Optimal control and convex programming.
Optimal control for investment program, obtaining solution through convex programming
OPTIMAL CONTROL↗
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Results for “solution 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 resolved rate law for kinematically redundant manipulators
The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators.
Bourgeois, B. J.↗
Viscous aerodynamic design using the adjoint variable approach
The use of classical optimal control methods, in particular variational methods, to solve the airfoil optimization problem, by deriving a set of adjoint (costate) equations and boundary conditions has already been done for inviscid (potential and Euler flows) and two dimensional, steady state, incompressible flow governed by the Navier-Stokes equations. The interior and boundary terms of the volume integral have been derived (in this work) for the steady Navier-Stokes equations in three dimensions for a viscous, compressible heat conducting fluid. This can be used to derive the adjoint equations and numerical boundary conditions for general classes of problems and hence paves the way for a solution to the aerodynamic optimization problem for compressible viscous flows. The next steps to the realization of that goal are projected as below. The usual square integral pressure functional as an objective function is being replaced by a more realistic drag functional subject to a lift constraint. The feasibility of attempting the more difficult time dependent problem is being investigated. It remains to get the full system of adjoint equations and boundary conditions with the new functional. The state and adjoint equations must be discretized and coded. An appropriate optimization program must be used (steepest descents seems inadequate) and various known airfoil shapes should be recovered in test cases of the computer program.
DeRise, George↗
Significance of Strain in Formulation in Theory of Solid Mechanics
The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.
Patnaik, Surya N.↗
Optimal filtering in the presence of unmodeled time correlated driving disturbances.
In many realistic data filtering problems, the cross correlation of the state estimation error and the state forcing function is unknown due to the poor knowledge of the time history of the forcing function. In this paper, the conservative and minimal approximation to the cross correlation terms is presented. It requires only the knowledge of the estimation error covariance and the forcing function covariance, with the choice of an associated free parameter left to the user. If the estimation error covariance and/or the forcing function covariance are bounded from above but not known exactly, the cross correlation approximation using those upper bounds remains conservative. This cross correlation approximation leads to a conservative approximation to the estimation error covariance matrix differential equation between measurement times. The free parameter is determined as the analytic solution to an associated optimal control problem. The procedure is expanded to include discrete linear measurement incorporation.
Fraser, D. C.↗
Quantum Adiabatic Optimization with Rydberg Arrays: Localization Phenomena and Encoding Strategies
Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead associated with such mappings is easily quantifiable and typically polynomial in problem size, it is much harder to quantify their overhead on the quantum algorithm, e.g., the transformation of the adiabatic timescale. In this work, we address this challenge on the concrete example of the encoding scheme proposed in [Nguyen , PRX Quantum , 010316 (2023)], which is designed to map optimization problems on arbitrarily connected graphs into Rydberg atom arrays. We consider the fundamental building blocks underlying this encoding scheme and determine the scaling of the minimum gap with system size along adiabatic protocols. Even when the original problem is trivially solvable, we find that the encoded problem can exhibit an exponentially closing minimum gap. We show that this originates from a quantum coherent effect, which gives rise to an unfavorable localization of the ground-state wave function. On the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose quantum-aware modifications of the encoding scheme that avoid this quantum bottleneck and lead to an exponential improvement in the adiabatic performance. This highlights the crucial importance of accounting for quantum effects when designing strategies to encode classical problems onto quantum platforms. Published by the American Physical Society 2025
Bombieri, Lisa (ORCID:0009000950422897)↗
Asymptotic continuation method for trajectory optimization
A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.
Washburn, R. B., Jr.↗
ADS-1 - A new general-purpose optimization program
Today, numerous programs are available which may be coupled with finite element analysis or other analysis techniques to perform the optimization function in the solution of structural synthesis problems. However, most of these codes include only one or two algorithms and many have not been tested on problems of significant size and complexity. There is, therefore, a need for a reliable, general-purpose, publicly available code, containing a variety of modern algorithms for use in structural synthesis as well as general engineering design. The ADS-1 program (Automated Design Synthesis: Version 1) was written in response to this need. The present investigation has the objective to present the capabilities of the ADS program and to demonstrate its application to structural synthesis. The ADS program solves the general nonlinear constrained optimization problem in the standard form. At each level of the optimization process, several options are available.
Vanderplaats, G. N.↗
Time-domain finite elements in optimal control with application to launch-vehicle guidance
A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.
Bless, Robert R.↗
Optimal impulsive manoeuvres and aerodynamic braking
A method developed for obtaining solutions to the aerodynamic braking problem, using impulses in the exoatmospheric phases is discussed. The solution combines primer vector theory and the results of a suboptimal atmospheric guidance program. For a specified initial and final orbit, the solution determines: (1) the minimum impulsive cost using a maximum of four impulses, (2) the optimal atmospheric entry and exit-state vectors subject to equality and inequality constraints, and (3) the optimal coast times. Numerical solutions which illustrate the characteristics of the solution are presented.
