MPC Performances for Nonlinear Systems Using Several Linearization Models

It is now well known that dynamics of nonlinear systems can be lifted to higher or infinite dimensional spaces and represented as linear systems. We call such linear system representations and approximations, 'lifting linear' representations. Once we have such a linear system representation, we can apply linear control theorems to the previous nonlinear systems. The behavior of the lifting linear system are closer to the original systems than those of Taylor series approximations. In this paper, we compare performances of MPC (Model Predictive Control) for nonlinear systems using several different approximated linear models. When the systems are represented as linear systems, MPC can be solved by convex quadratic optimization methods if the constraints are linear. It will be shown that computational times become much shorter and the optimality of the solutions are improved using particular lifting linearizations.