State-Constrained Control of Nonlinear Systems in Regular Form

A method that enforces asymmetrical limits on part of the state of a nonlinear system in Regular Form is presented. To that end, a particular artificial potential function that incorporates the domain of interest is used and conditions for the stabilizability of a nonlinear system over a gradient vector field are introduced. Necessary and sufficient conditions are given for the state's first block to be enforced to stay within the set of allowed values by the state's second block; whenever such conditions hold, state's first block is said to be a constraintable vector. For all initial conditions inside the domain of interest, the resulting closed loop of a stabilizable system over the artificial potential function's gradient vector field shows a conservative behavior, i.e., the state of the system exhibits periodical responses. A geometrical approach is introduced to estimate an admissible lower bound for the constraints to be enforced on the state's first block. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.