Feedback Linearisation with State Constraints
For control engineers using FBL, this work provides a way to handle state constraints without increasing constraint complexity, though it is an incremental extension of existing FBL techniques.
This paper addresses the challenge of state constraints in feedback linearisation (FBL) by augmenting system dynamics before applying FBL, and overcomes ill-defined relative degrees at constraint boundaries using a switching FBL controller. Numerical experiments demonstrate the method's capability.
Feedback Linearisation (FBL) is a widely used technique that applies feedback laws to transform input-affine nonlinear control systems into linear control systems, allowing for the use of linear controller design methods such as pole placement. However, for problems with state constraints, controlling the linear system induced by FBL can be more challenging than controlling the original system. This is because simple state constraints in the original nonlinear system become complex nonlinear constraints in the FBL induced linearised system, thereby diminishing the advantages of linearisation. To avoid increasing the complexity of state constraints under FBL, this paper introduces a method to first augment system dynamics to capture state constraints before applying FBL. We show that our proposed augmentation method leads to ill-defined relative degrees at state constraint boundaries. However, we show that ill-defined relative degrees can be overcome by using a switching FBL controller. Numerical experiments illustrate the capabilities of this method for handling state constraints within the FBL framework.