Control of a Chain of Power Integrators with High-order Nonlinearity: A Bi-directional Approach

摘要

In this paper, we consider a control problem for a chain of power integrators with perturbed high-order nonlinearity. The main feature distinguishing the system considered in this study from those in prior works is that the high-order nonlinearity is bi-directional, in that it can be in either the lower triangular or upper triangular forms. To deal with such a system, we propose an unified switching controller wherein one of two dynamic gains is chosen depending on the form of nonlinearity. Our new control approach is to utilize dual adaptive gains where one gain is to suppress high-order nonlinearity and the other gain is to derive the system states into (small) bounds. With our control scheme, all states of the controlled systems are shown to be bounded. Moreover, a discussion is provided to demonstrate a way to achieve smaller bounds through the selection of control parameters. The effectiveness of our control scheme is illustrated via numerical examples.