Maciej Ławryńczuk

A Family of Model Predictive Control Algorithms With Artificial Neural Networks

A Family of Model Predictive Control Algorithms With Artificial Neural Networks This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used on-line to determine local linearisation and a nonlinear free trajectory. Single-point and multi-point linearisation methods are discussed. The MPC-NPL structure is far more reliable and less computationally demanding in comparison with the MPC-NO one because it solves a quadratic programming problem, which can be done efficiently within a foreseeable time frame. At the same time, closed-loop performance of both algorithm classes is similar. Finally, a hybrid MPC algorithm with Nonlinear Prediction, Linearisation and Nonlinear optimisation (MPC-NPL-NO) is discussed.

Computationally Efficient Model Predictive Control Algorithms

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Nonlinear predictive control based on neural multi-models

Nonlinear predictive control based on neural multi-models 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.

Nonlinear predictive control for Hammerstein-Wiener systems.

This paper discusses a nonlinear Model Predictive Control (MPC) algorithm for multiple-input multiple-output dynamic systems represented by cascade Hammerstein-Wiener models. The block-oriented Hammerstein-Wiener model, which consists of a linear dynamic block embedded between two nonlinear steady-state blocks, may be successfully used to describe numerous processes. A direct application of such a model for prediction in MPC results in a nonlinear optimisation problem which must be solved at each sampling instant on-line. To reduce the computational burden, a linear approximation of the predicted system trajectory linearised along the future control scenario is successively found on-line and used for prediction. Thanks to linearisation, the presented algorithm needs only quadratic optimisation, time-consuming and difficult on-line nonlinear optimisation is not necessary. In contrast to some control approaches for cascade models, the presented algorithm does not need inverse of the steady-state blocks of the model. For two benchmark systems, it is demonstrated that the algorithm gives control accuracy very similar to that obtained in the MPC approach with nonlinear optimisation while performance of linear MPC and MPC with simplified linearisation is much worse.

An efficient nonlinear predictive control algorithm with neural models and its application to a high-purity distillation process

This paper is concerned with a computationally efficient (suboptimal) nonlinear model-based predictive control (MPC) algorithm and its application to a high-purity high-pressure ethylene-ethane distillation column. A neural model of the process is used on-line to determine the local linearisation and the nonlinear free response. In comparison with general nonlinear MPC technique, which hinges on non-convex optimisation, the presented structure is far more reliable and less computationally demanding because it results in a quadratic programming problem, whereas its closed-loop control performance is similar.

Neural Networks in Model Predictive Control

This work is concerned with Model Predictive Control (MPC) algorithms in which neural models are used on-line. Model structure selection, training and stability issues are thoroughly discussed. Computationally efficient algorithms are recommended which use on-line linearisation of the neural model and need solving on-line quadratic optimisation tasks. It is demonstrated that they give very good results, comparable to those obtained when nonlinear optimisation is used on-line in MPC. In order to illustrate the effectiveness of discussed approaches, a chemical process is considered. The development of appropriate models for MPC is discussed, the control accuracy and the computational complexity of recommended MPC are shown.This work is concerned with Model Predictive Control (MPC) algorithms in which neural models are used on-line. Model structure selection, training and stability issues are thoroughly discussed. Computationally efficient algorithms are recommended which use online linearisation of the neural model and need solving on-line quadratic optimisation tasks. It is demonstrated that they give very good results, comparable to those obtained when nonlinear optimisation is used on-line in MPC. In order to illustrate the effectiveness of discussed approaches, a chemical process is considered. The development of appropriate models for MPC is discussed, the control accuracy and the computational complexity of recommended MPC are shown.

Software Implementation of Explicit DMC Algorithm with Improved Dependability

The paper presents an approach to improve the dependability of software implementation of the explicit DMC (Dynamic Matrix Control) Model Predictive Control (MPC) algorithm. The investigated DMC algorithm is implemented for a control system of a rectification column - a process with strong cross-couplings and significant time delays. The control plant has two manipulated inputs and two outputs. The fault sensitivity of the proposed implementation is verified in experiments with a software implemented fault injector. The experimental results prove the efficiency of proposed software improvements.

Modelling and predictive control of a neutralisation reactor using sparse support vector machine Wiener models

This paper has two objectives: (a) it describes the problem of finding a precise and uncomplicated model of a neutralisation process, (b) it details development of a nonlinear Model Predictive Control (MPC) algorithm for the plant. The model has a cascade Wiener structure, i.e. a linear dynamic part is followed by a nonlinear steady-state one. A Least-Squares Support Vector Machine (LS-SVM) approximator is used easily, it suffers from a huge number of parameters. Two pruning methods of the LS-SVM Wiener model are described and compared with a classical pruning algorithm. The described pruning methods make it possible to remove as much as 70% of support vectors without any significant deterioration of model accuracy. Next, the pruned model is used in a computationally efficient MPC algorithm in which a linear approximation of the predicted output trajectory is successively found on-line and used for prediction. The control profile is calculated on-line from a quadratic optimisation problem. It is demonstrated that the described MPC algorithmwith on-line linearisation based on the pruned LS-SVMWiener model gives practically the same trajectories as those obtained in the computationally complex MPC approach based on the full model with on-line nonlinear optimisation repeated at each sampling instant. & 2016 Elsevier B.V. All rights reserved.

Nonlinear State-Space Predictive Control With On-Line Linearisation And State Estimation

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.

Explicit nonlinear predictive control algorithms with neural approximation

This paper describes two nonlinear Model Predictive Control (MPC) algorithms with neural approximation. The first algorithm mimics the MPC algorithm in which a linear approximation of the model is successively calculated on-line at each sampling instant and used for prediction. The second algorithm mimics the MPC strategy in which a linear approximation of the predicted output trajectory is successively calculated on-line. The presented MPC algorithms with neural approximation are very computationally efficient because the control signal is calculated directly from an explicit control law, without any optimisation. The coefficients of the control law are determined on-line by a neural network (an approximator) which is trained off-line. Thanks to using neural approximation, successive on-line linearisation and calculations typical of the classical MPC algorithms are not necessary. Development of the described MPC algorithms and their advantages (good control accuracy and computational efficiency) are demonstrated in the control system of a high-purity high-pressure ethylene-ethane distillation column. In particular, the algorithms are compared with the classical MPC algorithms with on-line linearisation. & 2013 Elsevier B.V. All rights reserved.