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

Y. Yavin
1969 Journal of computer and system sciences (Print)  
Some problems in 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.  ... 
doi:10.1016/s0022-0000(69)80005-x fatcat:uejranp5gjf5teys74dgvl5kpq

Multiple constraints in optimal control problems

R. Singh
1970 IEEE Transactions on Automatic Control  
Abstract-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  ... 
doi:10.1109/tac.1970.1099375 fatcat:mn52j27l5ndtpnibcgbrotcrty

Distributed Multi-Parametric Quadratic Programming

N. Motee, A. Jadbabaie
2009 IEEE Transactions on Automatic Control  
One 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.  ... 
doi:10.1109/tac.2009.2014916 fatcat:nucoj3p7rze73a4es5zz5ppuqe

Optimal Control of Spatially Distributed Systems

Nader Motee, Ali Jadbabaie
2008 IEEE Transactions on Automatic Control  
In this paper, we study 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.  ... 
doi:10.1109/tac.2008.929366 fatcat:qbcqaaeluvdmdh4xyptm5y23ie

Optimal Control of Spatially Distributed Systems

Nader Motee, Ali Jadbabaie
2007 American Control Conference (ACC)  
In this paper, we study 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.  ... 
doi:10.1109/acc.2007.4282897 dblp:conf/acc/MoteeJ07 fatcat:gcwhctgdejchdlmyn4agmh6ufq

Control Cost in Adaptive Systems with an Identifier under Disturbance Description Uncertainties

Bunich A..
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    ... 
doi:10.25728/assa.2017.17.1.265 fatcat:ba3n54wiizh6lauuci424snqwe

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

Ulrich Hohenester
2014 Computer Physics Communications  
OCTBEC is 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.  ... 
doi:10.1016/j.cpc.2013.09.016 fatcat:zzip3mdnp5b4vgp4bfpkg4gbr4

Some Approaches to Ergodic and Adaptive Control of Stochastic Semilinear Systems [chapter]

T. E. Duncan
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.  ... 
doi:10.1007/978-0-387-35359-3_24 fatcat:jyyrzj2lbjg5xhzhf6wmvmgipu

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

Gianluca Meneghello, Paolo Luchini, Thomas Bewley
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  ... 
arXiv:1701.01777v1 fatcat:72vpfcoolvhw5gyakga2ijowve

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]

Bala Kameshwar Poolla, John W. Simpson-Porco, Nima Monshizadeh, Florian Dörfler
2020 arXiv   accepted
We consider 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.  ... 
arXiv:1909.02792v2 fatcat:4jfvvj7mi5ebzj4oqjnm3zopjq

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

Kirsten Morris, Michael A. Demetriou, Steven D. Yang
2015 IEEE Transactions on Automatic Control  
This paper is concerned with 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  ... 
doi:10.1109/tac.2014.2346676 fatcat:3si24p4jnjendekeoyksz4gm4m

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

Djordje N. Dihovicni
2011 Communications - Scientific Letters of the University of Zilina  
Methods 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.  ... 
doi:10.26552/com.c.2011.2.74-77 fatcat:axy5hnhlgfhwjmr45r3bon4f3q
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