Parametric Approach to Nonlinear Model Predictive Control

In model predictive control (MPC), a dynamic optimization problem (DOP) is solved at each sampling instance for a given value of the initial condition. In this work we show how the computational burden induced by the repetitive solving of the DOP for nonlinear systems can be reduced by transforming the unconstrained DOP to a suboptimal DOP with horizon one. The,approach is based on solving the stationary Hamilton-Jacobi-Bellman (HJB) equation along a given path while constructing control Lyapunov function (CLF). It is illustrated that for particular cases the problem can be further simplified to a set of differential algebraic equations (DAE) for which an explicit solution can be found without performing optimization.