Some sufficient conditions for minimax control
Matrix algebra and integral solution to optimal control and guidance and control problems
OPTIMAL CONTROL↗
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Automatic control
Numerical solution of optimal control and programming problems
FEEDBACK CONTROL SYSTEM↗
Remarks on the infinite dimensional Riccati equation.
Existence and uniqueness theorem of Riccati equation arising in solution of optimal linear regulator problems in Hilbert space
UNIQUENESS THEOREM↗
Integer programming formulation of constrained reliability problems.
Constrained reliability optimization problems solution by integer programming noting parallel redundancy systems, formulation for standby redundant units and cost minimization
Liittschwager, J. M.↗
A Frequency Domain Approach to Optimal Control
Development of linear optimal control solutions using transfer matrix
Wolovich, W. A.↗
Asymptotic expansion of an impulse for an optimal finite burn
Closed form expressions are derived for the position and velocity of a spacecraft during a finite burn using the method involving the theory of asymptotic expansion of the optimal impulsive solution. The small parameter is given by the reciprocal of the mass flow rate. The expansion is given in terms of the impulsive solution and holds up through third-order for the velocity and fourth-order for the position.
Pines, S.↗
A solution to the problem of optimizing the fuel bias for a liquid propellant rocket by an application of the central limit theorem
A method of determining the fuel bias for a bipropellant liquid rocket that minimizes outage associated penalties on payload potential is presented. A fuel bias so derived is normally called the optimum fuel bias. The subjects discussed are: (1) probability density function of outage, (2) computer program listing, and (3) choosing the optimum fuel bias.
Viera, W. J.↗
Kidney cell electrophoresis
A kidney cell electrophoresis technique is described in four parts: (1) the development and testing of electrophoresis solutions; (2) optimization of freezing and thawing; (3) procedures for evaluation of separated kidney cells; and (4) electrophoretic mobility characteristics of kidney cells.
Todd, P.↗
Preliminary design procedure for insulated structures subjected to transient heating
Minimum-mass designs were obtained for insulated structural panels loaded by a general set of inplane forces and a time dependent temperature. Temperature and stress histories in the structure are given by closed-form solutions, and optimization of the insulation and structural thicknesses is performed by nonlinear mathematical programming techniques. Design calculations are described to evaluate the structural efficiency of eight materials under combined heating and mechanical loads: graphite/polyimide, graphite/epoxy, boron/aluminum, titanium, aluminum, Rene 41, carbon/carbon, and Lockalloy. The effect on design mass of intensity and duration of heating were assessed. Results indicate that an optimum structure may have a temperature response well below the recommended allowable temperature for the material.
Adelman, H. M.↗
Kidney cell electrophoresis
The following aspects of kidney cell electrophoresis are discussed: (1) the development and testing of electrophoresis solutions; (2) optimization of freezing and thawing; (3) procedures for evaluation of separated kidney cells; and (4) electrophoretic mobility characterization of kidney cells.
Todd, P.↗
Implicit model following and parameter identification of unstable aircraft
A transformation in the s-plane is described which has utility in implicit model-following optimal control design application and in estimation or parameter identification problems. The objective of the transformation is, for the control problem, to achieve an unstable closed-loop system, and, for the estimation problem, to alleviate algorithm convergence problems that may arise in identifying unstable systems. For the control problem, the transformation is a shift along the real (sigma) axis of the plant and model poles and zeros. This transformation is shown to be equivalent to a modified performance index but offers the advantage of compatibility with existing optimal control solution algorithms. For the estimation problem, the data are multiplied by an exponential function and the assumed measurement and process noise covariances are appropriately modified. Examples of both control and estimation applications are presented.
Lebacqz, J. V.↗
Algorithm for fuel conservative horizontal capture trajectories
A real time algorithm for computing constant altitude fuel-conservative approach trajectories for aircraft is described. The characteristics of the trajectory computed were chosen to approximate the extremal trajectories obtained from the optimal control solution to the problem and showed a fuel difference of only 0.5 to 2 percent for the real time algorithm in favor of the extremals. The trajectories may start at any initial position, heading, and speed and end at any other final position, heading, and speed. They consist of straight lines and a series of circular arcs of varying radius to approximate constant bank-angle decelerating turns. Throttle control is maximum thrust, nominal thrust, or zero thrust. Bank-angle control is either zero or aproximately 30 deg.
Neuman, F.↗
A model for the submarine depthkeeping team
The most difficult task the depthkeeping team must face occurs during periscope-depth operations during which they may be required to maintain a submarine several hundred feet long within a foot of ordered depth and within one-half degree of ordered pitch. The difficulty is compounded by the facts that wave generated forces are extremely high, depth and pitch signals are very noisy and submarine speed is such that overall dynamics are slow. A mathematical simulation of the depthkeeping team based on the optimal control models is described. A solution of the optimal team control problem with an output control restriction (limited display to each controller) is presented.
Ware, J. R.↗
On-line optimization of aircraft altitude and flight path angle dynamics
The optimization of aircraft altitude and flight path angle dynamics is addressed in a form suitable for on-line computation and control. The approach here is a direct extension of the work reported by Calise (1979), where singular perturbation methods were used to optimize position, energy and heading dynamics; it thus represents an optimal control solution that models all of the primary trajectory related dynamics. It is pointed out that the resulting algorithm can be regarded as a nonlinear feedback control law. The minimum time intercept of a fixed terminal point is used in setting the framework in which the analytical results are developed. The main theoretical result is that the dynamics, while not completely separable, can be approximated by singular perturbation methods when the control model includes relative position dynamics.
Calise, A. J.↗
Considerations of open-loop, closed-loop, and adaptive multicyclic control systems
Four different types of self-tuning regulators were studied for multicyclic control of helicopter vibration. A numerical simulation of the helicopter is made, using a multivariable frequency-domain model, in terms of transfer function with six input control harmonics and six output harmonics. The model characteristics vary with flight speed. An off-line identification of model characteristics is made, using the least-squared-error method and using a succession of input and output measurements. The on-line identification of model characteristics is made using the Kalman filter solution. The optimal controls are calculated from the minimization of quadratic performance function based on response and multicyclic inputs. The performance of various regulators or controllers is judged from the stability, transient response, convergence time, and amplitude of the steady state.
Chopra, I.↗
New analytical results for AOTV guidance
Minimum energy-loss turns of an Aero-assisted, Orbital Transfer Vehicle (AOTV) performing the atmospheric portion of an orbital-plane-change maneuver are developed using the heading angle as the independent variable. Because the heading angle is monotonic, several difficulties previously encountered using the flight path angle, which is not monotonic, as the independent variable are eliminated. In addition, the solution of the optimal control problem reduces to the solution of a fourth-order polynomial which can be accomplished analytically.
Hull, D. G.↗
Effects of the law for nongravitational forces on the precession model of comet Encke
The precession model for P/Encke formulated by Whipple and Sekanina (1979) is reexamined in the light of the recent measurements of the OH and H production rates. An optimized precession solution derived using the production law of A'Hearn et al. (1985) is shown to require unacceptably small nucleus dimensions and to offer an inferior fit to observed variations in the orientation of the comet's perihelion fan-shaped coma. Observed changes in the emission fan suggest that both the thrust on the nucleus exerted by unit mass of sublimating ice and the average lag in outgassing are substantially greater before than after perihelion. It is concluded that at this time the Whipple-Sekanina model remains the best available precession solution for this comet.
Sekanina, Z.↗
Polynomial compensation, inversion, and approximation of discrete time linear systems
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
Baram, Yoram↗