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In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain...
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
We propose a general approach for the numerical approximation of
optimal control problems governed by a linear advection–diffusion
equation, based on a stabilization method applied to the
Lagrangian functional, rather than stabilizing the state and
adjoint equations separately. This approach yields a coherently
stabilized control problem. Besides, it allows a straightforward
a posteriori error estimate in which estimates of higher order terms
are needless. Our a posteriori estimates stems from...
The paper presents some results related to
the optimal control approachs applying to inverse radiative transfer
problems, to the theory of reflection operators, to the solvability of the
inverse problems on boundary function and to algorithms for solution of
these problems.
Necessary conditions for some optimal control problem for a nonlinear 2-D system are considered. These conditions can be obtained in the form of a quasimaximum principle.
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are...
We consider a distributed system in which the state q is
governed by a parabolic equation and a pair of controls v = (h,k)
where h and k play two different roles: the control k is
of controllability type while h expresses that the state q
does not move too far from a given state.
Therefore, it is natural to introduce the control
point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method...
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