New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Control of a modified double inverted pendulum using machine learning based model predictive control

Abstract: A machine learning-based controller (MLC) has been developed for a modified double inverted pendulum on a cart (MDIPC). First, the governing differential equations of the system are derived using the Lagrangian method. Then, a dataset is generated to train and test the machine learning-based models of the plant. Different types of machine learning models such as artificial neural networks (ANN), deep neural networks (DNN), long-short-term memory neural networks (LSTM), gated recurrent unit (GRU), and recurrent neural networks (RNN) are employed to capture the system’s dynamics. DNN and LSTM are selected due to their superior performance compared to other models. Finally, different variations of the Model Predictive Controller (MPC) are designed, and their performance is evaluated in terms of running time and tracking error. The proposed control methods are shown to have an advantage over the conventional nonlinear and linear model predictive control methods in simulation.Communication présentée lors du congrès international tenu conjointement par Canadian Society for Mechanical Engineering (CSME) et Computational Fluid Dynamics Society of Canada (CFD Canada), à l’Université de Sherbrooke (Québec), du 28 au 31 mai 2023