A convexity‐based homotopy method for nonlinear optimization in model predictive control

This paper presents a convexity-based homotopy solution procedure to non-convex optimal control problems (OCP) arising in model predictive control. The approach deals with a special class of OCP formulations, where the dynamic system involved is control-affine and the objective is a penalty on deviations from a state reference trajectory. The non-convex OCP is modified by introducing a penalized pseudo state and a homotopy parameter which gradually transforms the original problem into a convex one. The method solves first this convex formulation and uses the result to initialize the solution of the next problem on the zero path, recovering the original OCP. The proposed methodology is evaluated for the benchmark control problem of an isothermal chemical reactor with Van de Vusse reactions and input multiplicity. For the simple case with control horizon one, the method is able to find the global solution due to the convex initialization, while local optimization techniques only lead to a local minimum.