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  • 1
    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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  • 2
    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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    Paper (German National Licenses)
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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Optimal control of systems governed by a class of nonlinear evolution equations in a reflexive Banach space (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 57-81 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear evolution equations ; reflexive Banach spaces ; existence theorems ; time-optimal control ; Bolza problem ; terminal control ; velocity field ; set-valued map ; weak Cesari property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper presents a closure theorem for the attainable trajectories of a class of control systems governed by a large class of nonlinear evolution equations in reflexive Banach spaces. Several existence theorems for optimal controls are proven that include a terminal control problem, a time-optimal control problem, and a special Bolza problem. Some results of independent interest are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933255
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  • 8
    Electronic Resource
    Electronic Resource
    Parameter identification for partially observed diffusions (1992)
    Springer
    Journal of optimization theory and applications 75 (1992), S. 33-50 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear filtering ; likelihood ratio ; parameter identification ; optimal control ; distributed-parameter systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the identification problem of drift and dispersion parameters for a class of partially observed systems governed by Ito equations. Using the pathwise description of the Zakai equation, we formulate the original identification problem as a deterministic control problem in which the unnormalized conditional density (solution of the Zakai equation) is treated as the state, the unknown parameters as controls, and the likelihood ratio as the objective functional. The question of existence of elements in the parameter set that maximize the likelihood ratio is discussed. Further, using variational arguments and the Gateaux differentiability of the unnormalized density on the parameter set, we obtain the necessary conditions for optimal identification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939904
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal control of infinite-dimensional uncertain systems (1994)
    Springer
    Journal of optimization theory and applications 80 (1994), S. 261-272 
    Details
    ISSN: 1573-2878
    Keywords: Uncertain evolution equations ; strongly nonlinear systems ; monotone operators ; optimal control ; existence of optimal controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a minimax problem of optimal control for a class of strongly nonlinear uncertain evolution equations on a Banach space. We prove the existence of optimal controls. A nontrivial example of a class of systems governed by a nonlinear partial differential equation with uncertain spatial parameters is presented for illustration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192935
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  • 10
    Electronic Resource
    Electronic Resource
    Necessary conditions of optimality for a class of second-order hyperbolic systems with spatially dependent controls in the coefficients (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 423-446 
    Details
    ISSN: 1573-2878
    Keywords: Parameter optimization ; hyperbolic systems ; necessary conditions of optimality ; existence of optimal or suboptimal policies ; quadratic cost function ; power system voltage regulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the paper, we consider the problem of parameter optimization for a class of second-order hyperbolic systems with distributional forcing terms. After necessary preparations in Sections 1 and 3, we develop in Section 4 the necessary conditions of optimality for the system with quadratic cost function. In Section 5, we extend these results to cover a wider class of controls; we also prove the existence of suboptimal policies. An example is presented indicating possible application to power system regulation problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935347
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