Optimal model predictive control solution approximation using Takagi Sugeno for linear and a class of nonlinear systems

The universal approximation property of Takagi-Sugeno fuzzy systems is exploited here to build a fuzzy approximation of the optimal solution of linear and nonlinear model predictive control (MPC). The nonlinear systems considered are affine in the control law. The fuzzy approximator introduced prese...

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Bibliographic Details
Published in:International journal of dynamics and control 2022-08, Vol.10 (4), p.1265-1278
Main Authors: Boumaza, Hamza, Belarbi, Khaled
Format: Article
Language:English
Subjects:
Approximation
Complexity
Control
Control and Systems Theory
Control systems
Control theory
Dynamical Systems
Engineering
Feedback control
Fuzzy control
Fuzzy systems
Mathematical analysis
Nonlinear control
Nonlinear systems
Predictive control
Stability analysis
State feedback
Vibration
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Summary:The universal approximation property of Takagi-Sugeno fuzzy systems is exploited here to build a fuzzy approximation of the optimal solution of linear and nonlinear model predictive control (MPC). The nonlinear systems considered are affine in the control law. The fuzzy approximator introduced presents some properties not generally shown by the previous approximators. In particular it is constituted by a set of state feedback control laws which are merged to obtain the final nonlinear control law. The constructed control law is very similar to the explicit solution of the linear MPC. The a posteriori stability is analysed based on a novel theoretical test previously published for both the linear and nonlinear MPC. Examples treated in the simulation part have shown the prompt and the good results which prove the effectiveness of the developed control strategy.
ISSN:2195-268X
2195-2698
DOI:10.1007/s40435-021-00875-4