Combined optimal control and estimation.
Combined optimization problem, equivalent to dual control problem, considering determination of optimal control policies for plant under random disturbances, using iterative equations
CONTROL SYSTEM↗
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Results for “DUAL CONTROL PROBLEM”
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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Lagrange duality theory for convex control problems
The Lagrange dual to a control problem is studied. The principal result based on the Hahn-Banach theorem proves that the dual problem has an optimal solution if there exists an interior point for the constraint set. A complementary slackness condition holds, if the primal problem has an optimal solution. A necessary and sufficient condition for the optimality of solutions to the primal and the dual problem is also presented.
Hager, W. W.↗
On primal and dual methods for solving discrete optimal control problems
Primal and dual algorithms for discrete optimal control incorporating antijamming procedures
Polak, E.↗
A dual method for optimal control problems with initial and final boundary constraints.
This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.
Pironneau, O.↗
Dual adaptive control: Design principles and applications
The design of an actively adaptive dual controller based on an approximation of the stochastic dynamic programming equation for a multi-step horizon is presented. A dual controller that can enhance identification of the system while controlling it at the same time is derived for multi-dimensional problems. This dual controller uses sensitivity functions of the expected future cost with respect to the parameter uncertainties. A passively adaptive cautious controller and the actively adaptive dual controller are examined. In many instances, the cautious controller is seen to turn off while the latter avoids the turn-off of the control and the slow convergence of the parameter estimates, characteristic of the cautious controller. The algorithms have been applied to a multi-variable static model which represents a simplified linear version of the relationship between the vibration output and the higher harmonic control input for a helicopter. Monte Carlo comparisons based on parametric and nonparametric statistical analysis indicate the superiority of the dual controller over the baseline controller.
Mookerjee, Purusottam↗
Dual-Use Partnership Addresses Performance Problems with "Y" Pattern Control Valves
A Dual-Use Cooperative Agreement between the Propulsion Test Directorate (PTD) at Stennis Space Center (SSC) and Oceaneering Reflange, Inc. of Houston, TX has produced an improved 'Y' pattern split-body control valve for use in the propulsion test facilities at Stennis Space Center. The split-body, or clamped bonnet technology, provides for a 'cleaner' valve design featuring enhanced performance and increased flow capacity with extended life expectancy. Other points addressed by the partnership include size, weight and costs. Overall size and weight of each valve will be reduced by 50% compared to valves currently in use at SSC. An initial procurement of two 10 inch valves will result in an overall cost reduction of 15% or approximately $50,000 per valve.
Bailey, John W.↗
On a problem of letov in optical control.
Optimal regulator problem for linear plant with bounded control variable and quadratic index performance
DUAL CONTROL PROBLEM↗
On Linear Product Codes and Their Duals Scientific Report No. 4
Tensor products of linear codes, and product codes with dual cyclic component codes
TENSOR FIELD↗
An Integrated Control and Minimum Mass Structural Optimization Algorithm for Large Space Structures
A new approach is discussed for solving dual structural control optimization problems for high-order flexible space structures, where reduced-order structural models are employed and minimum mass designs are sought. For a given initial structural design, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the structural design variables is then determined and used to obtain successive structural redesigns, using a constrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. The minimum mass design is obtained by solving a sequence of neighboring optimal constant mass designs, where the sequence of optimal performance indices has a minimum at the optimal minimum mass design. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.
Messac, A.↗
Dual structural-control optimization of large space structures
A new approach is proposed for solving dual structural-control optimization problems for high-order flexible space structures where reduced-order structural models are employed. For a given initial structural dessign, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the stuctural design variables is then determined and used to obtain successive structural redesigns using a contrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.
Messac, A.↗
Fuel-optimal angular momentum vector control for spinning and dual-spin spacecraft.
