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This book focuses on how to implement optimal control problems via
the variational method. It studies how to implement the extrema of
functional by applying the variational method and covers the
extrema of functional with different boundary conditions, involving
multiple functions and with certain constraints etc. It gives the
necessary and sufficient condition for the (continuous-time)
optimal control solution via the variational method, solves the
optimal control problems with different boundary conditions,
analyzes the linear quadratic regulator & tracking problems
respectively in detail, and provides the solution of optimal
control problems with state constraints by applying the
Pontryagin's minimum principle which is developed based upon the
calculus of variations. And the developed results are applied to
implement several classes of popular optimal control problems and
say minimum-time, minimum-fuel and minimum-energy problems and so
on. As another key branch of optimal control methods, it also
presents how to solve the optimal control problems via dynamic
programming and discusses the relationship between the variational
method and dynamic programming for comparison. Concerning the
system involving individual agents, it is also worth to study how
to implement the decentralized solution for the underlying optimal
control problems in the framework of differential games. The
equilibrium is implemented by applying both Pontryagin's minimum
principle and dynamic programming. The book also analyzes the
discrete-time version for all the above materials as well since the
discrete-time optimal control problems are very popular in many
fields.
This book focuses on the design of decentralized optimization
methods applied to charging strategies for large-scale PEVs in
electrical power systems. It studies several classes of charging
coordination problems in large-scale PEVs by considering the
distinct characteristics of PEV populations and electrical power
systems, and subsequently designs decentralized methods based on
distinct optimization schemes - such as non-cooperative games,
mean-field games, and auction games - to achieve optimal/nearly
optimal charging strategies. In closing, several performance
aspects of the proposed algorithms, such as their convergence,
computational complexity and optimality etc., are rigorously
verified and demonstrated in numerical simulations. Given its
scope, the book will benefit researchers, engineers, and graduate
students in the fields of optimization, game theory, auction games,
electrical power systems, etc., and help them design decentralized
methods to implement optimal charging strategies in large-scale
PEVs.
This book focuses on the design of efficient & dynamic methods
to allocate divisible resources under various auction mechanisms,
discussing their applications in power & microgrid systems and
the V2G & EV charging coordination problems in smart grids. It
describes the design of dynamic methods for single-sided and
double-sided auction games and presents a number of simulation
cases verifying the performances of the proposed algorithms in
terms of efficiency, convergence and computational complexity.
Further, it explores the performances of certain auction mechanisms
in a hierarchical structure and with large-scale agents, as well as
the auction mechanisms for the efficient allocation of multi-type
resources. Lastly, it generalizes the main and demonstrates their
application in smart grids. This book is a valuable resource for
researchers, engineers, and graduate students in the fields of
optimization, game theory, auction mechanisms and smart grids
interested in designing dynamic auction mechanisms to implement
optimal allocation of divisible resources, especially electricity
and other types of energy in smart grids.
This book focuses on the design of efficient & dynamic methods
to allocate divisible resources under various auction mechanisms,
discussing their applications in power & microgrid systems and
the V2G & EV charging coordination problems in smart grids. It
describes the design of dynamic methods for single-sided and
double-sided auction games and presents a number of simulation
cases verifying the performances of the proposed algorithms in
terms of efficiency, convergence and computational complexity.
Further, it explores the performances of certain auction mechanisms
in a hierarchical structure and with large-scale agents, as well as
the auction mechanisms for the efficient allocation of multi-type
resources. Lastly, it generalizes the main and demonstrates their
application in smart grids. This book is a valuable resource for
researchers, engineers, and graduate students in the fields of
optimization, game theory, auction mechanisms and smart grids
interested in designing dynamic auction mechanisms to implement
optimal allocation of divisible resources, especially electricity
and other types of energy in smart grids.
This book focuses on how to implement optimal control problems via
the variational method. It studies how to implement the extrema of
functional by applying the variational method and covers the
extrema of functional with different boundary conditions, involving
multiple functions and with certain constraints etc. It gives the
necessary and sufficient condition for the (continuous-time)
optimal control solution via the variational method, solves the
optimal control problems with different boundary conditions,
analyzes the linear quadratic regulator & tracking problems
respectively in detail, and provides the solution of optimal
control problems with state constraints by applying the
Pontryagin's minimum principle which is developed based upon the
calculus of variations. And the developed results are applied to
implement several classes of popular optimal control problems and
say minimum-time, minimum-fuel and minimum-energy problems and so
on. As another key branch of optimal control methods, it also
presents how to solve the optimal control problems via dynamic
programming and discusses the relationship between the variational
method and dynamic programming for comparison. Concerning the
system involving individual agents, it is also worth to study how
to implement the decentralized solution for the underlying optimal
control problems in the framework of differential games. The
equilibrium is implemented by applying both Pontryagin's minimum
principle and dynamic programming. The book also analyzes the
discrete-time version for all the above materials as well since the
discrete-time optimal control problems are very popular in many
fields.
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