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  • 2010-2014
  • 2000-2004  (11)
  • 1985-1989  (11)
  • 1935-1939
  • 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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  • 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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  • 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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  • 12
    Electronic Resource
    Electronic Resource
    The importance of chronicity and controllability of stress in the context of stress-illness relationships (1989)
    Springer
    Journal of behavioral medicine 12 (1989), S. 357-372 
    Details
    ISSN: 1573-3521
    Keywords: illness ; chronic ; stress ; controllability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Psychology
    Notes: Abstract The primary purpose of the present study was to increase our understanding of the roles of chronicity and controllability in the measurement of stress within the context of stress-illness relationships. Controllability and chronicity were assessed directly using a modified version of the Everyday Problems Scale. In addition to this scale, measures of depression, psychosomatic symptoms, and social support were administered to 128 women and 100 men. The results indicated that, for both men and women, the number of stressors was the best single predictor of symptoms. However, for women, chronicity and controllability of the stressors accounted for a significant amount of the variance in health outcomes over and above that accounted for by the number of stressors endorsed; for men, the addition of neither chronicity nor controllability consistently increased the strength of the association. While available social support was not found to influence the stress-illness relationships, greater willingness to utilize social support was associated with lower levels of depression.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00844929
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  • 13
    Electronic Resource
    Electronic Resource
    Local invariants of smooth control systems (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 191-237 
    Details
    ISSN: 1572-9036
    Keywords: Primary ; 49B10 ; 49E15 ; Nonlinear control systems ; geometric/Lie algebraic methods ; chronological calculus ; nilpotent polynomial approximation ; controllability ; attainable sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Methods are presented for locally studying smooth nonlinear control systems on the manifoldM. The technique of chronological calculus is intensively exploited. The concept of chronological connection is introduced and is used when obtaining the invariant expressions in the form of Lie bracket polynomials for high-order variations of a nonlinear control system. The theorem on adduction of a family of smooth vector fields to the canonical form proved in Section 4 is then applied to the construction of a nilpotent polynomial approximation for a control system. Finally, the relation between the attainable sets of an original system and an approximating one is established; it implies some conclusions on the local controllability of these systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01307214
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  • 14
    Electronic Resource
    Electronic Resource
    Equilibrium description of a particle system in a heat bath (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 239-258 
    Details
    ISSN: 1572-9036
    Keywords: 82A30 ; 82A05 ; 93B05 ; 93E15 ; 60J65 ; Statistical physics ; invariant measure ; controllability ; stochastic stability ; Langevin equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract AnN particle system evolving in 3-space under the action of a friction force, an external potential and a fluctuating force is studied, using the Langevin equation. Necessary and sufficient conditions are given for both (a) the existence and (b) the Maxwell-Boltzmann character of an invariant measure. Both probabilistic and system theoretical tools play an important part in this study. In addition, the general results mentioned above are applied to the study of a system ofn oscillators coupled through velocity, with a first-neighbour-only type of interaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01307215
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  • 15
    Electronic Resource
    Electronic Resource
    On control problems (1989)
    Springer
    Periodica mathematica Hungarica 20 (1989), S. 13-25 
    Details
    ISSN: 1588-2829
    Keywords: 1980/85 ; Primary 35C10, 35B37 ; Secondary 93B05, 93C20 ; Vibration of a string ; Fourier's method ; controllability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01849497
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  • 16
    Electronic Resource
    Electronic Resource
    On Russell's method of controllability via stabilizability (1987)
    Springer
    Journal of optimization theory and applications 52 (1987), S. 279-290 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear control systems ; stabilizing feedback control ; controllability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Russell has observed that a linear system is controllable provided it is stabilizable in both positive and negative time. We give a version of this result valid for nonlinear systems, and illustrate its use by giving new proofs of two classical results from control theory, the first involving bounded perturbations of controllable linear systems, and the second involving controllability of linear systems by bounded controls.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941287
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  • 17
    Electronic Resource
    Electronic Resource
    Dual-lattice theorems in the geometric approach (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 229-244 
    Details
    ISSN: 1573-2878
