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Optimal control for a class of distributed parameter systems where the cost functions are norms

1969
*
Journal of computer and system sciences (Print)
*

Some problems in

doi:10.1016/s0022-0000(69)80005-x
fatcat:uejranp5gjf5teys74dgvl5kpq
*optimal**control*,*for**a**class**of*linear*distributed**parameter**systems*,*are*posed. ... In addition, two*optimal**control*problems, in linear lumped*parameter**systems**are*posed. ... Theorem 9 is identical to*the*necessary and sufficient condition obtained from Pontryagin's maximum principle [6] ,*for*Problem E. ...##
###
Multiple constraints in optimal control problems

1970
*
IEEE Transactions on Automatic Control
*

Abstract-

doi:10.1109/tac.1970.1099375
fatcat:mn52j27l5ndtpnibcgbrotcrty
*The*origin*of*multiple constraints on*a**control**function*in both lumped and*distributed**systems*is investigated. Equivalence and comparability notions*are*discussed. ... Let*the*t.mo*normed*constraints on*the**control**function*~(t) be defined as a.nd [1] E. Friedland, "*The*structure*of*optimum*control**systems*." Trans. J = ASME, J. ...*optimal*feedback scheme is, in general, higher than*the**cost*.*function*sets in & [*A*], L, [O,b] , and L, [O,T] , respectively,*for*1 < p < <*a*. o f an*optimal**system*xhere all stat-*are*actually measured ...##
###
Distributed Multi-Parametric Quadratic Programming

2009
*
IEEE Transactions on Automatic Control
*

One

doi:10.1109/tac.2009.2014916
fatcat:nucoj3p7rze73a4es5zz5ppuqe
*of**the*fundamental problems in*the*area*of*large-scale*optimization*is to study locality features*of*spatially*distributed**optimization*problems in which*the*variables*are*coupled in*the**cost**function*...*The**class**of*spatially decaying matrices is introduced to capture couplings between*optimization*variables in*the**cost**function*and*the*constraints. ...*For**a*given spatial domain and*a**parameterized*coupling characteristic*function*, we define*the**class**of*infinite-dimensional matrices defined by*the*off-diagonal decay*of*their entries. ...##
###
Optimal Control of Spatially Distributed Systems

2008
*
IEEE Transactions on Automatic Control
*

In this paper, we study

doi:10.1109/tac.2008.929366
fatcat:qbcqaaeluvdmdh4xyptm5y23ie
*the*structural properties*of**optimal**control**of*spatially*distributed**systems*. ... We prove that given*a**control**system*with*a*state-space representation consisting*of*SD operators,*the*solution*of*operator Lyapunov and Riccati equations*are*SD. ... ACKNOWLEDGMENT*The*authors would like to thank B. Bamieh*for*his valuable comments and suggestions which led to*the*proof*of*theorem 6. ...##
###
Optimal Control of Spatially Distributed Systems

2007
*
American Control Conference (ACC)
*

In this paper, we study

doi:10.1109/acc.2007.4282897
dblp:conf/acc/MoteeJ07
fatcat:gcwhctgdejchdlmyn4agmh6ufq
*the*structural properties*of**optimal**control**of*spatially*distributed**systems*. ... We prove that given*a**control**system*with*a*state-space representation consisting*of*SD operators,*the*solution*of*operator Lyapunov and Riccati equations*are*SD. ... ACKNOWLEDGMENT*The*authors would like to thank B. Bamieh*for*his valuable comments and suggestions which led to*the*proof*of*theorem 6. ...##
###
Control Cost in Adaptive Systems with an Identifier under Disturbance Description Uncertainties

2017
*
Advances in Systems Science and Applications
*

*A*problem

*of*

*the*criterion

*optimization*

*of*

*a*linear-quadratic

*system*with

*a*stationary disturbance and set transfer

*function*on

*control*is considered. ... To solve

*the*problem,

*a*regularized method

*of*substitution

*of*estimates

*of*

*the*spectral density

*of*

*the*disturbance into

*the*

*control*

*cost*

*functional*is proposed. ...

*controller*, is

*the*ring

*of*rational

*functions*without poles in

*the*closed disk }. 1 | {| z Due to

*the*completeness

*of*

*the*affine

*parameterization*

*of*

*control*

*systems*by

*the*

*functional*

*parameter* ...

##
###
OCTBEC—A Matlab toolbox for optimal quantum control of Bose–Einstein condensates

2014
*
Computer Physics Communications
*

OCTBEC is

doi:10.1016/j.cpc.2013.09.016
fatcat:zzip3mdnp5b4vgp4bfpkg4gbr4
*a*Matlab toolbox designed*for**optimal*quantum*control*, within*the*framework*of**optimal**control*theory (OCT),*of*Bose-Einstein condensates (BEC). ...*The**systems*we have in mind*are*ultracold atoms in confined geometries,*where**the*dynamics takes place in one or two spatial dimensions, and*the*confinement potential can be*controlled*by some external ... Alfio Borzì and Greg von Winckel*are*cordially acknowledged*for*their contributions to*the*OCT implementation. ...##
###
Some Approaches to Ergodic and Adaptive Control of Stochastic Semilinear Systems
[chapter]

1999
*
IFIP Advances in Information and Communication Technology
*

*The*development

*of*adaptive

*control*

*for*stochastic

*distributed*

*parameter*

*systems*is described commencing with adaptive

*control*problems

*for*linear stochastic

*systems*with quadratic

*cost*

*functionals*. ... Some ergodic and adaptive

*control*problems

*for*stochastic semilinear

*systems*

*are*described. ... These adaptive

*control*problems use

*the*

*optimal*

*controls*

*for*deterministic, linear

*distributed*

*parameter*

*systems*with infinite time horizon, quadratic

*cost*

*functionals*. ...

