scholarly journals Nonlinear predictive control based on neural multi-models

2010 ◽  
Vol 20 (1) ◽  
pp. 7-21 ◽  
Author(s):  
Maciej Ławryńczuk ◽  
Piotr Tatjewski
Keyword(s):  
Predictive Control ◽  
Prediction Error ◽  
Control Policy ◽  
External Input ◽  
Multi Layer Perceptron ◽  
Computationally Efficient ◽  
Nonlinear Predictive Control ◽  
Nonlinear Optimisation ◽  
On Line ◽  
Auto Regressive

Nonlinear predictive control based on neural multi-modelsThis 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.

scholarly journals Efficient Nonlinear Predictive Control Based on Structured Neural Models

2009 ◽  
Vol 19 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Maciej Ławryńczuk
Keyword(s):  
Predictive Control ◽  
Neural Model ◽  
External Input ◽  
Computationally Efficient ◽  
Neural Models ◽  
Loop Control ◽  
Nonlinear Predictive Control ◽  
On Line ◽  
Auto Regressive ◽  
Narx Models

Efficient Nonlinear Predictive Control Based on Structured Neural ModelsThis 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.

scholarly journals Nonlinear State–Space Predictive Control with On–Line Linearisation and State Estimation

2015 ◽  
Vol 25 (4) ◽  
pp. 833-847 ◽  
Author(s):  
Maciej Ławryńczuk
Keyword(s):  
State Estimation ◽  
State Space ◽  
Predictive Control ◽  
Control Policy ◽  
Computationally Efficient ◽  
State Observers ◽  
Constant Type ◽  
The Future ◽  
On Line ◽  
Sampling Instant

Abstract 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.

scholarly journals Computationally Efficient Nonlinear Model Predictive Control Using the L1 Cost-Function

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5835
Author(s):  
Maciej Ławryńczuk ◽  
Robert Nebeluk
Keyword(s):  
Model Predictive Control ◽  
Cost Function ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Performance Indicator ◽  
Computationally Efficient ◽  
L1 Norm ◽  
On Line ◽  
Efficient Alternative ◽  
Classical Control

Model Predictive Control (MPC) algorithms typically use the classical L2 cost function, which minimises squared differences of predicted control errors. Such an approach has good numerical properties, but the L1 norm that measures absolute values of the control errors gives better control quality. If a nonlinear model is used for prediction, the L1 norm leads to a difficult, nonlinear, possibly non-differentiable cost function. A computationally efficient alternative is discussed in this work. The solution used consists of two concepts: (a) a neural approximator is used in place of the non-differentiable absolute value function; (b) an advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is obtained in place of the nonlinear one. Advantages of the presented solution are discussed for a simulated neutralisation benchmark. It is shown that the obtained trajectories are very similar, practically the same, as those possible in the reference scheme with nonlinear optimisation. Furthermore, the L1 norm even gives better performance than the classical L2 one in terms of the classical control performance indicator that measures squared control errors.

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