scholarly journals On the existence of a solution for some distributed optimal control hyperbolic system

2000 ◽  
Vol 23 (5) ◽  
pp. 297-311 ◽  
Author(s):  
Dariusz Idczak ◽  
Stanislaw Walczak
Keyword(s):  
Optimal Control ◽  
Hyperbolic System ◽  
Convex Set ◽  
Linear Time ◽  
Time Varying ◽  
Optimal Process ◽  
Existence Of A Solution ◽  
Distributed Optimal Control ◽  
Absolutely Continuous ◽  
State Variable

We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.

Optimal Control for Partially Observed Nonlinear Interval Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
T. E. Dabbous
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Control Problem ◽  
Linear Time ◽  
Control Process ◽  
Extension Principle ◽  
Time Varying ◽  
State Observation ◽  
Partially Observed ◽  
And Control

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.

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