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Tytuł książki

Synthesis of optimal control for nonlinear third order systems

Seria
Rozprawy Matematyczne tom/nr w serii: 256 wydano: 1986
Zawartość
Warianty tytułu
Abstrakty
EN
The paper is devoted to a certain problem in the theory of synthesis of optimal control. The fundamental results of research in the synthesis of optimal control for second order systems are given in [1], [2], [5], [10]. In particular, in [2] and [5] some specific nonlinear systems are investigated, namely the systems related with the differential equations of the form
s̈ + F(s,ṡ) = u or s̈ + F(s,ṡ,u) = 0
where u is a control parameter in the interval [—1,1]. Some results concerning third order linear systems are presented in [7], [8], [9] and [12]. The main purpose of this paper is the formulation of the synthesis of optimal control for a class of nonlinear dynamic systems of the third order corresponding to a differential equation of the form
(1) ͘s̈ = F(s,ṡ,s̈,u) where u ∈ [-1,1].
EN

CONTENTS
1. Formulation of the problem.......................................................................................................................5
2. Necessary conditions for the optimality of control.....................................................................................7
3. Some properties of extremal trajectories.................................................................................................12
4. Inequalities describing the mutual position of the trajectories $K^+(0)$,K¯(p),K¯(0),$K^+(q)$................31
5. Remark on the existence of common points of the trajectories K¯(0), K¯(p) and $K^+(r)$ and of the trajectories $K^+(0)$, $K^+(q)$ and K¯(s)...........................................................................................................................................................37
6. Mutual position of the trajectories $K^+(r)$ and $K¯(s)$.........................................................................47
7. The uniqueness of an extremal control. Synthesis of optimal control......................................................56
References.................................................................................................................................................60
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 256
Liczba stron
60
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLVI
Daty
wydano
1986
Twórcy
  • Oleska 45 m. 16. 45-052 Opole, Poland
Bibliografia
  • [1] M. M. Baitman, Synthesis of Optimal. Trajectories in the Plane, Zinatne, Riga 1971 (in Russian).
  • [2] V. G. Boltyanskii, Mathematical Methods of Optimal Control, Nauka, Moscow 1969 (in Russian).
  • [3] A. F. Filippov, On certain problems in optimal control theory, Vestnik Moskov. Univ. Ser. Mat. Mekh. Astronom. Fiz. 1959, no. 2, 25-32 (in Russian).
  • [4] P. Harlman, Ordinary Differential Equations, Russian od., Mir, Moscow 1970.
  • [5] E. B. Lee and L. Markus, Foundations of Optimal Control Theory, Russian ed., Mir, Moscow 1972.
  • [6] V. I. Lovchakov and A. A. Fomichev, Synthesis of control systems for a certain class of nonlinear objects with lag, Izv. Akad. Nauk SSSR Tekhn. Kibernet. 1980, no. 4, 157-165 (in Russian).
  • [7] A. I. Moroz, Synthesis of time-optimal control for linear third-order systems, Avtomat. i Telemekh. 1969, no. 5, 5-17 (in Russian).
  • [8] A. I. Moroz, Synthesis of time-optimal control for linear third-order systems II, ibid. 1969, no. 7, 18-29 (in Russian).
  • [9] A. I. Moroz, Synthesis of time-optimal control for linear third-order systems III, ibid. 1969, no. 9, 5-15 (in Russian).
  • [10] A. A. Pavlov, Synthesis of Relay Systems, Optimal in Speed of Action, Nauka, Moscow 1966 (in Russian).
  • [11] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Fizmatgiz, Moscow 1961 (in Russian).
  • [12] E. P. Ryan, On the synthesis of a third-order tome-fuel optimal control system, IEEE Trans. Automat. Control 23 (1978), no. 5.
  • [13] T. Wazewski, Systèmes des équations et des inégalités différentielles ordinaires aux deuxièmes membres monotones et leurs applications, Ann. Soc. Polon. Math. 23 (1950), 112-166.
  • [14] R. T. Yanushevskii, Synthesis of a certain class of absolutely stable nonlinear control systems. Izv. Akad. Nauk SSSR Tekhn. Kibernet. 1979, no. 2, 199-204 (in Russian).
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-6dff8f4c-c746-4445-98ee-f8be924bde59
Identyfikatory
ISBN
83-01-06842-6
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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