##
###
A probabilistic framework for the control of systems with discrete states and stochastic excitation
[article]

2017
*
arXiv
*
pre-print

*A*probabilistic framework is proposed

*for*

*the*

*optimization*

*of*efficient switched

*control*strategies

*for*physical

*systems*dominated by stochastic excitation. ... In this framework,

*the*equation

*for*

*the*state trajectory is replaced with an equivalent equation

*for*its probability

*distribution*

*function*in

*the*constrained

*optimization*setting. ... FIG. 4 : 4 Comparison

*of*

*control*rules: (

*a*)

*control*

*cost*w = E [ |u| ] as

*a*

*function*

*of*

*the*dimensionless

*parameter*R

*for*

*the*two different

*control*rules;

*the*two

*control*

*costs*

*are*almost indistinguishable ...

##
###
Page 1326 of Mathematical Reviews Vol. 42, Issue 5
[page]

1971
*
Mathematical Reviews
*

Author’s summary: “This paper deals with

*the*time-*optimal**control**of**a**class**of*linear-*distributed**systems*with*a*composite-*norm*constraint. ... output*of*order m (m<vn),*the**cost**functional**for**the*regulator being*of**the*usual based on*the*minimal-order |*SYSTEMS*,*CONTROL**, %, or £,*(t) * fit, x*(t), u(t, x*(t),*A**(t))),*where*u,(t)=,(t, x(t) ...##
###
Quadratic Performance Analysis of Secondary Frequency Controllers
[article]

2020
*
arXiv
*
accepted

We consider

arXiv:1909.02792v2
fatcat:4jfvvj7mi5ebzj4oqjnm3zopjq
*a*quadratic objective accounting*for**the**cost**of*reserve procurement and provide exact analytical formulae*for**the*performance*of*continuous-time aggregated averaging*controllers*. ... Finally,*distributed*averaging-based*controllers*scale sub-linearly with size and*are*independent*of**system*size in*the*high-gain limit. ... ACKNOWLEDGMENTS*The*authors thank Tjerk Stegink*for*his input on primaldual frequency*control*stability and design. ...##
###
Page 3744 of Mathematical Reviews Vol. , Issue 83i
[page]

1983
*
Mathematical Reviews
*

Using Chang’s idea

*for*vector*optimization**of*ordinary differential equation*systems*, we prove*a*necessary condition*of*nonimprovement*of**the**control**function**for**systems*with*distributed**parameters*.” ... K. 831:49005b On*the*existence*of**optimal**control*in*a*nonlinear*system*with*distributed**parameters*. ...##
###
Using $\BBH_{2}$-Control Performance Metrics for the Optimal Actuator Location of Distributed Parameter Systems

2015
*
IEEE Transactions on Automatic Control
*

This paper is concerned with

doi:10.1109/tac.2014.2346676
fatcat:3si24p4jnjendekeoyksz4gm4m
*the*use*of*H 2 -*control*performance metrics in finding*optimal*actuator locations*for**a**class**of*infinite-dimensional*systems*. ... Numerical studies*for**a*cantilever beam and*a*diffusion problem*are*used to demonstrate*the*effects*of**the*spatial*distribution**of*disturbances on*the**optimal*actuator location. ... Theorem 1: Consider*the**system*(*A*, B,C, 0) with transfer*function*G*where**A*is*the*infinitesimal generator*of*an exponentially stable C 0 -semigroup and either B and C*are*both trace*class*or one*of*B ...##
###
Page 3058 of Mathematical Reviews Vol. , Issue 86g
[page]

1986
*
Mathematical Reviews
*

*of*bilinear

*systems*subject to

*a*quadratic

*cost*

*functional*. ... In this paper we consider

*the*bilinear

*system*z = Az + uBrz

*for*

*a*scalar

*control*u,

*where*

*A*and B

*are*bounded operators on

*a*separable Hilbert space H, together with

*the*quadratic

*cost*J = (z,Gz) + Io‘ ...

##
###
Constructing Knowledge Database in Decision Making

2011
*
Communications - Scientific Letters of the University of Zilina
*

Methods

doi:10.26552/com.c.2011.2.74-77
fatcat:axy5hnhlgfhwjmr45r3bon4f3q
*of*analysis*of**control**systems*and simulation methods, which*are*used*for*observing dynamic behavior*of*linear*systems*with time delay, and*distributed**parameter**systems*, based on linear algebra ... G*Cost*group is used*for**the**optimal**cost*effect. ...
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