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Erschienen in: Journal of Computer and Systems Sciences International 4/2019

01.07.2019 | CONTROL IN SYSTEMS WITH DISTRIBUTED PARAMETERS

Method for Parametric Optimization in Problems of the Multichannel Control of Systems with Distributed Parameters

verfasst von: E. Ya. Rapoport

Erschienen in: Journal of Computer and Systems Sciences International | Ausgabe 4/2019

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Abstract

We propose a constructive technology for solving parametrizable problems of multichannel optimal control in systems with distributed parameters under conditions of a given accuracy of uniform approximating the resultant spatial distribution of the controlled variable to the desired state. The developed technique uses the parametrization procedure of the sought control actions and the subsequent reduction to the special form of the task of semi-infinite optimization, which is solved by the scheme of the alternance method proposed earlier; this scheme is generalized to the investigated situation. We present an example (which is of interest by itself) of time-optimization of the process of nonstationary heat conductivity with two boundary control actions.

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Fußnoten
1
The computations were performed by N.A. Il’ina.
 
Literatur
1.
Zurück zum Zitat A. G. Butkovskii, The Theory of Optimal Control of Systems with Distributed Parameters (Nauka, Moscow, 1965) [in Russian]. A. G. Butkovskii, The Theory of Optimal Control of Systems with Distributed Parameters (Nauka, Moscow, 1965) [in Russian].
2.
Zurück zum Zitat A. G. Butkovskii, Control Methods for Distributed Systems (Nauka, Moscow, 1975) [in Russian]. A. G. Butkovskii, Control Methods for Distributed Systems (Nauka, Moscow, 1975) [in Russian].
3.
Zurück zum Zitat F. P. Vasil’ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian]. F. P. Vasil’ev, Optimization Methods (Faktorial, Moscow, 2002) [in Russian].
4.
Zurück zum Zitat E. Ya. Rapoport, Optimal Control of Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2009) [in Russian]. E. Ya. Rapoport, Optimal Control of Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2009) [in Russian].
5.
Zurück zum Zitat E. Ya. Rapoport, Analysis and Synthesis of Control Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2005) [in Russian]. E. Ya. Rapoport, Analysis and Synthesis of Control Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2005) [in Russian].
6a.
Zurück zum Zitat E. Ya. Rapoport, “Chebyshev approximations in problems of parametric optimization of controlled processes I-III,” Avtom. Telemekh., No. 2, 60–67 (1992); E. Ya. Rapoport, “Chebyshev approximations in problems of parametric optimization of controlled processes I-III,” Avtom. Telemekh., No. 2, 60–67 (1992);
6b.
Zurück zum Zitat Avtom. Telemekh., No. 3, 59–64 (1992); Avtom. Telemekh., No. 3, 59–64 (1992);
6c.
Zurück zum Zitat Avtom. Telemekh., No. 4, 49–56 (1992). Avtom. Telemekh., No. 4, 49–56 (1992).
7.
Zurück zum Zitat E. Ya. Rapoport, “Alternance properties of optimal solutions and computational algorithms in problems of semi-infinite optimization of controlled systems,” J. Comput. Syst. Sci. Int. 35, 581 (1996).MATH E. Ya. Rapoport, “Alternance properties of optimal solutions and computational algorithms in problems of semi-infinite optimization of controlled systems,” J. Comput. Syst. Sci. Int. 35, 581 (1996).MATH
8.
Zurück zum Zitat E. Ya. Rapoport, Alternance Method in Optimization Applications (Nauka, Moscow, 2000) [in Russian].MATH E. Ya. Rapoport, Alternance Method in Optimization Applications (Nauka, Moscow, 2000) [in Russian].MATH
9.
Zurück zum Zitat E. Ya. Rapoport, “The alternance method in semi-infinite optimization problems,” in Nonlinear Control Theory and Its Applications: Dynamics, Control, Optimization, Ed. by V. M. Matrosov, S. N. Vasil’ev, and A. I. Moskalenko (Fizmatlit, Moscow, 2003), pp. 164–200 [in Russian]. E. Ya. Rapoport, “The alternance method in semi-infinite optimization problems,” in Nonlinear Control Theory and Its Applications: Dynamics, Control, Optimization, Ed. by V. M. Matrosov, S. N. Vasil’ev, and A. I. Moskalenko (Fizmatlit, Moscow, 2003), pp. 164–200 [in Russian].
10.
Zurück zum Zitat Yu. E. Pleshivtseva and E. Ya. Rapoport, “The successive parameterization method of control actions in boundary value optimal control problems for distributed parameter systems,” J. Comput. Syst. Sci. Int. 48, 351 (2009).MathSciNetCrossRefMATH Yu. E. Pleshivtseva and E. Ya. Rapoport, “The successive parameterization method of control actions in boundary value optimal control problems for distributed parameter systems,” J. Comput. Syst. Sci. Int. 48, 351 (2009).MathSciNetCrossRefMATH
11.
Zurück zum Zitat L. Collatz and W. Krabs, Approximationstheorie; Tschebyscheffsche Approximation mit Anwendungen (B. G. Teubner, Stuttgart, 1973).MATH L. Collatz and W. Krabs, Approximationstheorie; Tschebyscheffsche Approximation mit Anwendungen (B. G. Teubner, Stuttgart, 1973).MATH
