By Abdelhamid Mellouk
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Extra info for Advances in Reinforcement Learning
Xm [ k ]) = ∑ H ij ( X j [ k ]) (7) j =1 The interaction relations which can be expressed as Z[k] = H(X[k]) are considered to be the optimization constraints. So the Lagrangian can be defined as n n+1 k =0 k =0 L = Gn + 1 ( X [ n + 1] ) + ∑ Gk ( X [ k ] ,U [ k ] ) + ∑ β [ k ]T ( Z [ k ] − H ( X [ k ] ) ) (8) where β[k]’s are the Lagrange multipliers that we refer to them as the coordination parameters. t. m (9b) Xi [ k + 1] = Fi ( Xi [ k ],Ui [ k ], Zi [ k ]) Xi  = Xi 0 and also one second level problem expressed as: (10) A Reinforcement Learning Approach to Intelligent Goal Coordination of Two-Level Large-Scale Control Systems 41 Updating the coordination parameters β i [ k ] such that the interaction errors; Zi[k] – Hi (Xi[k] , … , Xm[k]) , become zero (Interaction Balance Principle).
The state conception is described as follows: A state (st) is defined as st (id, sort, CSET), where id denotes the state identifier; sort denotes the sort of this state; CSET= (c1,c2…ck) denotes its condition vector. The number of the 27 Cooperative Agent Learning Model in Multi-cluster Grid condition elements which condition vector includes is k, and all states of the same sort have the same value of k. , this state can be called the cooperative state. All states in MCG formed the state space (SSP).
279-292, ISSN: 08856125 (Print) 1573-0565 (Online). An Introduction to MultiAgent Systems, John Wiley & Sons (Chichester, England). ISBN: 0 47149691X. A. The concept of a linguistic variable and its application to approximate reason-ing, Information Sciences, Vol. 8, No. 3. (1975), pp. 199-249. R. &Wooldridge, M. 127-141, ISBN: 3-540-415947, Limerick, Ireland, 2000, Springer-Verlag New York, Inc. Secaucus, NJ, USA. Organizational rules as an abstraction for the analysis and design of multi-agent systems.
Advances in Reinforcement Learning by Abdelhamid Mellouk