Adaptive Control of a Class of Nonlinear Discrete-Time Systems with Online Kernel Learning

An Online Kernel Learning based Adaptive Control (OKL-AC) framework for discrete-time affine nonlinear systems is presented in this paper. A sparsity strategy is proposed to control the complexity of OKL identification model, meanwhile to make a trade-off between the demanded tracking precision and the complexity of the control law. The forward increasing and backward decreasing learning stages are performed, both incorporating efficient recursive updating algorithms. Owing to these advantages, the adaptive control law based on the OKL identification model is easily obtained and can be efficiently updated. Numerical simulations show that the proposed simple OKL-AC strategy has satisfactory performance, including good tracking performance and fast learning ability, in both deterministic and stochastic environments.