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This paper presents an iterative approach for solving the optimal control problem (OCP) with time-delayed terms and bounded control variables. The projection function is used to construct the iterative method to approximate the control law. Employing the approximation of control law the approximation of state and the co-state variables are obtained. To the best of our knowledge, this paper is the first attempt to solve bounded and delayed OCPs with a projection function. The convergence theorem for the proposed method is also proven. Several numerical examples are added, showing the developed method's effectiveness to solve the time-delayed OCPs with bounded control variables. [ABSTRACT FROM AUTHOR]

We develop a projection recurrent neural network (RNN) to obtain the solution of the shortest path problem (SPP). Our focus on the paper is to give a compact single-layer structure RNN model to solve the SPP. To present the RNN model, we utilise a mixed linear complementarity problem (MLCP). Moreover, the developed RNN is proved to be globally stable. Finally, some numerical simulations are stated to show the performance of the presented approach. We compare the results with some other methods. [ABSTRACT FROM AUTHOR]

Finished products and manufacturing plants are some elements of the production system in the supply chain, and there are other manufacturing plants. They produce work in process and finished products and hold them in warehouses. So, they need to plan and control production and inventories. Isolated planning and control by different manufacturers increase inventories in them, and then they must plan and control integratory. This paper presents an iterative approach for solving the optimal control problem with bounded control variables. The projection function constructs the iterative method to approximate the control law. Employing the approximation of control law, the approximation of state and the co-state variables are obtained. For this purpose, we apply the Hamiltonian of the optimal control problem. From the Hamiltonian, the approximation of control law and then the approximation of state law is obtained. A simple example is given to compare the results with another published paper. Also, a case study on production planning in a three-stock reverse logistics system with deteriorating items is derived to show the method's performance. [ABSTRACT FROM AUTHOR]

In this scientific research, a new technique to solve a linear quadratic optimal control problem with fuzzy variables is proposed. The problem by an efficient transformation reduces to a crisp problem, and the solution is obtained from the direct method. In fact, we use the approximation method with artificial neural network, and to obtain the solution, the perceptron neural network (PNN) is given. Finally, two numerical examples are presented to show the performance of the technique. [ABSTRACT FROM AUTHOR]