The Optimal Control Problem for Linear Systems of Non-integer Order with Lumped and Distributed Parameters

2015 ◽  
Vol 4 (4) ◽  
pp. 429-443 ◽  
Author(s):  
V.A. Kubyshkin ◽  
S.S. Postnov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Linear Systems ◽  
Integer Order ◽  
Distributed Parameters

scholarly journals SOLUTION TO THE OPTIMAL CONTROL PROBLEM BY SOURCES IN THE BOUNDARY CONDITIONS OF A HYPERBOLIC SYSTEM OF A NETWORK STRUCTURE

2021 ◽  
Vol 8 (1) ◽  
pp. 004-012
Author(s):  
Y. R. Ashrafova ◽  
◽  
S. R. Rasulova ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Initial Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Distributed Parameters ◽  
Long Duration ◽  
Internal Sources

The solution to the optimal control problem by power of external and internal sources acting on the multilink system in nonlocal boundary conditions is investigated. Each arc of the system is an object with distributed parameters, described by a differential equation of hyperbolic type and related only by boundary values, and in an arbitrary way. Due to the long duration of the object's functioning, the exact values of the initial conditions are not known, but a set of their possible values is given. Based on the results of additional measurements of the state of the process at the input or output ends of the arcs (which are not internal vertices), a target functional is constructed, for which minimization a formula for its gradient is obtained.

scholarly journals Solution of linear systems from an optimal control problem arising in wind simulation

2010 ◽  
Vol 17 (6) ◽  
pp. 895-915 ◽  
Author(s):  
M. Benzi ◽  
L. Ferragut ◽  
M. Pennacchio ◽  
V. Simoncini
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Linear Systems ◽  
Wind Simulation

scholarly journals REQUIRED OPTIMALITY CONDITIONS IN ONE OPTIMAL CONTROL PROBLEM WITH MULTIPOINT FUNCTIONAL

2020 ◽  
pp. 7-26
Author(s):  
Shahla Rasulzade ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Control Problems ◽  
The Maximum Principle ◽  
Distributed Parameters

One specific optimal control problem with distributed parameters of the Moskalenko type with a multipoint quality functional is considered. To date, the theory of necessary first-order optimality conditions such as the Pontryagin maximum principle or its consequences has been sufficiently developed for various optimal control problems described by ordinary differential equations, i.e. for optimal control problems with lumped parameters. Many controlled processes are described by various partial differential equations (processes with distributed parameters). Some features are inherent in optimal control problems with distributed parameters, and therefore, when studying the optimal control problem with distributed parameters, in particular, when deriving various necessary optimality conditions, non-trivial difficulties arise. In particular, in the study of cases of degeneracy of the established necessary optimality conditions, fundamental difficulties arise. In the present work, we study one optimal control problem described by a system of first-order partial differential equations with a controlled initial condition under the assumption that the initial function is a solution to the Cauchy problem for ordinary differential equations. The objective function (quality criterion) is multi-point. Therefore, it becomes necessary to introduce an unconventional conjugate equation, not in differential (classical), but in integral form. In the work, using one version of the increment method, using the explicit linearization method of the original system, the necessary optimality condition is proved in the form of an analog of the maximum principle of L.S. Pontryagin. It is known that the maximum principle of L.S. Pontryagin for various optimal control problems is the strongest necessary condition for optimality. But the principle of a maximum of L.S. Pontryagin, being a necessary condition of the first order, often degenerates. Such cases are called special, and the corresponding management, special management. Based on these considerations, in the considered problem, we study the case of degeneration of the maximum principle of L.S. Pontryagin for the problem under consideration. For this purpose, a formula for incrementing the quality functional of the second order is constructed. By introducing auxiliary matrix functions, it was possible to obtain a second-order increment formula that is constructive in nature. The necessary optimality condition for special controls in the sense of the maximum principle of L.S. Pontryagin is proved. The proved necessary optimality conditions are explicit.

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