Surface Roughness Prediction of Titanium Alloy during Abrasive Belt Grinding Based on an Improved Radial Basis Function (RBF) Neural Network.

Titanium alloys have become an indispensable material for all walks of life because of their excellent strength and corrosion resistance. However, grinding titanium alloy is exceedingly challenging due to its pronounced material characteristics. Therefore, it is crucial to create a theoretical roughness prediction model, serving to modify the machining parameters in real time. To forecast the surface roughness of titanium alloy grinding, an improved radial basis function neural network model based on particle swarm optimization combined with the grey wolf optimization method (GWO-PSO-RBF) was developed in this study. The results demonstrate that the improved neural network developed in this research outperforms the classical models in terms of all prediction parameters, with a model-fitting R2 value of 0.919.

Discrete-Time Impulsive Adaptive Dynamic Programming.

In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal impulsive control problems for infinite horizon discrete-time nonlinear systems. Considering the constraint of the impulsive interval, in each iteration, the iterative impulsive value function under each possible impulsive interval is obtained, and then the iterative value function and iterative control law are achieved. A new convergence analysis method is developed which proves an iterative value function to converge to the optimum as the iteration index increases to infinity. The properties of the iterative control law are analyzed, and the detailed implementation of the optimal impulsive control law is presented. Finally, two simulation examples with comparisons are given to show the effectiveness of the developed method.

Continuous-Time Time-Varying Policy Iteration.

A novel policy iteration algorithm, called the continuous-time time-varying (CTTV) policy iteration algorithm, is presented in this paper to obtain the optimal control laws for infinite horizon CTTV nonlinear systems. The adaptive dynamic programming (ADP) technique is utilized to obtain the iterative control laws for the optimization of the performance index function. The properties of the CTTV policy iteration algorithm are analyzed. Monotonicity, convergence, and optimality of the iterative value function have been analyzed, and the iterative value function can be proven to monotonically converge to the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Furthermore, the iterative control law is guaranteed to be admissible to stabilize the nonlinear systems. In the implementation of the presented CTTV policy algorithm, the approximate iterative control laws and iterative value function are obtained by neural networks. Finally, the numerical results are given to verify the effectiveness of the presented method.

Discrete-Time Stable Generalized Self-Learning Optimal Control With Approximation Errors.

In this paper, a generalized policy iteration (GPI) algorithm with approximation errors is developed for solving infinite horizon optimal control problems for nonlinear systems. The developed stable GPI algorithm provides a general structure of discrete-time iterative adaptive dynamic programming algorithms, by which most of the discrete-time reinforcement learning algorithms can be described using the GPI structure. It is for the first time that approximation errors are explicitly considered in the GPI algorithm. The properties of the stable GPI algorithm with approximation errors are analyzed. The admissibility of the approximate iterative control law can be guaranteed if the approximation errors satisfy the admissibility criteria. The convergence of the developed algorithm is established, which shows that the iterative value function is convergent to a finite neighborhood of the optimal performance index function, if the approximate errors satisfy the convergence criterion. Finally, numerical examples and comparisons are presented.