Cost-function characterization of systems
Cost function characterizations of dynamical control systems - Markov transition cost functions
MATHEMATICS↗
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On a cost functional for H2/H(infinity) minimization
A cost functional is proposed and investigated which is motivated by minimizing the energy in a structure using only collocated feedback. Defined for an H(infinity)-norm bounded system, this cost functional also overbounds the H2 cost. Some properties of this cost functional are given, and preliminary results on the procedure for minimizing it are presented. The frequency domain cost functional is shown to have a time domain representation in terms of a Stackelberg non-zero sum differential game.
Macmartin, Douglas G.↗
Analysis of Different Cost Functions in the Geosect Airspace Partitioning Tool
A new cost function representing air traffic controller workload is implemented in the Geosect airspace partitioning tool. Geosect currently uses a combination of aircraft count and dwell time to select optimal airspace partitions that balance controller workload. This is referred to as the aircraft count/dwell time hybrid cost function. The new cost function is based on Simplified Dynamic Density, a measure of different aspects of air traffic controller workload. Three sectorizations are compared. These are the current sectorization, Geosect's sectorization based on the aircraft count/dwell time hybrid cost function, and Geosect s sectorization based on the Simplified Dynamic Density cost function. Each sectorization is evaluated for maximum and average workload along with workload balance using the Simplified Dynamic Density as the workload measure. In addition, the Airspace Concept Evaluation System, a nationwide air traffic simulator, is used to determine the capacity and delay incurred by each sectorization. The sectorization resulting from the Simplified Dynamic Density cost function had a lower maximum workload measure than the other sectorizations, and the sectorization based on the combination of aircraft count and dwell time did a better job of balancing workload and balancing capacity. However, the current sectorization had the lowest average workload, highest sector capacity, and the least system delay.
Wong, Gregory L.↗
The structure of the software cost function
It is the purpose of this paper to analyze the structure of the cost estimating relationships that commercial cost models use and to test whether they are viable cost functions.
cost function cost estimating relationship wage ra↗
Cost function for low-dimensional manifold topology assessment
Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.
42 ENGINEERING↗
Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization
We derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as "inadmissible." For example, a cost functional which depends on the density, rather than on the pressure, is considered "inadmissible" for an optimization problem governed by the Euler equations. We show that for such problems additional terms should be included in the Lagrangian functional when deriving the adjoint equations. These terms are obtained from the restriction of the interior PDE to the control surface. Demonstrations of the explicit derivation of the adjoint equations for "inadmissible" cost functionals are given for the potential, Euler, and Navier-Stokes equations.
Arian, Eyal↗
Existence theorems for optimal problems with vector valued cost function
Existence theorems for optimal control problems with vector valued cost function
Olech, C.↗
Fixed order compensator design based on frequency shaped cost functionals
This paper treats the design of fixed order compensators using frequency shaped cost functionals. The formulation is done in an output feedback setting which exploits an observer canonical form to represent the compensator dynamics. The major advantages of the design approach are that the order of the compensator is fixed by the design process, and it is not necessary to realize the frequency shaping dynamics as an integral part of the compensator design. This avoids the two-step approach of full state feedback design followed by the design of an observer, which in the case of a full order observer requires a compensator of order n + nf where n is the order of the plant and nf is the order of the frequency shaping realization. The formulation also precludes the use of direct feedback of the plant output, thus reducing the effect of sensor noise and improving the robustness to high frequency unmodeled dynamics. A structural vibration model describing the fast dynamics of a lightweight flexible arm is used as an example to illustrate the design procedure.
Calise, Anthony J.↗
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is Ο(logn). Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.
97 MATHEMATICS AND COMPUTING↗
Mapping Ocean-Reflected Radio Frequency Interference for the GPM Microwave Imager Using Normalized Retrieval Cost Function
By adapting an approach originally developed for WindSat, we identify regions where GMI is affected by radio frequency interference from ocean-reflected geostationary satellite emissions. Around North America, K-band emissions from geostationary satellites affect the GMI 18.7-GHz brightness temperatures, resulting in increases in the retrieval cost function. The method does not detect any 10.7-GHz RFI reflected of the ocean surrounding Europe. This study, which depends on the physically-based forward model for non-raining ocean retrievals, confirms results from a previous study that employed an empirical methodology.
