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  • 2020-2022
  • 2000-2004  (11)
  • 1955-1959
  • 1890-1899
  • 1870-1879
  • controllability
  • 1
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (III)—Multiple time-delay case (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1063-1074 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; controllable set ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437638
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  • 2
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (II)—Single time-delay case (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1051-1062 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; controllable set ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the oneperiodic, multiple-periodic controllability of periodic-type systems and controllability of periodic systems are presented, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437637
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Controllability of a class of hybrid dynamic systems (I)—Basic properties and preliminary results (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1041-1050 
    Details
    ISSN: 1573-2754
    Keywords: hybrid dynamic system ; switched linear system ; time-delay ; controllability ; generalized cyclic invariant subspace ; switching sequence ; switching path ; TP13 ; TP273 ; O317 ; 93B05 ; 93B27 ; 93C99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437636
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Control Synthesis for Čaplygin Polynomial Systems (2000)
    Springer
    Acta applicandae mathematicae 60 (2000), S. 199-212 
    Details
    ISSN: 1572-9036
    Keywords: nonlinear systems ; differential forms ; controllability ; control synthesis ; polynomial systems ; vector fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses new control synthesis for certain cascade type polynomial systems addressed in the paper as Čaplygin systems. A numerical control synthesis as well as characterization of reachability set are presented. The results of the paper are important for various branches of system theory, where the control synthesis is concerned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006474511627
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  • 5
    Electronic Resource
    Electronic Resource
    Classification of Controllable Systems on Low-Dimensional Solvable Lie Groups (2000)
    Springer
    Journal of dynamical and control systems 6 (2000), S. 159-217 
    Details
    ISSN: 1573-8698
    Keywords: controllability ; right-invariant systems ; Lie groups ; solvable
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Right-invariant control systems on simply connected solvable Lie groups are studied. A complete and explicit description of controllable single-input right-invariant systems on such Lie groups up to dimension 6 is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009577803607
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  • 6
    Electronic Resource
    Electronic Resource
    On the Controllability Problem Arising in Financial Mathematics (2000)
    Springer
    Journal of dynamical and control systems 6 (2000), S. 353-363 
    Details
    ISSN: 1573-8698
    Keywords: parabolic differential equation ; controllability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper deals with the approximate controllability problem for a parabolic equation defined for $$x \in \mathbb{R},{\text{ }}t \in \;[0,T]$$ . It is possible to find a sequence of initial conditions with given compact support such that traces at $$x = 0$$ of corresponding solutions converge to the trace of a given solution. We obtain estimates of the rate of this convergence. These estimates are constructed in terms of eigenvalues of certain compact operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009514706199
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  • 7
    Electronic Resource
    Electronic Resource
    Controllability of Solvable Lie Algebras (2000)
    Springer
    Journal of dynamical and control systems 6 (2000), S. 453-459 
    Details
    ISSN: 1573-8698
    Keywords: solvable Lie algebras ; systems on Lie groups ; controllability ; maximal semigroups ; hyperplane subalgebras ; metabelian algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We call a Lie-algebra $$g$$ SID-controllable if there exist $$A,B \in g$$ such that the invariant control system on the simply connected group G given by $$\dot g = g(A\; + \;uB),\;\;u\;\; \in \;\;\mathbb{R}$$ , is controllable. This is tantamount to saying that the semigroup $$S(A, \pm B) = \langle \exp (\mathbb{R}^ + A + \mathbb{R}B)\rangle \subseteq G$$ is all of G. In his papers [4]–[7] Yu. Sachkov analyzed and characterized solvable SID-controllable Lie algebras. In this paper we improve his results by proving the following simple reduction criterion: a solvable Lie algebra $$g$$ is SID-controllable iff the factor-algebra $$g/D^2 g$$ is SID-controllable. For solvable $$g$$ this reduces the whole problem to metabelian algebras ( $$D^2 g = 0$$ ), a case which is completely solved in Sachkov's work. Our result also generalizes immediately to systems with multiple inputs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009522908016
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  • 8
    Electronic Resource
    Electronic Resource
    The invariant manifold method and the controllability of nonlinear control system (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1320-1330 
    Details
    ISSN: 1573-2754
    Keywords: nonlinear control system ; controllability ; oriented manifold ; invariant manifold ; dynamics of rigid body ; O231
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A. M. Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics of rigid body to nonlinear control system for the first time and obtained a series of efficient results. Based on Kovalev's oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition was discussed. At last, the motion of a rigid body with two rotors was investigated and the necessary condition which is satisfied by this system was proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459255
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  • 9
    Electronic Resource
    Electronic Resource
    Construction of the Control Realizing the Rotation of a Timoshenko Beam (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 51-68 
    Details
    ISSN: 1573-2878
    Keywords: Timoshenko beam ; controllability ; moment problem ; piecewise constant control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the linear model of a slowly rotating Timoshenko beam in a horizontal plane whose moment is controlled by the angular acceleration of the disk of the driving motor into which the beam is clamped. This work complements our previous results on the controllability of the beam from a position of rest into another position of rest; we give a method of construction of a piecewise constant control solving the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004652615867
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  • 10
    Electronic Resource
    Electronic Resource
    Controllability of Second-Order Differential Inclusions in Banach Spaces with Nonlocal Conditions (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 559-571 
    Details
    ISSN: 1573-2878
    Keywords: nonlocal conditions ; mild solutions ; evolution ; controllability ; fixed points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we establish sufficient conditions for the controllability ofsecond-order differential inclusions in Banach spaces with nonlocalconditions. We rely on a fixed-point theorem for condensing maps due toMartelli.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026447232030
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  • 11
    Electronic Resource
    Electronic Resource
    Bilinear Control and Application to Flexible a.c. Transmission Systems (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 621-637 
    Details
    ISSN: 1573-2878
    Keywords: bilinear systems ; optimal control ; controllability ; stabilization ; electric power
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series. While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004645224313
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