12.
Zurück zum Zitat V. A. Makovskii, Dynamics of Metallurgical Objects with Distributed Parameters (Metallurgiya, Moscow, 1971) [in Russian]. V. A. Makovskii, Dynamics of Metallurgical Objects with Distributed Parameters (Metallurgiya, Moscow, 1971) [in Russian].
13.
Zurück zum Zitat W. H. Ray, Advanced Process Control (McGraw-Hill, New York, 1981). W. H. Ray, Advanced Process Control (McGraw-Hill, New York, 1981).
14.
Zurück zum Zitat A. G. Butkovskii, Structural Theory of Distributed Systems (Nauka, Moscow, 1977) [in Russian]. A. G. Butkovskii, Structural Theory of Distributed Systems (Nauka, Moscow, 1977) [in Russian].
15.
Zurück zum Zitat I. Begimov, A. G. Butkovskii, and V. L. Rozhanskii, “Structural representation of physically inhomogeneous systems,” Avtom. Telemekh., No. 9, 25–35 (1982). I. Begimov, A. G. Butkovskii, and V. L. Rozhanskii, “Structural representation of physically inhomogeneous systems,” Avtom. Telemekh., No. 9, 25–35 (1982).
16.
Zurück zum Zitat I. Begimov, A. G. Butkovskii, and V. L. Rozhanskii, “Structural representation of two-dimensional inhomogeneous systems with distributed parameters,” Avtom. Telemekh., No. 5, 5–16 (1984). I. Begimov, A. G. Butkovskii, and V. L. Rozhanskii, “Structural representation of two-dimensional inhomogeneous systems with distributed parameters,” Avtom. Telemekh., No. 5, 5–16 (1984).
17.
Zurück zum Zitat N. D. Demidenko, Controlled Distributed Systems (Nauka, Novosibirsk, 1999) [in Russian]. N. D. Demidenko, Controlled Distributed Systems (Nauka, Novosibirsk, 1999) [in Russian].
18.
Zurück zum Zitat E. Ya. Rapoport, “Open-loop controllability of interconnected heterogeneous systems with distributed parameters,” J. Comput. Syst. Sci. Int. 56, 561 (2017).MathSciNetCrossRefMATH E. Ya. Rapoport, “Open-loop controllability of interconnected heterogeneous systems with distributed parameters,” J. Comput. Syst. Sci. Int. 56, 561 (2017).MathSciNetCrossRefMATH
19.
Zurück zum Zitat A. D. Polyanin, Handbook of Linear Equations of Mathematical Physics (Fizmatlit, Moscow, 2001) [in Russian].MATH A. D. Polyanin, Handbook of Linear Equations of Mathematical Physics (Fizmatlit, Moscow, 2001) [in Russian].MATH
20.
Zurück zum Zitat E. Ya. Rapoport, Structural Modeling of Objects and Control Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2003) [in Russian]. E. Ya. Rapoport, Structural Modeling of Objects and Control Systems with Distributed Parameters (Vyssh. Shkola, Moscow, 2003) [in Russian].
21.
Zurück zum Zitat Yu. V. Egorov, “Necessary conditions for optimality in a Banach space,” Mat. Sb. (Nov. Ser.) 64 (1), 79–101 (1964). Yu. V. Egorov, “Necessary conditions for optimality in a Banach space,” Mat. Sb. (Nov. Ser.) 64 (1), 79–101 (1964).
22.
Zurück zum Zitat E. Ya. Rapoport, Optimization of Metal Induction Heating Processes (Metallurgiya, Moscow, 1993) [in Russian]. E. Ya. Rapoport, Optimization of Metal Induction Heating Processes (Metallurgiya, Moscow, 1993) [in Russian].
23.
Zurück zum Zitat E. Rapoport and Yu. Pleshivtseva, Optimal Control of Induction Heating Processes (CRC, Taylor Francis Group, Boca Raton, London, New York, 2007). E. Rapoport and Yu. Pleshivtseva, Optimal Control of Induction Heating Processes (CRC, Taylor Francis Group, Boca Raton, London, New York, 2007).
24.
Zurück zum Zitat E. Ya. Rapoport and Yu. E. Pleshivtseva, Optimum Control of Temperature Regimes of Induction Heating (Nauka, Moscow, 2012) [in Russian]. E. Ya. Rapoport and Yu. E. Pleshivtseva, Optimum Control of Temperature Regimes of Induction Heating (Nauka, Moscow, 2012) [in Russian].
25.
Zurück zum Zitat E. Ya. Rapoport and Yu. E. Pleshivtseva, “Optimal control of induction heating of metals prior to warm and hot forming,” in ASM Handbook, Vol. 4C: Induction Heating and Heat Treatment (ASM Int., New York, 2014), pp. 366–401. E. Ya. Rapoport and Yu. E. Pleshivtseva, “Optimal control of induction heating of metals prior to warm and hot forming,” in ASM Handbook, Vol. 4C: Induction Heating and Heat Treatment (ASM Int., New York, 2014), pp. 366–401.
26.
Zurück zum Zitat A. V. Lykov, Heat Conduction Theory (Vyssh. Shkola, Moscow, 1967) [in Russian]. A. V. Lykov, Heat Conduction Theory (Vyssh. Shkola, Moscow, 1967) [in Russian].
27.
Zurück zum Zitat E. M. Kartashov, Analytical Methods in the Thermal Conductivity Theory of Solids (Vyssh. Shkola, Moscow, 2001) [in Russian]. E. M. Kartashov, Analytical Methods in the Thermal Conductivity Theory of Solids (Vyssh. Shkola, Moscow, 2001) [in Russian].
Metadaten
Titel
Method for Parametric Optimization in Problems of the Multichannel Control of Systems with Distributed Parameters
verfasst von
E. Ya. Rapoport
Publikationsdatum
01.07.2019
Verlag
Pleiades Publishing
Erschienen in
Journal of Computer and Systems Sciences International / Ausgabe 4/2019
Print ISSN: 1064-2307
Elektronische ISSN: 1555-6530
DOI
https://doi.org/10.1134/S1064230719040130

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