This paper considers two classes of large population stochastic differential games connected to optimal and robust decentralized control of large-scale multi-agent systems. The first problem (P1) is one where each agent minimizes an exponentiated cost function, capturing risk-sensitive behavior, whereas in the second problem (P2) each agent minimizes a worst-case riskneutral cost function, where the "worst case" stems from the presence of an adversary entering each agent's dynamics characterized by a stochastic differential equation. In both problems, the individual agents are coupled through the mean field term included in each agent's cost function, which captures the average or mass behavior of the agents.We solve both P1 and P2 via mean field game theory. Specifically, we first solve a generic risk-sensitive optimal control problem and a generic stochastic zero-sum differential game, where the corresponding optimal controllers are applied by each agent to construct the mean field systems of P1 and P2. We then characterize an approximated mass behavior effect on an individual agent via a fixed-point analysis of the mean field system. For each problem, P1 and P2, we show that the approximated mass behavior is in fact the best estimate of the actual mass behavior in various senses as the population size, N , goes to infinity. Moreover, we show that for finite N , there exist -Nash equilibria for both P1 and P2, where the corresponding individual Nash strategies are decentralized in terms of local state information and the approximated mass behavior. We also show that can be taken to be arbitrarily small when N is sufficiently large. We show that the -Nash equilibria of P1 and P2 are partially equivalent in the sense that the individual Nash strategies share identical control laws, but the approximated mass behaviors for P1 and P2 are different, since in P2, the mass behavior is also affected by the associated worst-case disturbance. Finally, we prove that the Nash equilibria for P1 and P2 both feature robustness, and as the parameter characterizing this robustness becomes infinite, the two Nash equilibria become identical and equivalent to that of the risk-neutral case, as in the one-agent risk-sensitive and robust control theory.

Fair and meaningful device performance comparison among luminescent solar concentratorphotovoltaic (LSC-PV) reports cannot be realized without a general consensus on reporting standards in LSC-PV research. Therefore, it is imperative to adopt standardized characterization protocols for these emerging types of PV devices that are consistent with other PV devices. This commentary highlights several common limitations in LSC literature and summarizes the best practices moving forward to harmonize with standard PV reporting, considering the

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This paper considers the stabilization problem for under-actuated rotary inverted pendulum systems (RotIPS) via a fuzzy-based continuous sliding mode control approach. Various sliding mode control (SMC) methods have been proposed for stabilizing the under-actuated RotIPS. However, there are two main drawbacks of these SMC approaches. First, the existing SMCs have a discontinuous structure; therefore, their control systems suffer from the chattering problem. Second, a complete proof of closed-loop system stability has not been provided. To address these two limitations, we propose a fuzzy-based (continuous) super-twisting stabilization algorithm (FBSTSA) for the under-actuated RotIPS. We first introduce a new sliding surface, which is designed to resolve the under-actuation problem, by combining the fully-actuated (rotary arm) and the under-actuated (pendulum) variables to define one sliding surface. Then, together with the proposed sliding surface, we develop the FBSTSA, where the corresponding control gains are adjusted based on a fuzzy logic scheme. Note that the proposed FBSTSA is continuous owing to the modified supertwisting approach, which can reduce the chattering and enhance the control performance. With the proposed FBSTSA, we show that the sliding variable can reach zero in finite time and then the closed-loop system state converges to zero asymptotically. Various simulation and experimental results are provided to demonstrate the effectiveness of the proposed FBSTSA. In particular, (i) compared with the existing SMC approaches, chattering is alleviated and better stabilization is achieved; and (ii) the robustness of the closed-loop system (with the proposed FBSTSA) is guaranteed under system uncertainties and external disturbances. INDEX TERMS Asymptotic stability, finite-time stability, fuzzy-based super-twisting sliding mode control, rotary inverted pendulum system, stabilization control.

Abstract-In this paper, we consider discrete-time linearquadratic-Gaussian (LQG) mean field games over unreliable communication links. These are dynamic games with a large number of agents where the cost function of each agent is coupled with other agents' states via a mean field term. Further, the individual dynamical system for each agent is subject to packet dropping. Under this setup, we first obtain an optimal decentralized control law for each agent that is a function of local information as well as packet drop information. We then construct a mean field system that provides the best approximation to the mean field term under appropriate conditions. We also show that the optimal decentralized controller stabilizes the individual dynamical system in the time-average sense. We prove an -Nash equilibrium property of the set of N optimal decentralized controllers, and show that can be made arbitrarily small as the number of agents becomes arbitrarily large. We note that the existence of the -Nash equilibrium obtained in this paper is primarily dependent on the underlying communication networks.

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