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  • 1
    Electronic Resource
    Electronic Resource
    Disturbance rejecting optimal regulation of hyperbolic systems (1995)
    Springer
    Mathematics of control, signals, and systems 8 (1995), S. 241-256 
    Details
    ISSN: 1435-568X
    Keywords: Robust control ; H ∞ control ; Disturbance rejection ; Hyperbolic systems ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract Optimal regulation of hyperbolic systems in the presence of unknown exogenous and initial disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of disturbances are developed. These necessary conditions have the form of a twopoint boundary-value problem along with certain equality and inequality conditions. The results also characterize the worst possible disturbances that are accommodated by the optimum controller without any serious performance degradation. Numerical results on the control of a vibrating beam are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211861
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal regulators for linear systems with no control cost (1991)
    Springer
    Dynamics and control 1 (1991), S. 341-355 
    Details
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This article is concerned with the theory of optimal feedback regulator for the linear system $$\dot x$$ =Ax +Bu with the cost functional given byJ(u) = 1/2(Mx(T),x(T)). Due to absence of the usual positive definite quadratic cost for controls, this is a nonstandard problem. Two sets of results are presented: one for bounded and one for unbounded controls. For bounded controls, the control law is given by solving a system of coupled nonlinear differential equations of the Riccati type; and for unbounded controls, the optimal control law is determined by solving a parameterized family of matrix Riccati differential equations. Questions about the existence of optimal controls, as they arise when considering the application of the Pontryagin minimum principle, are also treated in this article. The results presented here also hold for time-varying systems without requiring any modification and are also easily extended to the case $$J(u) = \frac{1}{2}(Mx(T),x(T)) + \frac{1}{2}\int_0^T {(Qx(t),x(t))dt} $$ . For illustration, some numerical results are presented for the unbounded case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02169765
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  • 3
    Electronic Resource
    Electronic Resource
    Modeling and control of flexible space stations (1992)
    Springer
    Dynamics and control 2 (1992), S. 5-33 
    Details
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this article, a preliminary formulation of large space structures and their stabilization is considered. The system consists of a (rigid) massive body and flexible configurations that consist of several beams, forming the space structure. The rigid body is located at the center of the space structure and may play the role of experimental modules. A complete dynamics of the system has been developed using Hamilton's principle. The equations that govern the motion of the complete system consist of six ordinary differential equations and several partial differential equations together with appropriate boundary conditions. The partial differential equations govern the vibration of flexible components. The ordinary differential equations describe the rotational and translational motion of the central body. The dynamics indicate very strong interaction among rigid-body translation, rigid-body rotation, and vibrations of flexible members through nonlinear couplings. Hence, any rotation of the rigid body induces vibration in the beams and vice versa. Also, any disturbance in the orbit induces vibration in the beams and wobbles in the body rotation and vice versa. This makes the system performance unsatisfactory for many practical applications. In this article, stabilization of the above-mentioned system subject to external disturbances is considered. The asymptotic stability of the perturbed system by application of velocity feedback controls is proved using Lyapunov's method. Numerical simulations are carried out in order to illustrate the impact of dynamic coupling or interaction among several members of the system and the effectiveness of the suggested feedback controls for stabilization. This study is expected to provide some insight into the complexity of modeling, analysis, and stabilization of actual space stations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02169803
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  • 4
    Electronic Resource
    Electronic Resource
    Feedback control of chaotic systems (1994)
    Springer
    Dynamics and control 4 (1994), S. 97-114 
    Details
    ISSN: 1573-8450
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A suboptimal feedback controller implemented by a multilayer feed-forward neural network is presented to control the unpredictable behavior of chaotic systems. The controller has been tested on the Lorenz and the Rössler systems using numerical simulation. Results show that chaotic systems, subject to feedback control, can be tamed to behave like a system having point attractors with associated basins of attraction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02115741
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A Powerful Numerical Technique Solving Zakai Equation for Nonlinear Filtering (1997)
    Springer
    Dynamics and control 7 (1997), S. 293-308 
    Details
    ISSN: 1573-8450
    Keywords: nonlinear filtering ; Zakai equation ; Galekin approximation ; Gaussian series ; measurement residual
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we have developed a simple but powerful numerical method forthe approximation of the unnormalized conditional (probability) density offiltered diffusion process which satisfies Zakai equation and solves thenonlinear filtering problem. Using Galerkin technique the solution of Zakaiequation is approximated by means of a sequence of nonstandard basisfunctions given by a parameterized family of Gaussian densities. The methodis then illustrated by some examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008206719489
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  • 6
    Electronic Resource
    Electronic Resource
    On the optimal controls of a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions (1979)
    Springer
    Annali di matematica pura ed applicata 122 (1979), S. 61-82 
    Details
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we consider the question of existence of optimal controls for a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions and with controls appearing in the coefficients. In Theorems2.2 and2.3 we present existence and uniqueness of solutions of the first boundary problems. In Theorems3.1 and3.2 we prove that whenever the coefficients of the system converge in the w*-topology (L1 topology on L∞) the corresponding solutions converge weakly in an appropriate Sobolev space. Using these basic results we present two theorems (Theorems4.1 and4.2) on the existence of optimal controls.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411688
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Stabilization of a class of hybrid systems arising in flexible spacecraft (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 83-108 
    Details
    ISSN: 1573-2878
    Keywords: Flexible spacecraft ; dynamic modelling ; coupled systems of ordinary and partial differential equations ; system stabilization ; Lyapunov's functionals ; feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the problem of rigorous modelling of flexible spacecraft and their stabilization. It is shown that the dynamics of the flexible spacecraft can be described by a coupled system of ordinary differential equations and partial differential equations (hybrid system). Lyapunov's approach is used to prove the stabilizability of the system. Simple feedback controls are suggested for stabilization of flexible spacecraft.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938479
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  • 9
    Electronic Resource
    Electronic Resource
    Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space (1986)
    Springer
    Journal of optimization theory and applications 50 (1986), S. 213-237 
    Details
    ISSN: 1573-2878
    Keywords: Differential inclusions ; Banach spaces having Radon-Nikodym property ; mild solutions ; Polish spaces ; relaxed controls ; measure-valued controls ; Cesari property ; distributed controls ; boundary controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using Cesari's approach, we prove the existence of optimal controls for a class of systems governed by differential inclusions on a Banach space having the Radon-Nikodym property. Theorem 3.1 gives the existence result for optimal relaxed controls under fairly general assumptions on the system and the admissible controls. This result depends on a fundamental result (Theorem 2.1) that proves the existence of mild solutions of differential inclusions on a Banach space, which has also independent interest. Further, the preparatory results, such as Lemma 3.1 and Lemma 3.2, are also useful in the study of time-optimal and terminal control problems. For illustration of the results, we present two examples, one on distributed controls for a class of systems governed by nonlinear parabolic equations and the other on boundary controls with discontinuous boundary operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939270
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  • 10
    Electronic Resource
    Electronic Resource
    Comments on a selector theorem in Banach spaces (1976)
    Springer
    Journal of optimization theory and applications 19 (1976), S. 117-118 
    Details
    ISSN: 1573-2878
    Keywords: Set-valued mappings ; selection theorem ; reflexive Banach spaces ; weakly compact sets ; Cesari's Q-property ; optimal control theory ; existence of optimal controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Cole (Ref. 1) presented a selection theorem in reflexive Banach spaces under certain convexity assumptions. In this paper, we present a proof of Cole's selection theorem without imposing the convexity condition. This makes the result more powerful for application in optimal control theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934055
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