Jezewski, D. J.↗
Optimum propellant usage for reaction jet systems of space vehicles
The on-off type control for reaction jet systems is proven to be the optimal fuel scheme. However, due to the nonlinear characteristics of this type control, no direct method of solution is known for this optimal process being applied to the attitude control of space vehicles. This paper will discuss the optimization of fuel usage for an attitude control of space vehicles. A computation technique is developed for the calculation of optimal control law. The method of calculus of variations is applied to the estimation of the changes of performance index as well as terminal constraints. Thus an algorithm is obtained by the steepest descent method. A numerical example is given in the paper.
Liu, T. C.↗
Fuel consumption in optimal control
A method has been developed for comparing three optimal control strategies based on fuel consumption. A general cost function minimization procedure was developed by applying two theorems associated with convex sets. Three cost functions associated with control saturation, pseudofuel, and absolute fuel are introduced and minimized. The first two cost functions led to the bang-bang and continuous control strategies, and the minimization of absolute fuel led to an impulsive strategy. The three control strategies were implemented on two elementary systems and a comparison of fuel consumption was made. The impulse control strategy consumes significantly less fuel than the continuous and bang-bang control strategies. This comparison suggests a potential for fuel savings in higher-order systems using impulsive control strategies. However, since exact solutions to fuel-optimal control for large-order systems are difficult if not impossible to achieve, the alternative is to develop near-optimal control strategies.
Redmond, Jim↗
Computation of optimal low- and medium-thrust orbit transfers
This paper presents the formulation of the optimal low- and medium-thrust orbit transfer control problem, numerical methods for solution, and numerical solutions of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and 3D noncoplanar nonaligned elliptic terminal orbits. We set up examples to demonstrate the ability of two indirect methods to solve the resulting two point boundary value problems (TPBVP). The methods demonstrated are the multiple point shooting method as formulated in Oberle's (1987) subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are tradeoffs to using either method. We present numerical solutions of planar transfers in which both the initial orbit exit and final orbit entry points have been optimized. These solutions include two- and three-burn transfers. The methods used show an ability to handle thrust down to at least T/W(o) = O(10 exp -3). They also show similar convergence abilities with or without the oblateness and drag terms. We discuss the issue of maximizing with respect to the final time and provide evidence that implies a local optimum at a maximum final time for a given number of burns.
Chuang, C.-H.↗
Preconditioned upwind methods to solve 3-D incompressible Navier-Stokes equations for viscous flows
A computational method for calculating low-speed viscous flowfields is developed. The method uses the implicit upwind-relaxation finite-difference algorithm with a nonsingular eigensystem to solve the preconditioned, three-dimensional, incompressible Navier-Stokes equations in curvilinear coordinates. The technique of local time stepping is incorporated to accelerate the rate of convergence to a steady-state solution. An extensive study of optimizing the preconditioned system is carried out for two viscous flow problems. Computed results are compared with analytical solutions and experimental data.
Hsu, C.-H.↗
Computer program for parameter optimization
Flexible, large scale digital computer program was designed for the solution of a wide range of multivariable parameter optimization problems. The program has the ability to solve constrained optimization problems involving up to one hundred parameters.
Glatt, C. R.↗
Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports
A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.
multidisciplinary optimization↗
Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports
A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.
low-boom supersonic transports↗
Integration of Low-Fidelity MDO and CFD-Based Redesign of Low-Boom Supersonic Transports
A mixed-fidelity low-boom multidisciplinary optimization (MDO) problem is formulated for integration of low-fidelity MDO and computational fluid dynamics (CFD) based low-boom inverse design optimization. The mixed-fidelity low-boom MDO problem aims to enforce the weight consistency for CFD-based low-boom inverse design optimization: the optimum low-boom configuration is designed for the weight at the start of cruise of the same configuration for the low-boom overland mission. Moreover, it also seeks the optimum trades among the maximum takeoff gross weight (MTOGW), cruise Mach, and range for the low-boom overland mission while meeting the requirement of flying a transatlantic overwater mission. A block coordinate optimization (BCO) method is developed to find an approximate solution of the mixed-fidelity low-boom MDO problem. The BCO method is successfully applied to generate two CFD-based low-boom configurations that closely match two reversed equivalent area targets with ground noise levels below 70 PLdB, respectively. Moreover, these CFD-based low-boom configurations can be obtained with minor wing modifications from the solutions of the low-fidelity MDO problem. The low-fidelity MDO solutions are Pareto points for constrained multiobjective optimization of MTOGW, low-boom cruise Mach, and low-boom range. The best low-boom concept has a predetermined fuselage shape tailored for passengers and main gear storage, carries 40 passengers at seat pitch of 48 in, flies a low-boom overland mission with cruise Mach of 1.8 and range of 2,950 nm, cruises overwater at Mach 1.8 with range of 3,600 nm, satisfies the specified constraints for landing/cruise/takeoff, has MTOGW of 145,164 lb, trims the low-boom cruise flight with fuel redistributions instead of control surface deflections, and has a reversed equivalent area distribution closely matching a target with ground noise level below 70 PLdB.
low-boom supersonic transports↗