Fast Linearization Algorithm for Predictive Control

The applicability of nonlinear predictive control algorithms is limited by the necessity of on-line solving an optimization problem. Complexity follows from nonlinearity of the model and from the extension of the prediction horizon, which result in constrained non-convex optimization problem. The common heuristic simplification bases on linear approximation, well-known as successive linearization or linearization along prediction trajectory. However still, the control algorithm can be numerically to complex, especially in fast sampling cases, mainly because of linearization procedure. The paper proposes a new and fast linearization algorithm using identification procedure. The non-linear noise-free model is assumed to be given. Impulse response of nonlinear model creates identification data and allows for flexible linearization where the vicinity of the operating point is discussed rather then point-sensitive linearization as in the standard procedures. There are two key-simplifications that makes the algorithm fast. The generic nonlinear model is usually given as time-continuous. 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 efficiency 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.