Efficient Model Predictive Control Algorithm with Fuzzy Approximations of Nonlinear Models

Advanced Construction of the Dynamic Matrix in Numerically Efficient Fuzzy MPC Algorithms

“…In the other method, the linearization of the process model for the MPC algorithm is obtained in each time step, and the linear prediction relative to control changes is formulated; see, e.g., [9,[33][34][35][36][37][38][39]. As a result, the optimization problem solved by the MPC algorithm in each time step is formulated as the quadratic one (like in LMPC algorithms).…”

“…In the algorithms using the fuzzy Takagi-Sugeno model, described in [36,39], both the free response and the dynamic matrix are obtained using the model obtained after the linearization. In the algorithms detailed in [33,37], the (classical) free response is calculated using the nonlinear model. In [12], the advanced free response, calculated using the nonlinear model (which can have any form of the model generating outputs on the basis of input signals), takes into consideration the previously calculated trajectory of the future control signals (it can be improved iteratively if needed; the approach is similar, though slightly different in details, to the iterative prediction improvement in the iterative learning-based approaches to batch control described in [40][41][42]); the dynamic matrix is generated using the easy-to-obtain fuzzy model.…”

“…Note that the values u m k+i|k−1 and ∆u m k+i|k−1 are known, as they were calculated in the last time step, and their influence on the output variables is contained in the free response (22), described in Section 2.1. Therefore, now the dynamic matrix (33) will be used to predict the influence of control corrections on the control plant outputs, and after using the free response (22) and the dynamic matrix (33), one obtains the following prediction:…”

Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

“…The other approach consists in online linearization of the process model at each MPC algorithm iteration; see for example, References [7,[30][31][32][33][34][35][36]. Then prediction is formulated in such a way that it is linear relative to decision variables in the optimization problem solved at each iteration of the algorithm.…”

Advanced Prediction Method in Efficient MPC Algorithm Based on Fuzzy Hammerstein Models

“…Moreover, in some cases numerical problems may occur. The drawbacks of the MPC algorithms formulated as nonlinear optimization problems caused that usually MPC algorithms utilizing a linear approximation of the control plant model, obtained at each iteration, are used [7,8,9,10,14]. Such algorithms are formulated as the standard quadratic programming problems.…”