The problem of fuel-optimal small-angle reorientation of the spin axis of a spinning or dual-spin spacecraft is examined. The results obtained show significant improvements over previously published optimization studies by virtue of the introduction of two innovations: (1) mass-explusion active control is utilized for angular momentum vector pointing only, with passive damping relied upon for stable vehicles to attenuate vehicle coning about the angular momentum vector, so that the task of the active controller changes from spin axis control to angular momentum vector control, and (2) several options are considered for type, number, and location of attitude control jets. The first of these considerations introduces a target set which is a smooth, two-dimensional linear manifold in the four-dimensional state space, whereas previous studies have adopted the origin as the target set. The second innovation amounts to consideration of a spectrum of control restraint sets.
Larson, V.↗
Design and evaluation of an optical fine-pointing control system for telescopes utilizing a digital star sensor
One of the most significant problems associated with the development of large orbiting astronomical telescopes is that of maintaining the very precise pointing accuracy required. A proposed solution to this problem utilizes dual-level pointing control. The primary control system maintains the telescope structure attitude stabilized within the field of view to the desired accuracy. In order to demonstrate the feasibility of optically stabilizing the star images to the desired accuracy a regulating system has been designed and evaluated. The control system utilizes a digital star sensor and an optical star image motion compensator, both of which have been developed for this application. These components have been analyzed mathematically, analytical models have been developed, and hardware has been built and tested.
Ostroff, A. J.↗
Optimal take-off trajectories in the presence of windshear
The present consideration of takeoff trajectory optimization in eight different fundamental problems involving wind shears assumes that the power setting is held at the maximum value, and that the aircraft is controlled with respect to angle-of-attack. While the first three problems are least-squares ones of the Bolza type, the remaining five are minimax problems of the Chebyshev type which can be converted to Bolza type by means of suitable transformations. All problems are solved on the basis of the dual sequential gradient-restoration algorithm for optimal control problems. The trajectory solutions obtained are superior to constant angle-of-attack trajectories.
Miele, A.↗
Dual approximations in optimal control
A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.
Hager, W. W.↗
A dual phase plane approach to the two-finite- burns minimum fuel rendezvous problem.
Two-finite burns minimum fuel rendezvous problem using dual phase plane description, determining control law
VARIATION METHOD↗
On the removal of ill conditioning effects in the computation of optimal controls
Dual type method solving discrete optimal control problems with linear plants, convex cost and constraint taking into account dynamic structure
Polak, E.↗
Multistage depressed collector with efficiency of 90 to 94 percent for operation of a dual-mode traveling wave tube in the linear region
An axisymmetric, multistage, depressed collector of fixed geometric design was evaluated in conjunction with an octave bandwidth, dual mode traveling wave tube (TWT). The TWT was operated over a wide range of conditions to simulate different applications. The collector performance was optimized (within the constraint of fixed geometric design) over the range of TWT operating conditions covered. For operation of the TWT in the linear, low distortion range, 90 percent and greater collector efficiencies were obtained leading to TWT overall efficiencies of 20 to 35 percent, as compared with 2 to 5 percent with an undepressed collector. With collectors of this efficiency and minimized beam interception losses, it becomes practical to design dual mode TWT's such that the low mode can represent operation well below saturation. Consequently, the required pulse up in beam current can be reduced or eliminated, and this mitigates beam control and dual mode TWT circuit design problems. For operation of the dual mode TWT at saturation, average collector efficiencies in excess of 85 percent were obtained for both the low and high modes across an octave bandwidth, leading to a three to fourfold increase in the TWT overall efficiency.
Ramins, P.↗
Optimization and gamma/theta guidance of flight trajectories in a windshear
Guidance schemes for near-optimum performance in wind shear are examined. The presence of a downdraft is assumed in addition to the horizontal shear. The takeoff problem is considered with reference to flight in a vertical plane. Trajectories for optimum performance in a wind shear are determined for different wind shear models and intensities. Methods of optimal control theory are used together with the dual sequential gradient-restoration algorithm for optimal control problems. Guidance schemes for near-optimum performance in a wind shear are developed, starting from optimal trajectories. These are gamma guidance, based on either the absolute of the relative path inclination, and theta guidance, based on the pitch attitude angle. These schemes are evaluated through numerical experiments in order to determine whether the resulting trajectories are sufficiently close to optimum and to compare these trajectories with those arising from alternative guidance schemes.
Miele, A.↗