A joint control protocol for a class of uncertain nonlinear systems with iteration-varying trial length

Abstract

This paper considers control protocol design for a class of discrete-time uncertain nonlinear systems with random iteration-varying trial length (RIVTL), where the input–output coupling parameter (IOCP) and the gain matrix of the system input are assumed to be unknown. Firstly, we prove that the control system either has complete learning ability or has no learning ability. And the learning ability is merely dependent on the IOCP. Secondly, by using the repetitiveness of the control system, a data-based observer is proposed to overcome the obstacle arising from the unknown IOCP and the unknown input matrix. Thirdly, a discrete-type random step function is utilised to model the RIVTL. Then, we develop a joint control protocol that is composed of a successive iterative learning scheme and a current state feedback, where iterative learning part is used to guarantee the convergence and state feedback part is used to improve the transient tracking performance. Finally, an example is delivered to validate the effectiveness of the findings.