Fast quadratic model predictive control based on sensitivity analysis and Wolfe method

Abstract

Abstract This paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis‐based QMPC (SA‐QMPC) algorithm. It is proved that the computational complexity of SA‐QMPC is O(Nn2) for a region of the initial conditions and O(N2n2) for sufficiently small sampling time and all initial conditions, where N and n are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm.

Keywords

• computational complexity
• control theory
• predictive control
• quadratic programming
• sensitivity analysis