A technique of quasi-optimum control.
Quasi-optimum control technique based on Hamiltonian to solve two-point boundary value problem for nonlinear system
BOUNDARY VALUE↗
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A statistical formulation of the estimation and the combined identification and control problems. Worst case initial condition Fifth quarterly report
Statistical formulation of estimation and combined identification and control problems of nonlinear dynamical systems
STATISTICAL ANALYSIS↗
Numerical Studies of the Non-linear Vlasov Equation
The subject of this dissertation is the numerical integration of the initial-value problem for the non-linear Vlasov equation. The Vlasov equation is used to describe the dynamics of a "collisionless", one-dimensional, classical electron gas confined between two perfectly reflecting boundaries. Only the long-range Coulomb interactions of the electrons are considered; effects associated with the discrete structure are neglected. The numerical results obtained for non-linear Landau damping compare well with similar results obtained by Knorr. A general statement of the results on stable initial conditions is: As the degree of non-linearity of the initial conditions is increased, the deviation from linear Landau damping appears sooner and is more severe. In some cases damping was observed to cease. Curves showing the time dependence of the damping decrement are derived and compared with predictions of non-linear theories. New results obtained in this study include the observation that for strongly non-linear cases, the damping of the electric field causes an initially Maxwellian fo (v, O) to develop a peak in the neighborhood of the phase velocity; strong growth of the second harmonic is seen after fo (v, t) develops such a peak. Also new in this study is the interpretation of the development of a certain class of strongly unstable initial conditions as approaching an inhomogeneous equilibrium.
NUMERICAL INTEGRATION↗
Decomposition of large-scale systems.
Decomposition of large-scale mathematical problems in nonlinear programming
NONLINEAR PROGRAMMING↗
An accelerated gradient method for parameter optimization with non-linear constraints.
Accelerated gradient method for numerical solution of parameter optimization problems with nonlinear constraints
NUMERICAL ANALYSIS↗
Two-point boundary-value-problem techniques.
Newton-Raphson method generalized for solution of two-point boundary value problems of nonlinear optimal control theory for digital solution
DIGITAL COMPUTER↗
Reciprocity in nonlinear networks
Reciprocity and quasilinearity in solving nonlinear network problems
Stern, T. E.↗
A Report on Session 12 IFAC Congress, 1966 (engeneering Philosophy of Optimization in the Problemof Analytical Design of Optima Controllers)
Summaries and abstracts on theory, design, optimization, and stability problems of nonlinear control systems
La Salle, J. P.↗
Generalized superposition.
Generalization of superposition principle for linear systems applied to classification of nonlinear systems and solution of nonlinear filtering problems
Oppenheim, A. V.↗
Asymptotic stability with output constraints.
Initial conditions estimation problem for nonlinear system asymptotic stability and satisfaction of output constraints on state variables
Julich, P. M.↗
The supersonic leading edge problem according to the ellipsoidal model.
Supersonic leading edge problem using nonlinear Boltzmann equation with ellipsoidal model, calculating molecular distribution functions for flow field
Huang, A. B.↗
Variational problems involving functional differential equations.
Variational or optimal control for delayed systems, involving integrated maximum principle for problems with nonlinear functional differential systems
Banks, H. T.↗
Slowly varying system x equals A/t/x
Slowly varying parameters as engineering problem in nonlinear lumped systems
Desoer, C. E.↗
The prediction of the nonlinear behavior of unstable liquid rockets
Analytical technique for solving nonlinear combustion problems associated with liquid propellant rocket engines
Powell, E. A.↗
Convergence rates for a method of centers algorithm
Convergence of centers algorithm for solving nonlinear programming problems
Mifflin, R. B.↗
Some applications of NASTRAN to the buckling of thin cylindrical shells with cutouts
The buckling of isotropic and waffle-stiffened circular cylinders with and without cutouts was studied using NASTRAN's Rigid Format 5 for the case of axial compressive loading. The results obtained for the cylinders without cutouts are compared with available reference solutions. The results for the isotropic cylinders containing a single circular cutout with selected radii are compared with available experimental data. For the waffle-stiffened cyclinder, the effect of two diametrically opposed rectangular cutouts was studied. A DMAP alter sequence was used to permit the necessary application of different prebuckling and buckling boundary conditions. Advantage was taken of available symmetry planes to formulate equivalent NASTRAN model segments which reduced the associated computational cost of performing the analyses. Limitations of the applicability of NASTRAN for the solution of problems with nonlinear characteristics are discussed.
Williams, J. G.↗
Similarity analysis of differential equations by Lie group.
Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analysis in a broader sense - namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations - is given with new and very general methods evolved for deriving the possible groups of transformations.
Na, T. Y.↗
Part 2: Oscillations of elastic systems
Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces. Four methods of solving the problem of the action of periodic instantaneous impulses are presented. The Tacoma catastrophe is analyzed and used as an example of aeroelastic oscillations. Problems of nonlinear system oscillations include the vibration maintenance of rotation, the Sommerfeld effect, and self-oscillations of a quasi-system with dry friction.
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