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Nonlinear state-space predictive control with on-line linearisation and state estimation

100%
Ławryńczuk M.
International Journal of Applied Mathematics and Computer Science
|
2015
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tom 25
|
nr 4
833-847
EN
This paper describes computationally efficient model predictive control (MPC) algorithms for nonlinear dynamic systems represented by discrete-time state-space models. Two approaches are detailed: in the first one the model is successively linearised on-line and used for prediction, while in the second one a linear approximation of the future process trajectory is directly found on-line. In both the cases, as a result of linearisation, the future control policy is calculated by means of quadratic optimisation. For state estimation, the extended Kalman filter is used. The discussed MPC algorithms, although disturbance state observers are not used, are able to compensate for deterministic constant-type external and internal disturbances. In order to illustrate implementation steps and compare the efficiency of the algorithms, a polymerisation reactor benchmark system is considered. In particular, the described MPC algorithms with on-line linearisation are compared with a truly nonlinear MPC approach with nonlinear optimisation repeated at each sampling instant.
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Nonlinear predictive control based on neural multi-models

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Ławryńczuk M., Tatjewski P.
International Journal of Applied Mathematics and Computer Science
|
2010
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tom 20
|
nr 1
7-21
EN
This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to avoid nonlinear optimisation, in the discussed suboptimal MPC algorithm the neural multi-model is linearised on-line and, as a result, the future control policy is found by solving of a quadratic programming problem.
3
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Efficient nonlinear predictive control based on structured neural models

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Ławryńczuk M.
International Journal of Applied Mathematics and Computer Science
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2009
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tom 19
|
nr 2
233-246
EN
This paper describes structured neural models and a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on such models. The structured neural model has the ability to make future predictions of the process without being used recursively. Thanks to the nature of the model, the prediction error is not propagated. This is particularly important in the case of noise and underparameterisation. Structured models have much better long-range prediction accuracy than the corresponding classical Nonlinear Auto Regressive with eXternal input (NARX) models. The described suboptimal MPC algorithm needs solving on-line only a quadratic programming problem. Nevertheless, it gives closed-loop control performance similar to that obtained in fully-fledged nonlinear MPC, which hinges on online nonconvex optimisation. In order to demonstrate the advantages of structured models as well as the accuracy of the suboptimal MPC algorithm, a polymerisation reactor is studied.
4
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Soft computing in modelbased predictive control footnotemark

100%
Tatjewski P., Ławrynczuk M.
International Journal of Applied Mathematics and Computer Science
|
2006
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tom 16
|
nr 1
7-26
EN
The application of fuzzy reasoning techniques and neural network structures to model-based predictive control (MPC) is studied. First, basic structures of MPC algorithms are reviewed. Then, applications of fuzzy systems of the Takagi-Sugeno type in explicit and numerical nonlinear MPC algorithms are presented. Next, many techniques using neural network modeling to improve structural or computational properties of MPC algorithms are presented and discussed, from a neural network model of a process in standard MPC structures to modeling parts or entire MPC controllers with neural networks. Finally, a simulation example and conclusions are given.
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