Dynamic Optimization for Switched Time-Delay Systems with State-Dependent Switching Conditions

This paper considers a dynamic optimization problem for a class of switched systems characterized by two key attributes: (i) the switching mechanism is invoked automatically when the state variables satisfy certain switching conditions; and (ii) the subsystem dynamics involve time-delays in the state variables. The decision variables in the problem, which must be selected optimally to minimize system cost, consist of a set of time-invariant system parameters in the initial state functions. To solve the dynamic optimization problem, we first show that the partial derivatives of the system state with respect to the system parameters can be expressed in terms of the solution of a set of variational switched systems. Then, on the basis of this result, we develop a gradient-based optimization algorithm to determine the optimal parameter values. Finally, we validate the proposed algorithm by solving an example problem arising in the production of 1,3-propanediol

Optimal Control in a Mathematical Model of Smoking

This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions

Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach