In this study, the optimal control problem of nonlinear parabolic partial differential equations (PDEs) is investigated. Optimal control of nonlinear PDEs is an open problem with applications that include fluid, thermal, biological, and chemically-reacting systems. Model predictive control with a fast numerical solution method has been well established to solve the optimal control problem of no...

For autonomous, nonlinear, smooth optimal control systems on n-dimensional manifolds we investigate the relationship between the discounted and the average yield optimal value of infinite horizon problems. It is shown that the value functions of discounted problems converge to the value function of the average yield problem as the discount rate tends to zero, if there exist approximately optima...

background: determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. the most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. this is because in these cases, the therapy not only kills the tumor cells, but also ki...

optimal reactive power dispatch (orpd) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. due to the stochastic behavior of loads, the orpd requires a probabilistic mathematical model. in this paper, monte carlo simulation (mcs) is used for modeling of load uncertainties in the orpd problem. the problem is formulated as a nonlinear constrained mul...

In the paper we investigate solvability of nonlinear optimal Thermal and Diffusion processes control problems defined by semi-linear parabolic equations when the source function nonlinearly depends on the controlling parameters, and nonlinear integral criterion of quality is minimized. We obtained the sufficient conditions of uniqueness of the solution of the boundary value problem and the adjo...

In this paper, a method for solving a class of nonlinear optimal control problems is presented. The method is based on replacing the dynamic nonlinear optimal control problem by a sequence of quadratic programming problems. To this end, the iterative technique developed by Banks is used to replace the original nonlinear dynamic system by a sequence of linear time-varying dynamic systems, then e...

In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based ...

A neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results...

This paper is concerned with the quaternary nonlinear hyperbolic boundary value problem (QNLHBVP) studding constraints optimal classical continuous control vector (CQOCCCV), cost function (CF), and equality inequality state (EIQSCCV). The existence of a CQOCCCV dominating by QNLHBVP stated demonstrated using Aubin compactness theorem (ACTH) under appropriate hypotheses (HYPs). Furthermore, math...