Performance limitations in a class of single-input two-output nonlinear systems

This paper shows that there exists a structural limitation in reducing the integral of the squared regulation error in strict-feedback nonlinear systems with more outputs (that is, performance variables) than inputs. This limitation arises from the fact that, in these systems, some outputs are controlled only indirectly through other outputs with lower relative degree. It is then impossible to uniformly reduce the overall regulation cost to zero, the infimum value of which is characterised by a reduced-order optimal regulation problem. Although essentially nonlinear, the results are similar in nature and have direct connections with their linear counterparts.