    Keywords: Controlled invariants ; (A, ℬ)-invariants ; conditioned invariants ; (ℒ,A)-invariants ; geometric approach ; controllability ; observability ; linear system theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A one-to-one correspondence is shown to exist between the lattice of all self-bounded (A, ℬ)-controlled invariants contained in ℒ and the lattice of all self-hidden (A, ℒ)-conditioned invariants containing ℬ. This correspondence, stated herein as the main dual-lattice theorem, allows a straightforward derivation of the universal bounds of the lattices, particularly when additional constraints are imposed, such as to contain a given subspace ℘ for the elements of the former lattice and to be contained in a given subspace ℒ for the elements of the latter. Then, two further minor dual-lattice theorems, dual to each other, are presented, and some connections and applications of the new theory to standard control and observation problems are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940671
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  • 18
    Electronic Resource
    Electronic Resource
    Complete controllability (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 69-82 
    Details
    ISSN: 1573-2878
    Keywords: Linear autonomous systems ; constraints ; controllability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A linear autonomous control system in ℝ n is said to be completely controllable iff there existsT〉0 such that eachx ∈ ℝ n can be steered to anyy ∈ ℝ n in timeT. This paper presents a geometric characterization of this property in the case in which there are constraints on the values which the control maps can assume. A necessary and sufficient condition to get instant controllability (i.e., complete controllability for anyT〉0) is also derived. This condition generalizes the well-known Kalman condition to the constrained case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938478
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  • 19
    Electronic Resource
    Electronic Resource
    On the intersection of controllable and reachable sets (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 267-278 
    Details
    ISSN: 1573-2878
    Keywords: Reachability ; controllability ; invariant sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we prove that the intersection of the controllable set to and the reachable set from a point target is connected, and that points within the intersection have the same controllable and reachable sets. We further demonstrate that the intersection is positive invariant whenever the intersection is not a single point. We then introduce the concept of a maneuverable set which allows us to generalize the results by replacing the point target with a maneuverable set. Use of the theory is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939273
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  • 20
    Electronic Resource
    Electronic Resource
    On the null-controllability of linear discrete-time systems with restrained controls (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 313-329 
    Details
    ISSN: 1573-2878
    Keywords: Discrete-time systems ; controllability ; eigenvectors ; cones
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is devoted to the null-controllability problem for linear, autonomous, discrete-time systems with restrained controls, i.e., systems described by the equationx k+1=Ax k+u k,u k∈ Г, where 0 ∈ Г, but is not necessarily an interior point of Г. Some criteria for local and global null controllability are given with proofs. These results can be considered as extensions to discrete-time systems of the known corresponding criteria for linear, continuous-time systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939276
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  • 21
    Electronic Resource
    Electronic Resource
    Solvability, controllability, and observability of singular systems (1985)
    Springer
    Journal of optimization theory and applications 45 (1985), S. 53-72 
    Details
    ISSN: 1573-2878
    Keywords: Control theory ; controllability ; observability ; singular systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problems of solvability, controllability, and observability for the singular systemKx(t)=Ax(t)+Bu(t) are studied, whereK is a singular, square matrix andu(t) is a complex vector function sufficiently differentiable. The classical theories of matrix pencils are first related to the solvability of singular systems. Then, the concepts of reachability, controllability, and observability of regular systems are extended to singular systems. Finally, the set of reachable states is described. The proposed matrix conditions for testing the controllability and observability of singular systems are simple and always feasible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940813
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  • 22
    Electronic Resource
    Electronic Resource
    Finite-time null controllability for a class of linear evolution equations on a Banach space with control constraints (1985)
    Springer
    Journal of optimization theory and applications 47 (1985), S. 129-158 
    Details
    ISSN: 1573-2878
    Keywords: Linear evolution equations ; Banach spaces ; controllability ; constrained controls ; existence of time-optimal controls ; maximum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present some necessary and sufficient conditions for null controllability for a class of general linear evolution equations on a Banach space with constraints on the control space. We also present a result on the existence of time-optimal controls and some partial results on the maximum principle. Some interesting insights that can be obtained from these results are discussed, and the paper is concluded with an application to a boundary control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940766
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