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.↗
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Results for “Discrete optimization”
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Necessary conditions for discrete parameter stochastic optimization problems
Necessary conditions for discrete parameter stochastic optimization problems
Kushner, H. J.↗
Gradient methods for the optimization of dynamic system parameters by hybrid computation.
Computer implementation of gradient method in continuous and discrete optimization of dynamic system
DISCRETE FUNCTION↗
Iterative solution of nonlinear optimal control problems.
Mathematical programming methods for solving nonlinear state-constrained discrete optimal control problems
DYNAMIC PROGRAMMING↗
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.
Cai, Z.↗
Optimal control of aperiodic discrete-time systems.
Optimal control and trajectory optimization in aperiodic discrete time functional systems
APERIODIC FUNCTION↗
Multi-level adaptive computations in fluid dynamics
The multi-level adaptive technique (MLAT) is a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization. It provides very fast solvers together with adaptive, nearly optimal discretization schemes to general boundary-value problems in general domains. Here the state of the art is surveyed, emphasizing steady-state fluid dynamics applications, from slow viscous flows to transonic ones. Various new techniques are briefly discussed, including distributive relaxation schemes, the treatment of evolution problems, the combined use of upstream and central differencing, local truncation extrapolations, and other 'super-solver' techniques.
Brandt, A.↗
Software For Integer Programming
Improved Exploratory Search Technique for Pure Integer Linear Programming Problems (IESIP) program optimizes objective function of variables subject to confining functions or constraints, using discrete optimization or integer programming. Enables rapid solution of problems up to 10 variables in size. Integer programming required for accuracy in modeling systems containing small number of components, distribution of goods, scheduling operations on machine tools, and scheduling production in general. Written in Borland's TURBO Pascal.
Fogle, F. R.↗
Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems
The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.
Brandt, A.↗
Application of A Dual-Quaternion Six Degree-of-Freedom Guidance to Human-Scale Mars Entry, Descent, and Landing
Landing humans on Mars comes with many challenges, including the execution of a safe and precise entry, descent, and landing (EDL) sequence. Various NASA studies have shown that there are a variety of EDL guidance methods that potentially offer solutions to the human-scale EDL precision landing problem and work is ongoing to assess new and novel methods. As part of these ongoing studies, a dual-quaternion-based six degree-of-freedom guidance algorithm was implemented in the Program to Optimize Simulated Trajectories II (POST2), a NASA-and industry-standard spacecraft trajectory and vehicle design tool. This algorithm considers both translational and rotational dynamics and casts the trajectory optimization problem as a quadratically constrained quadratic program (QCQP) with various constraints at discrete nodes throughout the trajectory. The QCQP problem is solved via an alternating direction method of multipliers (ADMM) approach, and the output is a discretized optimal trajectory. The guidance is applied to a NASA reference human-scale Mars EDL system, and results are compared and discussed.
Optimization↗
Application of A Dual-Quaternion Six Degree-of-Freedom Guidance to Human-Scale Mars Entry, Descent, and Landing
Landing humans on Mars comes with many challenges, including the execution of a safe and precise entry, descent, and landing (EDL) sequence. Various NASA studies have shown that there are a variety of EDL guidance methods that potentially offer solutions to the human-scale EDL precision landing problem and work is ongoing to assess new and novel methods. As part of these ongoing studies, a dual-quaternion-based six degree-of-freedom guidance algorithm was implemented in the Program to Optimize Simulated Trajectories II (POST2), a NASA-and industry-standard spacecraft trajectory and vehicle design tool. This algorithm considers both translational and rotational dynamics and casts the trajectory optimization problem as a quadratically constrained quadratic program (QCQP) with various constraints at discrete nodes throughout the trajectory. The QCQP problem is solved via an alternating direction method of multipliers (ADMM) approach, and the output is a discretized optimal trajectory. The guidance is applied to a NASA reference human-scale Mars EDL system, and results are compared and discussed.
Optimization↗
First-Order System Least-Squares for the Navier-Stokes Equations
This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.
Bochev, P.↗
Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis
A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.
Ambur, Damodar R.↗
Optimizing Proprotor Blades Using Coupled Aeroacoustic and Aerodynamic Sensitivities
A quieter and aerodynamically more efficient proprotor design requires high-fidelity and well-integrated optimization and analysis tools. To fulfill that requirement, the present paper delivers a methodology based on multidisciplinary, adjoint-based, discrete optimization. SU2-based code development involves the implementation of aeroacoustic analysis, adjoint computations, and integrations into a multidisciplinary rotorcraft optimization suite. Submodules utilized in the optimization are verified with wind tunnel data to demonstrate the accuracy of aerodynamic and aeroacoustic analyses. The developed code is used for NASA's helically twisted proprotor to maximize the aeroacoustic performance of the proprotor while holding thrust constant. The optimization process considers multiple flight conditions (hence, multipoint), which are forward flight and hovering. As an outcome of the analyses, the optimized blade design propagates lower noise as perceived by multiple observers in both flight conditions
R Omur Icke↗
Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints
A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and, strength constraints is developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory is used for the global analysis. Local buckling of skin segments are assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments are also assessed. Constraints on the axial membrane strain in the skin and stiffener segments are imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study are the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence, and stiffening configuration, where herein stiffening configuration is a design variable that indicates the combination of axial, transverse, and diagonal stiffener in the grid-stiffened cylinder. The design optimization process is adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads, and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configuration.
Jaunky, Navin↗
Optimal Design of General Stiffened Composite Circular Cylinders for Global Buckling with Strength Constraints
A design strategy for optimal design of composite grid-stiffened cylinders subjected to global and local buckling constraints and strength constraints was developed using a discrete optimizer based on a genetic algorithm. An improved smeared stiffener theory was used for the global analysis. Local buckling of skin segments were assessed using a Rayleigh-Ritz method that accounts for material anisotropy. The local buckling of stiffener segments were also assessed. Constraints on the axial membrane strain in the skin and stiffener segments were imposed to include strength criteria in the grid-stiffened cylinder design. Design variables used in this study were the axial and transverse stiffener spacings, stiffener height and thickness, skin laminate stacking sequence and stiffening configuration, where stiffening configuration is a design variable that indicates the combination of axial, transverse and diagonal stiffener in the grid-stiffened cylinder. The design optimization process was adapted to identify the best suited stiffening configurations and stiffener spacings for grid-stiffened composite cylinder with the length and radius of the cylinder, the design in-plane loads and material properties as inputs. The effect of having axial membrane strain constraints in the skin and stiffener segments in the optimization process is also studied for selected stiffening configurations.
Jaunky, N.↗
Optimal Design of Grid-Stiffened Panels and Shells With Variable Curvature
A design strategy for optimal design of composite grid-stiffened structures with variable curvature subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. Stiffening configuration is herein defined as a design variable that indicates the combination of axial, transverse and diagonal stiffeners in the stiffened panel. The design optimization process is adapted to identify the lightest-weight stiffening configuration and stiffener spacing for grid-stiffened composite panels given the overall panel dimensions. in-plane design loads, material properties. and boundary conditions of the grid-stiffened panel or shell.
Ambur, Damodar R.↗
ORACLS: A system for linear-quadratic-Gaussian control law design
A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
Armstrong, E. S.↗