Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    ISSN: 1573-2878
    Keywords: Linear control systems ; reachability set ; time-optimal problems ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present in this paper algorithms for calculating the reachability set of a linear control system with a bounded closed control set and a finite time interval. We also present algorithms for the time-optimal problem of the linear control that yields an approximation to the optimal time and the corresponding control function. We give numerical examples of the computer implementation of these algorithms.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 2
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; secant methods ; hessian matrix sizing strategies ; trust-region methods ; BFGS update ; DFP update ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this study, we develop and test a strategy for selectively sizing (multiplying by an appropriate scalar) the approximate Hessian matrix before it is updated in the BFGS and DFP trust-region methods for unconstrained optimization. Our numerical results imply that, for use with the DFP update, the Oren-Luenberger sizing factor is completely satisfactory and selective sizing is vastly superior to the alternatives of never sizing or first-iteration sizing and is slightly better than the alternative of always sizing. Numerical experimentation showed that the Oren-Luenberger sizing factor is not a satisfactory sizing factor for use with the BFGS update. Therefore, based on our newly acquired understanding of the situation, we propose a centered Oren-Luenberger sizing factor to be used with the BFGS update. Our numerical experimentation implies that selectively sizing the BFGS update with the centered Oren-Luenberger sizing factor is superior to the alternatives. These results contradict the folk axiom that sizing should be done only at the first iteration. They also show that, without sufficient sizing, DFP is vastly inferior to BFGS; however, when selectively sized, DFP is competitive with BFGS.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 3
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; methods of feasible direction ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A variation of the Polak method of feasible directions for solving nonlinear programming problems is shown to be related to the Topkis and Veinott method of feasible directions. This new method is proven to converge to a Fritz John point under rather weak assumptions. Finally, numerical results show that the method converges with fewer iterations than that of Polak with a proper choice of parameters.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
  • 4
    ISSN: 1573-2878
    Keywords: Flight mechanics ; landing ; feedback control ; windshear problems ; differential games ; longitudinal motion ; lateral motion ; numerical methods ; linear differential games ; switch surfaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of the feedback control of an aircraft landing in the presence of windshear is considered. The landing process is investigated up to the time when the runway threshold is reached. It is assumed that the bounds on the wind velocity deviations from some nominal values are known, while information about the windshear location and wind velocity distribution in the windshear zone is absent. The methods of differential game theory are employed for the control synthesis. The complete system of aircraft dynamic equations is linearized with respect to the nominal motion. The resulting linear system is decomposed into subsystems describing the vertical (longitudinal) motion and lateral motion. For each subsystem, an, auxiliary antagonistic differential game with fixed terminal time and convex payoff function depending on two components of the state vector is formulated. For the longitudinal motion, these components are the vertical deviation of the aircraft from the glide path and its time derivative; for the lateral motion, these components are the lateral deviation and its time derivative. The first player (pilot) chooses the control variables so as to minimize the payoff function; the interest of the second player (nature) in choosing the wind disturbance is just opposite. The linear differential games are solved on a digital computer with the help of corresponding numerical methods. In particular, the optimal (minimax) strategy is obtained for the first player. The optimal control is specified by means of switch surfaces having a simple structure. The minimax control designed via the auxiliary differential game problems is employed in connection with the complete nonlinear system of dynamical equations. The aircraft flight through the wind downburst zone is simulated, and three different downburst models are used. The aircraft trajectories obtained via the minimax control are essentially better than those obtained by traditional autopilot methods.
    Type of Medium: Electronic Resource
    Signatur Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...