Finite-time Reachability for Constrained, Partially Uncontrolled Nonlinear Systems

Abstract

This paper presents a technique to drive the state of a constrained nonlinear system to a specified target state in finite time, when the system suffers a partial loss in control authority. Our technique builds on a recent method to control constrained nonlinear systems by building a simple, linear driftless approximation at the initial state. We construct a partition of the finite time horizon into successively smaller intervals, and design controlled inputs based on the approximate dynamics in each partition. Under conditions that bound the length of the time horizon, we prove that these inputs result in bounded error from the target state in the original nonlinear system. As successive partitions of the time horizon become shorter, the error reduces to zero despite the effect of uncontrolled inputs. A simulation example on the model of a fighter jet demonstrates that the designed sequence of controlled inputs achieves the target state despite the system suffering a loss of control authority over one of its inputs.