An off-line MPC strategy for nonlinear systems based on SOS programming

A novel moving horizon control strategy for input-saturated nonlinear polynomial systems is proposed. The control strategy makes use of the so called sum-of-squares (SOS) decomposition, i.e. a convexification procedure able to give sufficient conditions on the positiveness of polynomials. The complexity of SOS based numerical methods is polynomial in the problem size and, as a consequence, computationally attractive. SOS programming is used here to derive an "off-line" model predictive control (MPC) scheme and analyze in depth its relevant properties. The main contribution here is to show that such an approach may lead to less conservative MPC strategies than most existing methods based on global linearization approaches. An illustrative example is provided to show the effectiveness of the proposed SOS-based algorithm. © 2009 Springer Berlin Heidelberg.