Fast linearization algorithm for predictive control

TL;DR: A new and fast linearization algorithm which uses identification procedure and bases on perturbation algorithm and discretizes obtained continuous-time linear model using modified scaling and squaring method is proposed.

Abstract: The applicability of nonlinear predictive control algorithms is limited by the necessity of on-line solving an optimization problem. Complexity follows from non-linearity of the model and from the extension of the prediction horizon, which result in non-convex constrained optimization problem. To overcome these barriers, dierent nonlinear optimization schemes have been proposed as e.g. in recent Zavada and Biegler (2009) where nonlinear programming has been extended through a simple reformulation of the nonlinear predictive control problem into advanced- step controller. However still, the heuristic simplification of nonlinear problem namely successive linearization or linearization along predicted trajectory is very competitive. The most important advantage is the constant processing time. The only problem arises if short sampling period is used and processing time has to be reduced. In this case numerical complexity follows from time-consuming linearization procedure. The paper proposes a new and fast linearization algorithm which uses identification procedure. It is assumed that non-linear noise-free model is given. Data for identification are created with the model impulse response. This allows for more flexible linearization where the vicinity of the operating point is discussed rather then point-sensitive linearization provided by the standard procedures. There are two key-simplifications which make the algorithm fast. The generic non-linear model is usually given in continuous time. The lack of the nonlinear discrete counterpart causes that the linearization has to be done first and discretization afterwards. The method proposed in the paper coupled these two operations. The second simplification comes from the Toeplitz-type of the matrix being inverted in the identification Least- Mean-Square algorithm. It is shown in the paper that the number of matrix elements is reduced usually 4-5 times. Then fast algorithms can be used to invert the final general-Toeplitz matrix (e.g. Martinsson-Rokhlin-Tygert, 2005). The eciency of the resulting algorithm is illustrated in the paper by comparison of the computation-time with standard linearization procedure, which bases on perturbation algorithm and discretizes obtained continuous-time linear model using modified scaling and squaring method.