LQ Nash Games With Random Entrance: An Infinite Horizon Major Player and Minor Players of Finite Horizons

Kordonis, Ioannis; Papavassilopoulos, George P.

doi:10.1109/tac.2015.2396642

Cited by 29 publications

(22 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Theorem 1: The quantity is a symmetric matrix of signed measures and its evolution is given by (6). Furthermore, the following hold:…”

Section: Stability Analysismentioning

confidence: 99%

“…Assuming that there exists a Markovian model for the uncertainty, design problems involving MJLS with continuous state space Markov chain will be obtained and will lead to less conservative stability conditions. Another example, which also motivates the current work, comes from the optimal control problems, arising in the mean field approximation of LQ games involving a large number of randomly entering players [6], where the players are considered to belong to a continuum. The first work studying the mean square stability of MJLS with finite state space Markov chain was [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Stability and LQ Control of MJLS With a Markov Chain With General State Space

Kordonis

Papavassilopoulos

2014

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

We study the mean square stability and the LQ control of discrete time Markov Jump Linear Systems where the Markov chain has a general state space. The mean square stability is characterized by the spectral radius of an operator describing the evolution of the second moment of the state vector. Two equivalent tests for the mean square stability are obtained based on the existence of a positive definite solution to a Lyapunov equation and a uniformity result respectively. An algorithm for testing the mean square stability is also developed based on the uniformity result. The finite and infinite horizon LQ problems are considered and their solutions are characterized by appropriate Riccati integral equations. An application to Networked Control Systems (NCS) is finally presented and a simple example is studied via simulation.Index Terms-Markov jump linear systems, stochastic optimal control, stochastic stability.

show abstract

“…Theorem 1: The quantity is a symmetric matrix of signed measures and its evolution is given by (6). Furthermore, the following hold:…”

Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Stability and LQ Control of MJLS With a Markov Chain With General State Space

Kordonis

Papavassilopoulos

2014

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar remarks hold for the interplay of existence questions between finite and infinite time analogues). Stochastic analogues pertaining in particular to random entries, and exits of the short time players is another interesting topic, see [15] for some early results.…”

Section: Discussionmentioning

confidence: 99%

“…Related work has been reported in [14], [15], [18]. The present work is an extension of [14], where the same framework was considered with all the players playing Linear Memoryless Closed Loop strategies that satisfy the Dynamic Programming Principle whereas here we consider that the long-term player plays Open Loop.…”

Section: Introductionmentioning

confidence: 99%

A Nash Game with long-term and short-term players

Papavassilopoulos

Abou-Kandil

Jungers

2013

52nd IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

We formulate and study a game where there is a player who is involved for a long time interval and several small players who stay in the game for short time intervals. The longterm player plays open loop whereas the short-term players play memoryless closed loop or open loop. This is motivated by the fact that the long-term player is a player who usually represents a state or institutional authority that has to commit himself to long-term plans and regulations that are announced in advance and remain unchanged for a long time, whereas the short-term players not having such an institutional role can change policies arbitrarily often. We study this game for Nash strategies in a Linear Quadratic discrete time deterministic set-up. For the memoryless closed loop strategies we confine ourselves to strategies linear in the state. The derived associated Riccati-type equations are of a novel character and are of interest as such. Comparisons with the case where all players play memoryless closed loop or open loop are carried out.

show abstract

“…Particularly, Kordonis et al [13] consider a player with infinite time horizon, called major player, and many players with finite time horizons, called minor players. The number of new players entering the game at any time is a random variable that has a distribution which depends only on the number of active players at that moment.…”

Section: Introductionmentioning

confidence: 99%

A matrix approach to modeling and optimization for dynamic games with random entrance

Zhao

Wang

2016

Applied Mathematics and Computation

View full text Add to dashboard Cite

LQ Nash Games With Random Entrance: An Infinite Horizon Major Player and Minor Players of Finite Horizons

Cited by 29 publications

References 32 publications

On Stability and LQ Control of MJLS With a Markov Chain With General State Space

On Stability and LQ Control of MJLS With a Markov Chain With General State Space

A Nash Game with long-term and short-term players

A matrix approach to modeling and optimization for dynamic games with random entrance

Contact Info

Product

Resources

About