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.
Optimal Control for Partially Observed Nonlinear Interval Systems
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received June 17, 2017; final manuscript received January 22, 2019; published online May 2, 2019. Assoc. Editor: Yongchun Fang.
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Dabbous, T. E. (May 2, 2019). "Optimal Control for Partially Observed Nonlinear Interval Systems." ASME. J. Dyn. Sys., Meas., Control. September 2019; 141(9): 091004. https://doi.org/10.1115/1.4042670
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