Dabbous T E
Department of Electrical Engineering, Higher Technological Institute, P.O. Box 228, Ramadan 10th City, Sharkia K1N-6NP, Egypt e-mail:
J Dyn Syst Meas Control. 2019 Sep;141(9):0910041-910049. doi: 10.1115/1.4042670. Epub 2019 May 2.
In this paper, we consider the optimal control problem for a class of systems governed by nonlinear time-varying partially observed interval differential equations. The control process is assumed to be governed by linear time varying interval differential equation driven by the observed process. Using the fact that the state, observation, and control processes possess lower and upper bounds, we have developed sets of (ordinary) differential equations that describe the behavior of the bounds of these processes. Using these differential equations, the interval control problem can be transformed into an equivalent ordinary control problem in which interval mathematics and extension principle of Moore are not required. Using variational arguments, we have developed the necessary conditions of optimality for the equivalent (ordinary) control problem. Finally, we present some numerical simulations to illustrate the effectiveness of the proposed control scheme.
在本文中，我们考虑一类由非线性时变部分观测区间微分方程所描述系统的最优控制问题。假设控制过程由受观测过程驱动的线性时变区间微分方程所支配。利用状态、观测和控制过程具有上下界这一事实，我们推导出了描述这些过程边界行为的（常）微分方程组。借助这些微分方程，区间控制问题可转化为一个等价的普通控制问题，在此问题中无需区间数学和摩尔扩展原理。通过变分论证，我们推导出了等价（普通）控制问题的最优性必要条件。最后，我们给出一些数值模拟以说明所提控制方案的有效性。
