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Design of robust positively invariant set for nonholonomic vehicle

The properties of the (robust) positively invariant sets play a fundamental role in variant techniques of (robust) control, such as the constrained control, robust analysis, synthesis and optimization. In this paper, we consider the robust control for the simultaneous tracking and regulation problem (STRP) of nonholonomic vehicle (whose control input is subject to the saturation constraint and the bounded disturbance), and design a robust positively invariant (RPI) set and an associated feedback controller. Under the associated feedback controller with saturation and bounded disturbance, the nonholonomic vehicle entering into the RPI set will stay in it forever and asymptotically achieve the desired control objective of STRP. These properties are illustrated by both the theoretical proof and the simulation example.