Optimal actuator placement in adaptive optics systems

2021 ◽  
pp. 107754632110324
Author(s):  
Berk Altıner ◽  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Cost Function ◽  
Adaptive Optics ◽  
Disturbance Attenuation ◽  
Linear Quadratic ◽  
Placement Problem ◽  
Convex Optimization Problem ◽  
Wavefront Aberrations ◽  
The Cost ◽  
Actuator Placement ◽  
Quadratic Cost Function

Adaptive optics systems are powerful tools that are implemented to degrade the effects of wavefront aberrations. In this article, the optimal actuator placement problem is addressed for the improvement of disturbance attenuation capability of adaptive optics systems due to the fact that actuator placement is directly related to the enhancement of system performance. For this purpose, the linear-quadratic cost function is chosen, so that optimized actuator layouts can be specialized according to the type of wavefront aberrations. It is then considered as a convex optimization problem, and the cost function is formulated for the disturbance attenuation case. The success of the presented method is demonstrated by simulation results.

scholarly journals Actuator Placement for Active Surge Control in a Multi-Stage Axial Compressor

1996 ◽  
Author(s):  
M. Montazeri-Gh. ◽  
D. J. Allerton ◽  
R. L. Elder
Keyword(s):  
Cost Function ◽  
Mass Flow ◽  
Controller Design ◽  
Axial Compressor ◽  
Minimum Cost ◽  
Linear Quadratic Regulator ◽  
Algebraic Riccati Equation ◽  
Linear Quadratic ◽  
Non Linear ◽  
Actuator Placement

This paper describes an actuator placement methodology for the active control of purely one-dimensional instabilities of a seven-stage axial compressor using an air bleeding strategy. In this theoretical study, using stage-by-stage non-linear modelling based on the conservation equations of mass, momentum, and energy, a scheduling LQR (Linear Quadratic Regulator) controller is designed for several actuator locations in a compressor from the first stage to the plenum. In this controller design, the LQR weighting matrices are selected so that the associated cost function includes only air bleeding mass flow leading to the minimisation of the air bleed. The LQR cost function represents a measure of the consumption of air bleeding and can be calculated analytically using the solution of an Algebraic Riccati Equation. From analysis of the cost at different compressor stages, the location of an air bleeding actuator is selected at the stage with the minimum cost. Finally, using an ACSL simulation program, the scheduling controller has been integrated with a non-linear. stage-by-stage model and the time response of the air bleeding mass flow at different locations has been obtained to confirm the results from the analytical approach. Results are presented to show actively stabilised compressor flow beyond the surge point where the air bleed is minimised. These results also indicate the preferred location of the actuator at the compressor downstream stages for both low and high compressor speeds.

scholarly journals Proliferation of non-linear excitations in the piecewise-linear perceptron

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Antonio Sclocchi ◽  
Pierfrancesco Urbani
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Hard Spheres ◽  
Piecewise Linear ◽  
Power Laws ◽  
Universality Class ◽  
Local Minima ◽  
Convex Optimization Problem ◽  
Non Linear ◽  
The Cost

We investigate the properties of local minima of the energy landscape of a continuous non-convex optimization problem, the spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable and displaying a set of pseudogaps, singularities and non-linear excitations whose properties appear to be in the same universality class of jammed packings of hard spheres. The piecewise linear perceptron problem appears as an evolution of the purely linear perceptron optimization problem that has been recently investigated in [1]. Its cost function contains two non-analytic points where the derivative has a jump. Correspondingly, in the non-convex/glassy phase, these two points give rise to four pseudogaps in the force distribution and this induces four power laws in the gap distribution as well. In addition one can define an extended notion of isostaticity and show that local minima appear again to be isostatic in this phase. We believe that our results generalize naturally to more complex cases with a proliferation of non-linear excitations as the number of non-analytic points in the cost function is increased.

scholarly journals Economies of Scale in the Floriculture Industry

2003 ◽  
Vol 35 (3) ◽  
pp. 497-507 ◽  
Author(s):  
Sara K. Schumacher ◽  
Thomas L. Marsh
Keyword(s):  
United States ◽  
Cost Function ◽  
Economies Of Scale ◽  
The United States ◽  
Cost Structure ◽  
Cost Advantage ◽  
Quadratic Cost ◽  
Cost Efficiencies ◽  
The Cost ◽  
Quadratic Cost Function

This study investigated the cost structure of the floriculture industry in the United States. Economies of scale and input elasticities were estimated with a normalized quadratic cost function. Results suggest that economies of scale exist in the floriculture industry. As producers become large and more automated, they have a cost advantage relative to smaller producers who are producing the same output product mix. The existence of economies of scale suggests that average grower size can increase in the future as growers increase in size to take advantage of cost efficiencies.

scholarly journals When more competition may damage welfare with socially responsible firms

Ekonomia ◽  
2018 ◽  
Vol 23 (3) ◽  
pp. 123-134
Author(s):  
Luciano Fanti ◽  
Domenico Buccella
Keyword(s):  
Social Responsibility ◽  
Cost Function ◽  
Production Costs ◽  
Linear Quadratic ◽  
Socially Responsible ◽  
Common View ◽  
Duopoly Model ◽  
The Common ◽  
The Cost ◽  
Welfare Changes

When more competition may damage welfare with socially responsible firmsConsidering a Cournot monopoly/duopoly model with linear/quadratic production costs and Cor­porate Social Responsibility CSR activities, this note shows that, in contrast to the common view, entry may reduce social welfare. Moreover, we remark that the higherthe CSR activities are, the more likely the welfare-damaging entry effect may occur, and thesocial welfare changes following a firm’s entry crucially depend on the degree of convexity of the cost function.

Time-Multiplied Guaranteed Cost Control of Linear Delay Systems

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Junling Wang ◽  
James Lam ◽  
Shengyuan Xu ◽  
Zhan Shu
Keyword(s):  
Cost Function ◽  
Linearization Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
Quadratic Cost ◽  
Linear Delay ◽  
Guaranteed Cost ◽  
Delay Dependent ◽  
Quadratic Cost Function

This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

Quantifying the Costs of Intertemporal Taxable Income Shifting: Theory and Evidence from the Property-Casualty Insurance Industry

2005 ◽  
Vol 80 (1) ◽  
pp. 315-348 ◽  
Author(s):  
David W. Randolph ◽  
Gerald L. Salamon ◽  
Jim A. Seida
Keyword(s):  
Cost Function ◽  
Insurance Industry ◽  
Tax Incentives ◽  
Income Shifting ◽  
Parameter Estimates ◽  
Taxable Income ◽  
Quadratic Cost ◽  
The Cost ◽  
Quadratic Cost Function ◽  
Insight Into

This paper presents a model of optimal tax-motivated intertemporal income shifting given a quadratic cost function that relates the costs associated with shifting income to the amount of income shifted. By formally modeling the income-shifting decision, we: (1) show how parameter estimates of the income-shifting cost function can be extracted from a linear regression where a proxy for income shifted is the dependent variable, (2) provide insight into prior tax-motivated income-shifting research, and (3) clarify the interpretation of independent variables that capture the interaction between tax incentives and nontax costs. We then provide an empirical application of our method for quantifying the costs to shift federal taxable income by investigating the income-shifting behavior of firms in the property and casualty (P&C) insurance industry following the Tax Reform Act of 1986. Our results suggest that the parameters of the cost function are negatively related to firm size, the cost to shift a significant amount of income is nontrivial, and the marginal cost to shift income increases as more income is shifted.

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

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