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  • 1
    Electronic Resource
    Electronic Resource
    Sequential filter design for precision orbit determination and physical constant refinement (1974)
    Springer
    Celestial mechanics and dynamical astronomy 8 (1974), S. 481-494 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Earth-based spacecraft tracking data have historically been processed with classical least squares filtering techniques both for navigation purposes and for physical constant determination. The small, stochastic non-gravitational forces acting on the spacecraft are described to motivate the use of sequential estimation as an alternative to the least squares fitting procedures. The stochastic forces are investigated both in terms of their effect on the tracking data and their influence on estimation accuracy. A flexiible sequential filter design which leaves the existing trajectory, variational equations, data observable and partial computations undisturbed is described. A detailed filter design is presented that meets the precision demands and flexibility requirements of deep space navigation and scientific problems, one which provides a high degree of numerical integrity and numerical analysis capability, facilitates the efficient computation of multiple solutions, and makes few demands on the supporting computational structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01227800
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  • 2
    Electronic Resource
    Electronic Resource
    Extensions in quasilinearization techniques for optimal control (1968)
    Springer
    Journal of optimization theory and applications 2 (1968), S. 316-330 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents several extensions in quasilinearization techniques for optimal control problems. Techniques are developed that facilitate the application of quasilinearization to control problems where bounds on the controls exist. Toward this end, quadratic convergence for bounded continuous control is shown. A method for extending the region over which the method converges is presented, and the theoretical advantage of the extended method is shown. The work of Long is modified to provide more accurate integration while preserving its usefulness in solving problems where the final time is free. A companion paper presents computational results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00928756
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  • 3
    Electronic Resource
    Electronic Resource
    Computational results for extensions in quasilinearization techniques for optimal control (1968)
    Springer
    Journal of optimization theory and applications 2 (1968), S. 395-410 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a companion paper (Ref. 1), several extensions in quasilinearization were presented. These results are studied computationally in this paper for two problems: the brachistochrone problem and the reentry vehicle problem. For the brachistochrone free-time problem, it is shown that much more rapid convergence is obtained than that presented in previous literature (Ref. 2). It is also shown that, if the techniques of the companion paper are used, the normal region of convergence is extended significantly. Similar results are obtained for the reentry vehicle problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00925745
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  • 4
    Electronic Resource
    Electronic Resource
    Differential games with noise-corrupted measurements (1979)
    Springer
    Journal of optimization theory and applications 28 (1979), S. 233-251 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic differential games ; secure strategies ; boundary-value problems ; differential equations ; Hilbert space ; payoff relationships ; differential games ; pursuit-evasion game
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, readily computable strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are developed. Of particular significance is the fact that the governing differential equations no longer require the solution of an often difficult nonlinear, two-point boundary-value problem, but again satisfy the separation principle of linear-quadratic optimal control. The implications of the payoff relationships are considered. In a subsequent paper, we will apply the theory developed in this paper to a detailed example of a pursuit-evasion game. We discuss a missile and an airplane system where the missile supported by its launch platform has perfect state measurements and the airplane has noise-corrupted measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933244
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  • 5
    Electronic Resource
    Electronic Resource
    On-line solution of a stochastic pursuit-evasion game (1979)
    Springer
    Journal of optimization theory and applications 28 (1979), S. 411-428 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic differential games ; secure strategies ; boundary-value problems ; differential equations ; Hilbert space ; payoff relationships ; pursuit-evasion game
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the concepts of prior-commitment and delayed-commitment strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are applied to a detailed example of a pursuit-evasion game. Quasilinearization is used to solve the nonlinear two-point boundary-value problem of the prior-commitment game. A closed form solution is obtained for the delayed-commitment strategies. Comparison of the payoff functionals confirms the relationships discussed in Ref. 1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933383
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  • 6
    Electronic Resource
    Electronic Resource
    An appreciation of Professor Richard Bellman (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 399-406 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934029
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  • 7
    Electronic Resource
    Electronic Resource
    Singular linear quadratic differential games with bounds on control (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 341-348 
    Details
    ISSN: 1573-2878
    Keywords: Zero-sum differential games ; singular arcs ; saddle points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of two-persons zero-sum differential games with the possibility of singular arcs is considered. Under some assumptions, a sufficient condition for the existence of a saddle-point solution is derived. In this approach, the properties of convexity and concavity of the performance index are used to find the sufficient condition. It is observed that, unlike total singularity, the occurrence of partially singular arcs does not cause any problems for the existence of a unique saddle-point solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935229
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  • 8
    Electronic Resource
    Electronic Resource
    Optimization approach to the design of frequency sampling filters (1993)
    Springer
    Journal of optimization theory and applications 79 (1993), S. 253-272 
    Details
    ISSN: 1573-2878
    Keywords: Digital filters ; finite impulse response ; frequency sampling ; Lagrange multiplier optimization ; interpolation ; discrete Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940581
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  • 9
    Electronic Resource
    Electronic Resource
    An extended quasilinearization algorithm (1973)
    Springer
    Journal of optimization theory and applications 12 (1973), S. 268-284 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The quasilinearization algorithm for the solution of two-point boundary-value problems is extended to handle a general class of multipoint boundary value problems involving multiple subarcs, state and/or control variable inequality constraints, and discontinuous state and/or adjoint variables. The corner and final times are unspecified since they are implicitly defined by the satisfaction of subarc stopping conditions. The inequality constraints are handled directly without the use of penalty functions. The extended algorithm is applied to a discontinuous version of the brachistochrone problem, and good convergence properties are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935109
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  • 10
    Electronic Resource
    Electronic Resource
    Singular differential game numerical techniques (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 69-87 
    Details
    ISSN: 1573-2878
    Keywords: Differential games ; singular arcs ; saddle points ; two-point boundary-value problems ; switching times ; closed-loop solutions ; inverse systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934367
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