225,865 research outputs found
Sobolev type fractional dynamic equations and Optimal multi-integral controls with fractional nonlocal conditions
We prove existence and uniqueness of mild solutions to Sobolev type fractional nonlocal dynamic equations in Banach spaces. The Sobolev nonlocal condition is considered in terms of a Riemann-Liouville fractional derivative. A Lagrange optimal control problem is considered, and existence of a multi-integral solution obtained. Main tools include fractional calculus, semigroup theory, fractional power of operators, a singular version of Gronwall's inequality, and Leray-Schauder fixed point theorem. An example illustrating the theory is given
Optimal boundary control of distributed systems involving dynamic boundary conditions
In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls, B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented
Mean field games based on the stable-like processes
In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of LĀ“evy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable- like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents
Optimal Pricing Effect on Equilibrium Behaviors of Delay-Sensitive Users in Cognitive Radio Networks
This paper studies price-based spectrum access control in cognitive radio
networks, which characterizes network operators' service provisions to
delay-sensitive secondary users (SUs) via pricing strategies. Based on the two
paradigms of shared-use and exclusive-use dynamic spectrum access (DSA), we
examine three network scenarios corresponding to three types of secondary
markets. In the first monopoly market with one operator using opportunistic
shared-use DSA, we study the operator's pricing effect on the equilibrium
behaviors of self-optimizing SUs in a queueing system. %This queue represents
the congestion of the multiple SUs sharing the operator's single \ON-\OFF
channel that models the primary users (PUs) traffic. We provide a queueing
delay analysis with the general distributions of the SU service time and PU
traffic using the renewal theory. In terms of SUs, we show that there exists a
unique Nash equilibrium in a non-cooperative game where SUs are players
employing individual optimal strategies. We also provide a sufficient condition
and iterative algorithms for equilibrium convergence. In terms of operators,
two pricing mechanisms are proposed with different goals: revenue maximization
and social welfare maximization. In the second monopoly market, an operator
exploiting exclusive-use DSA has many channels that will be allocated
separately to each entering SU. We also analyze the pricing effect on the
equilibrium behaviors of the SUs and the revenue-optimal and socially-optimal
pricing strategies of the operator in this market. In the third duopoly market,
we study a price competition between two operators employing shared-use and
exclusive-use DSA, respectively, as a two-stage Stackelberg game. Using a
backward induction method, we show that there exists a unique equilibrium for
this game and investigate the equilibrium convergence.Comment: 30 pages, one column, double spac
Answer-Type Modification without Tears: Prompt-Passing Style Translation for Typed Delimited-Control Operators
The salient feature of delimited-control operators is their ability to modify
answer types during computation. The feature, answer-type modification (ATM for
short), allows one to express various interesting programs such as typed printf
compactly and nicely, while it makes it difficult to embed these operators in
standard functional languages.
In this paper, we present a typed translation of delimited-control operators
shift and reset with ATM into a familiar language with multi-prompt shift and
reset without ATM, which lets us use ATM in standard languages without
modifying the type system. Our translation generalizes Kiselyov's direct-style
implementation of typed printf, which uses two prompts to emulate the
modification of answer types, and passes them during computation. We prove that
our translation preserves typing. As the naive prompt-passing style translation
generates and passes many prompts even for pure terms, we show an optimized
translation that generate prompts only when needed, which is also
type-preserving. Finally, we give an implementation in the tagless-final style
which respects typing by construction.Comment: In Proceedings WoC 2015, arXiv:1606.0583
Well-posedness and Stability for Interconnection Structures of Port-Hamiltonian Type
We consider networks of infinite-dimensional port-Hamiltonian systems
on one-dimensional spatial domains. These subsystems of
port-Hamiltonian type are interconnected via boundary control and observation
and are allowed to be of distinct port-Hamiltonian orders .
Wellposedness and stability results for port-Hamiltonian systems of fixed order
are thereby generalised to networks of such. The abstract
theory is applied to some particular model examples.Comment: Submitted to: Control Theory of Infinite-Dimensional System. Workshop
on Control Theory of Infinite-Dimensional Systems, Hagen, January 2018.
Operator Theory: Advances and Applications. (32 pages, 5 figures
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