In this work, two modifications on Levenberg-Marquardt algorithm for feedforward neural networks are studied. One modification is made on performance index, while the other one is on calculating gradient information. The modified algorithm gives a better convergence rate compared to the standard Levenberg-Marquard (LM) method and is less computationally intensive and requires less memory. The performance of the algorithm has been checked on several example problems.

SUMMARYThis work presents a novel predictive model-based proportional integral derivative (PID) tuning and control approach for unknown nonlinear systems. For this purpose, an NARX model of the plant to be controlled is obtained and then it used for both PID tuning and correction of the control action. In this study, for comparison, neural networks (NNs) and support vector machines (SVMs) have been used for modeling. The proposed structure has been tested on two highly nonlinear systems via simulations by comparing control and convergence performances of SVM-and NN-Based PID controllers. The simulation results have shown that when used in the proposed scheme, both NN and SVM approaches provide rapid parameter convergence and considerably high control performance by yielding very small transient-and steady-state tracking errors. Moreover, they can maintain their control performances under noisy conditions, while convergence properties are deteriorated to some extent due to the measurement noises.

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This paper proposes a novel non-linear model predictive control mechanism for non-linear systems. The idea behind the mechanism is that the so-called Runge–Kutta model of a continuous-time non-linear system can be regarded as an approximate discrete model and employed in a generalized predictive control loop for prediction and derivative calculation purposes. Additionally, the Runge–Kutta model of the system is used for state estimation in the extended Kalman filter framework and online parameter adaptation. The proposed method has been tested on two different non-linear systems. Simulation results have revealed the effectiveness of the proposed method for different cases.

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