Proportional-Integral Funnel Control of Unknown Lower-Triangular Nonlinear Systems

This article is concerned with the high-performance control problem for the nonlinear systems in the sense of not only fast accurate reference tracking but also active damping of error oscillations caused by disturbances and unmodeled dynamics. A novel proportional-integral (PI) funnel control approach with rigorous theoretical insurance is put forward to handle this problem. In contrast with the existing solutions that work for weekly nonlinear systems or rely on available knowledge of the system nonlinearities, it is applicable to the lower-triangular systems with unknown multiplicative and additive nonlinearities, unmatched disturbances, and time-varying parameters. Moreover, it preserves the unique simplicity of PI control and funnel control, without the needs for function approximation, parameter identification, disturbance estimation, derivative calculation, or command filtering. The above theoretical findings are illustrated by a comparative simulation on a jet engine compressor.