Input to state stabilising nonlinear model predictive control based on QP

This paper proposes a framework for dealing with certain classes of nonlinear model predictive control (MPC) problems by solving a quadratic programming (QP) optimisation at each sampling time. This feature broadens the applicability of nonlinear MPC since many efficient tools for solving QP problems (both numerical algorithms and explicit solutions) are available. A key concept that enables this formulation, the input-state linear horizon (ISLH), is introduced. The ISLH characterises the length of the linear window in the relationship between the input and the state variables of a nonlinear system. In addition, the issue of input to state stability with respect to disturbance inputs is handled by incorporating a set of extra linear inequality constraints into the QP. Thus, the proposed scheme has two very attractive properties; namely, simplicity of the solution and guaranteed stability and robustness.