in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

This paper, which is the natural continuation of [21], studies a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to build. In [21] the problem is embedded in a suitable Hilbert space H and the regularity of the associated ...

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state. Our fram...

In this paper, optimal control for linear partial differential algebraic equations (PDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the PDAE is transformed into a differential algebraic equations (DAE). Hence, the optimal control of PDAE can be found out by finding the optimal control of the corresponding DAE. The goal is to provide optimal control wit...

Abstract. The ergodic control problem for a non-degenerate controlled diffusion controlled through its drift is considered under a uniform stability condition that ensures the well-posedness of the associated Hamilton–Jacobi– Bellman (HJB) equation. A nonlinear parabolic evolution equation is then proposed as a continuous time continuous state space analog of White’s ‘relative value iteration’ ...