Ian S. Adams↗
Bounds Estimation Via Regression with Asymmetric Cost Functions
This paper addresses a significant but mostly-neglected class of problems that we call bounds estimation. This includes learning empirical best-case and worst-case algorithmic complexity bounds and red-line bounds on sensor data.
regression-based learning algorithm bounds estimat↗
A descent numerical method for optimization problems with nondifferentiable cost functionals
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Bertsekas, D. P.↗
General quadratic cost functions for optimal partial state feedback
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Martin, C.↗
Fixed-order compensator design based on frequency-shaped cost functionals
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Calise, Antony J.↗
ANL/RBC: A computer code for the analysis of Rankine bottoming cycles, including system cost evaluation and off-design performance
This report describes, and is a User's Manual for, a computer code (ANL/RBC) which calculates cycle performance for Rankine bottoming cycles extracting heat from a specified source gas stream. The code calculates cycle power and efficiency and the sizes for the heat exchangers, using tabular input of the properties of the cycle working fluid. An option is provided to calculate the costs of system components from user defined input cost functions. These cost functions may be defined in equation form or by numerical tabular data. A variety of functional forms have been included for these functions and they may be combined to create very general cost functions. An optional calculation mode can be used to determine the off-design performance of a system when operated away from the design-point, using the heat exchanger areas calculated for the design-point.
Mclennan, G. A.↗
Automated path planning of the Payload Inspection and Processing System
The Payload Changeout Room Inspection and Processing System (PIPS) is a highly redundant manipulator intended for performing tasks in the crowded and sensitive environment of the Space Shuttle Orbiter payload bay. Its dexterity will be exploited to maneuver the end effector in a workspace populated with obstacles. A method is described by which the end effector of a highly redundant manipulator is directed toward a target via a Lyapunov stability function. A cost function is constructed which represents the distance from the manipulator links to obstacles. Obstacles are avoided by causing the vector of joint parameters to move orthogonally to the gradient of the workspace cost function. A C language program implements the algorithm to generate a joint history. The resulting motion is graphically displayed using the Interactive Graphical Robot Instruction Program (IGRIP) produced by Deneb Robotics. The graphical simulation has the potential to be a useful tool in path planning for the PIPS in the Shuttle Payload Bay environment.
Byers, Robert M.↗
Redundant manipulators for momentum compensation in a micro-gravity environment
This paper is concerned with the implementation and assessment of joint motion management strategies for kinematically redundant robotic manipulators operating in the micro-gravity environment of Space Station. These robots must be capable of conducting experiments and manufacturing processes without disturbing the micro-gravity environment through base reactions/motions. The redundant degrees of freedom of the manipulator permit the inverse kinematic problem to be solved simultaneously with the minimization of a cost function. The cost function in this case is the weighted sum of the squares of the base forces and moments and is minimized over discrete time segments. The Generalized Inverse Method and Rayleigh Ritz technique are used to solve the combined optimization/inverse kinematics problem. Numerical examples include various robotic configurations and degrees of manipulator redundancy.
Quinn, R. D.↗
A Two-Dimensional Variational Analysis Method for NSCAT Ambiguity Removal: Methodology, Sensitivity, and Tuning
In this study, we apply a two-dimensional variational analysis method (2d-VAR) to select a wind solution from NASA Scatterometer (NSCAT) ambiguous winds. 2d-VAR determines a "best" gridded surface wind analysis by minimizing a cost function. The cost function measures the misfit to the observations, the background, and the filtering and dynamical constraints. The ambiguity closest in direction to the minimizing analysis is selected. 2d-VAR method, sensitivity and numerical behavior are described. 2d-VAR is compared to statistical interpolation (OI) by examining the response of both systems to a single ship observation and to a swath of unique scatterometer winds. 2d-VAR is used with both NSCAT ambiguities and NSCAT backscatter values. Results are roughly comparable. When the background field is poor, 2d-VAR ambiguity removal often selects low probability ambiguities. To avoid this behavior, an initial 2d-VAR analysis, using only the two most likely ambiguities, provides the first guess for an analysis using all the ambiguities or the backscatter data. 2d-VAR and median filter selected ambiguities usually agree. Both methods require horizontal consistency, so disagreements occur in clumps, or as linear features. In these cases, 2d-VAR ambiguities are often more meteorologically reasonable and more consistent with satellite imagery.
Hoffman, R. N.↗