MinMax Mean-Field Team Approach for a Leader–Follower Network: A Saddle-Point Strategy

Abstract

This paper investigates a soft-constrained MinMax control problem of a leader-follower network. The network consists of one leader and an arbitrary number of followers that wish to reach consensus with minimum energy consumption in the presence of external disturbances. The leader and followers are coupled in the dynamics and cost function. Two non-classical information structures are considered: mean-field sharing and intermittent mean-field sharing, where the meanfield refers to the aggregate state of the followers. In meanfield sharing, every follower observes its local state, the state of the leader and the mean field while in the intermittent mean-field sharing, the mean-field is only observed at some (possibly no) time instants. A social welfare cost function is defined, and it is shown that a unique saddle-point strategy exists which minimizes the worst-case value of the cost function under mean-field sharing information structure. The solution is obtained by two scalable Riccati equations, which depend on a prescribed attenuation parameter, serving as a robustness factor. For the intermittent mean-field sharing information structure, an approximate saddle-point strategy is proposed, and its converges to the saddle-point is analyzed. Two numerical examples are provided to demonstrate the efficacy of the obtained results.

Deep Structured Teams in Arbitrary-Size Linear Networks: Decentralized Estimation, Optimal Control and Separation Principle

“…In addition, the local and global gains θ * t and θ * t are obtained by two scale-free Riccati equations in (17) as…”

“…Note that the separation principle is weaker than the certainty equivalence principle [34]. The remaining problem is an optimal LQ deep structured team with (perfect) deep state sharing whose solution is obtained from the Riccati equations in (17); see [8], [9], [11] for more details.…”

“…Furthermore, we demonstrate in [9] that today's most common feed-forward deep neural networks (i.e., those with rectified linear unit activation function) may be viewed as a special case of deep structured teams, where layers are time steps and neurons are simple integrator agents whose goal is to collaborate in order to minimize a common loss (cost) function. For more applications of deep structured models, the reader is referred to reinforcement learning [8], [13], [14], nonzerosum game [12], [15], minmax optimization [17], leaderfollowers [18], [19], epidemics [20], smart grids [21], meanfield teams [22]- [25], and networked estimation [26], [27].…”

Data Collection Versus Data Estimation: A Fundamental Trade-Off in Dynamic Networks

“…In this case, the data dynamics becomes more complex but the proposed approach still works because the dynamics does not depend on the action of the decision maker. For an example of partially exchangeable network, see a leader-follower network in [39] with n exchangeable followers and one non-exchangeable leader.…”

“…Inspired by recent developments in networked control systems [31]- [33] and deep teams [3], [4], [39], we consider a networked remote estimation problem for a deep linear quadratic control system, where n networked controllers use a deep structured optimal state-feedback strategy. In this case, the dynamics of the deep state (weighted average of the states of the controllers) is in the form of (9).…”