainty term. On this basis, we consequently propose an observer-based SMFAC (ObSMFAC) scheme, including a sampled-data parameter estimator to estimate the unknown partial derivatives and a sampled-data observer to estimate the residual nonlinear uncertainty, respectively. Note that the sampling period is incorporated explicitly in the proposed ObSMFAC which enhances the control performance by reducing its negative influence on the system stability. The constraint on the input rate is also considered in the control law as the transition condition of the input updating algorithms. The convergence of the proposed ObSMFAC is proved by using the contraction mapping principle. The simulation study demonstrates the theoretical results.