Discrete optimizing.
Discrete optimization problem approach and evaluation of results of applying it to variety of traveling salesman problems
OPTIMIZATION↗
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Results for “Discrete Optimization”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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An optimal discrete control strategy for terminal guidance.
Optimal discrete control strategy for terminal guidance using computation procedure based on theory of dynamic programming
DYNAMIC PROGRAMMING↗
On primal and dual methods for solving discrete optimal control problems
Primal and dual algorithms for discrete optimal control incorporating antijamming procedures
Polak, E.↗
Search for good algorithms for practical solutions to discrete optimization problems Final report
Applying method of stochastic algorithms to solution of discrete optimization problems
Sherman, G. R.↗
Optimal Discrete Event Supervisory Control of Aircraft Gas Turbine Engines
This report presents an application of the recently developed theory of optimal Discrete Event Supervisory (DES) control that is based on a signed real measure of regular languages. The DES control techniques are validated on an aircraft gas turbine engine simulation test bed. The test bed is implemented on a networked computer system in which two computers operate in the client-server mode. Several DES controllers have been tested for engine performance and reliability.
Litt, Jonathan↗
Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem
The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.
Halyo, N.↗
Time scale analysis of a closed-loop discrete optimal control system
A two-time scale discrete control system is considered. The closed-loop optimal linear quadratic (LQ) regulator for the system requires the solution of a full-order algebraic matrix Riccati equation. Alternatively, the original system is decomposed into reduced-order slow and fast subsystems. The closed-loop optimal control of the subsystems requires the solution of two algebraic matrix Riccati equations of order lower than that required for the full-order system. A composite, closed-loop suboptimal control is created from the sum of the slow and fast feedback optimal controls. Numerical results obtained for an aircraft model show a very close agreement between the exact (optimal) solutions and computationally simpler composite (suboptimal) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the closed-loop optimal control of digital flight systems.
Naidu, D. S.↗
Discrete optimal control approach to a four-dimensional guidance problem near terminal areas
Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.
Nagarajan, N.↗
A method for nonlinear optimization with discrete design variables
A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.
Olsen, Gregory R.↗
Bell-Curve Genetic Algorithm for Mixed Continuous and Discrete Optimization Problems
In this manuscript we have examined an extension of BCB that encompasses a mix of continuous and quasi-discrete, as well as truly-discrete applications. FVe began by testing two refinements to the discrete version of BCB. The testing of midpoint versus fitness (Tables 1 and 2) proved inconclusive. The testing of discrete normal tails versus standard mutation showed was conclusive and demonstrated that the discrete normal tails are better. Next, we implemented these refinements in a combined continuous and discrete BCB and compared the performance of two discrete distance on the hub problem. Here we found when "order does matter" it pays to take it into account.
Kincaid, Rex K.↗
Active flutter control using discrete optimal constrained dynamic compensators
A method for synthesizing digital active flutter suppression controllers using the concept of optimal output feedback is presented. A recently developd convergent algorithm is employed to determine constrained control law parameters that minimize an infinite-time discrete quadratic performance index. Low-order compensator dynamics are included in the control law and the compensator parameters are computed along with the output feedback gain as part of the optimization process. An input noise adjustment procedure is used to improve the stability margins of the digital active flutter controller. Results from investigations into sample rate variation, prefilter pole variation, and effects of varying flight condtions are discussed. The study indicates that a digital control law which accommodates computation delay can stabilize the wing with reasonable rms performance and adequate stability margins.
Broussard, J. R.↗
An optimal discrete control strategy for interplanetary guidance.
Guiding one state of linear dynamical system to prescribed rms terminal accuracy in presence of injection, measurement and engine-mechanization error
ROOT-MEAN-SQUARE ERROR↗
A constrained discrete optimal guidance strategy for low-thrust space flight
A low-thrust guidance algorithm suitable for operational use is formulated. Using linear stochastic control theory, a linear feedback control law is obtained for a minimum terminal miss performance criterion. The control variables are restricted to constant values over specified time intervals and are explicitly limited. Both fixed and variable time-of-arrival guidance are considered. Guidance equations are presented in deterministic (operational) and in statistical form; and computational procedures necessary for implementation are outlined. The performance of the guidance algorithm is evaluated by applying it to the approach phase of the 1980 rendezvous mission with the comet Encke.
Jacobson, R. A.↗
The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations
The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.
Parrish, E. A.↗
Time-scale synthesis of a closed-loop discrete optimal control system
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Naidu, D. S.↗
A second-order variational method for discrete-time optimal control problems.
Discrete time optimal control problems solved by second order variational algorithm, developing recurrence relations for perturbation equations
Koivo, A. J.↗
Structure and stability of discrete-time optimal systems
Discrete-time optimal linear systems structure and stability, assuming quadratic costs and perfect observability
Rappaport, D.↗
Solar collector parameter identification from unsteady data by a discrete-gradient optimization algorithm
A discrete-gradient optimization algorithm is used to identify the parameters in a one-node and a two-node capacitance model of a flat-plate collector. Collector parameters are first obtained by a linear-least-squares fit to steady state data. These parameters, together with the collector heat capacitances, are then determined from unsteady data by use of the discrete-gradient optimization algorithm with less than 10 percent deviation from the steady state determination. All data were obtained in the indoor solar simulator at the NASA Lewis Research Center.
Hotchkiss, G. B.↗