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research-article

Optimal control for partially observed nonlinear interval systems

[+] Author and Article Information
Tayel Dabbous

Dep. of Elec. Eng., Higher Technological Institute, Ramadan 10th City, Egypt
tayel-dab@yahoo.com

1Corresponding author.

ASME doi:10.1115/1.4042670 History: Received June 17, 2017; Revised January 22, 2019

Abstract

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 posses lower and upper bounds, we have developed sets of (ordinary) differential equations that describe the behaviour 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 principal 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.

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