Sieci neuronowe w efektywnych obliczeniowo algorytmach regulacji predykcyjnej

• Autorzy: Ławryńczuk M.

Warianty tytułu

EN

Neural networks in computationally efficient model predictive control algorithms

• Języki publikacji: PL

Abstrakty

PL

Celem monografii jest szerokie ukazanie możliwości zastosowania sieci neuronowych w nieliniowych algorytmach regulacji predykcyjnej. Bezpośrednie użycie do predykcji modelu neuronowego prowadzi do nieliniowego zadania optymalizacji, które musi być rozwiązywane w każdej iteracji algorytmu. Obszarem zainteresowania pracy są algorytmy suboptymalne, w których do predykcji stosuje się cyklicznie obliczane przybliżenie liniowe modelu neuronowego. Wspólna cecha omawianych algorytmów jest efektywność obliczeniowa, gdyż zamiast złożonej obliczeniowo i zawodnej nieliniowej optymalizacji stosuje się optymalizację kwadratową. Omówiono dokładnie kilka, różniących się sposobem linearyzacji, suboptymalnych algorytmów regulacji predykcyjnej. Przedstawiono również wersje analityczne tych algorytmów, w których zamiast optymalizacji kwadratowej stosuje się mniej złożony obliczeniowo rozkład macierzy. Podano szczegóły implementacji omówionych algorytmów dla kilku klas modeli neuronowych: rozważa się klasyczne modele neuronowe (sieci perceptronowych z jedną warstwą ukrytą), neuronowe modele szeregowe (kaskadowe) o strukturze Hammersteina i Wienera, modele neuronowe w przestrzeni stanu oraz zespoły modeli neuronowych. Omówiono również algorytmy regulacji predykcyjnej z aproksymacją neuronową, których cechą jest brak cyklicznej linearyzacji modelu. Szczególnie efektywne obliczeniowo są wersje analityczne tych algorytmów, gdyż aproksymator neuronowy wyznacza współczynniki prawa regulacji, nie ma potrzeby wykonywania obliczeń typowych dla klasycznych algorytmów analitycznych. Omówiono także modyfikacje przedstawionych algorytmów suboptymalnych, mające na celu zagwarantowanie stabilności i odporności. Końcowa część monografii poświęcona jest współpracy algorytmów regulacji predykcyjnej oraz algorytmów optymalizacji punktu pracy. Zaprezentowano trzy struktury sterowania z cykliczną linearyzacją oraz szczegóły implementacji dla trzech klas modeli neuronowych. Przedstawione wyniki symulacji świadczą o dużej skuteczności omawianych algorytmów suboptymalnych. Dla kilku reprezentatywnych silnie nieliniowych procesów technologicznych, takich jak reaktory chemiczne i kolumna destylacyjna (dla których klasyczne liniowe algorytmy regulacji predykcyjnej działają nieprawidłowo), trajektorie algorytmów suboptymalnych są bardzo podobne do trajektorii otrzymanych w "idealnym" algorytmie z nieliniową optymalizacją. Skuteczność jednego z algorytmów suboptymalnych została również potwierdzona przez działający prototyp systemu wentylacji przeciwpożarowej, dla którego podano wyniki rzeczywistych eksperymentów.

EN

The objective of this monograph is to thoroughly discuss possibilities of using neural networks in nonlinear Model Predictive Control (MPC) algorithms. When a neural model is directly used for prediction in MPC, a nonlinear optimisation problem must be solved on-line at each sampling instant. This book is concerned with suboptimal MPC algorithms, in which a linear approximation of the neural model is successively calculated on-line and used for prediction. Thanks to linearisation, the discussed algorithms are computationally efficient, since quadratic optimisation is used instead of computationally demanding and unreliable nonlinear optimisation. A few suboptimal MPC algorithms are discussed, with different linearisation methods. Explicit (analytical) algorithms are also presented, in which quadratic optimisation is not used but the solution is found from a matrix decomposition task, which is less computationally demanding. Implementation details of the discussed algorithms are given for a few classes of neural models : (perceptron networks with one hidden layer), neural Hammerstein and Wiener models, state-space neural models as well as neural multi-models are considered. MPC algorithms with neural approximation are next discussed, in which on-line model linearisation is not used. Explicit versions of such algorithms are particulary very computationally efficient since the neural approximator directly determines on-line coefficients of the control law, it is not necessary to carry out calculations typical of the classical explicit MPC algorithms. Modifications of the suboptimal MPC algorithms are also discussed which guarantee stability and robustness. Finally, the problem of cooperation between the discussed MPC algorithms and set-point optimisation is discussed. Three different system structures are presented with on-line linearisation, implementation details for three classes of neural models are given. Presented simulation results indicate that the discussed suboptimal MPC algorithms are very efficient. For a few representative highly nonlinear technological processes, such as chemical reactors and a distillation column (for which the classical linear MPC algorithms do not work properly), trajectories of the suboptimal algorithms are very silmilar to trajectories obtained in the "ideal" MPC scheme with on-line nonlinear optimisation. Efficiency of a chosen suboptimal MPC algorithm has been confirmed by a successfully working prototype of a fire protection ventilation system, for which results of real experiments are given.

Słowa kluczowe

PL

automatyka; regulacja predykcyjna; optymalizacja punktu pracy; modele nieliniowe; sieci neuronowe; optymalizacja

EN

process control; model predictive control; set-point optimisation; nonlinear models; neural networks; optimisation

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2012
• Tom: z. 180
• Strony: 5--317
• Opis fizyczny: Bibliogr. 359 poz., tab., rys., wykr.

Twórcy

autor

Ławryńczuk M.

• Instytut Automatyki i Informatyki Stosowanej

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