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Register a new userA Dynamic Population Model of Strategic Interaction and Migration under Epidemic Risk
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In this paper, we show how a dynamic population game can model the strategic interaction and migration decisions made by a large population of agents in response to epidemic prevalence. Specifically, we consider a modified susceptible-asymptomatic-infected-recovered (SAIR) epidemic model over multiple zones. Agents choose whether to activate (i.e., interact with others), how many other agents to interact with, and which zone to move to in a time-scale which is comparable with the epidemic evolution. We define and analyze the notion of equilibrium in this game, and investigate the transient behavior of the epidemic spread in a range of numerical case studies, providing insights on the effects of the agents degree of future awareness, strategic migration decisions, as well as different levels of lockdown and other interventions. One of our key findings is that the strategic behavior of agents plays an important role in the progression of the epidemic and can be exploited in order to design suitable epidemic control measures.
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The multi-period dynamics of energy storage (ES), intermittent renewable generation and uncontrollable power loads, make the optimization of power system operation (PSO) challenging. A multi-period optimal PSO under uncertainty is formulated using the chance-constrained optimization (CCO) modeling paradigm, where the constraints include the nonlinear energy storage and AC power flow models. Based on the emerging scenario optimization method which does not rely on pre-known probability distribution functions, this paper develops a novel solution method for this challenging CCO problem. The proposed meth-od is computationally effective for mainly two reasons. First, the original AC power flow constraints are approximated by a set of learning-assisted quadratic convex inequalities based on a generalized least absolute shrinkage and selection operator. Second, considering the physical patterns of data and motived by learning-based sampling, the strategic sampling method is developed to significantly reduce the required number of scenarios through different sampling strategies. The simulation results on IEEE standard systems indicate that 1) the proposed strategic sampling significantly improves the computational efficiency of the scenario-based approach for solving the chance-constrained optimal PSO problem, 2) the data-driven convex approximation of power flow can be promising alternatives of nonlinear and nonconvex AC power flow.
In this paper, we first consider a pinning node selection and control gain co-design problem for complex networks. A necessary and sufficient condition for the synchronization of the pinning controlled networks at a homogeneous state is provided. A quantitative model is built to describe the pinning costs and to formulate the pinning node selection and control gain design problem for different scenarios into the corresponding optimization problems. Algorithms to solve these problems efficiently are presented. Based on the developed results, we take the existence of a malicious attacker into consideration and a resource allocation model for the defender and the malicious attacker is described. We set up a leader-follower Stackelberg game framework to study the behaviour of both sides and the equilibrium of this security game is investigated. Numerical examples and simulations are presented to demonstrate the main results.
We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller , the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player (Controller) chooses actions, and the second player (Agents) resolves non-determinism for each agent. The game with m agents is called the m-population game. This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can Controller control the m-population game for all $m $in$ N$ whatever Agents does? In this paper, we prove that the population control problem is decidable, and it is a EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cutoff techniques, produces winning strategies which are symbolic, that is, they do not need to count precisely how the population is spread between states. We also show that if there is no winning strategy, then there is a population size M such that Controller wins the m-population game if and only if $m $le$ M$. Surprisingly, M can be doubly exponential in the number of states of the NFA, with tight upper and lower bounds.
Ramp merging is considered as one of the major causes of traffic congestion and accidents because of its chaotic nature. With the development of connected and automated vehicle (CAV) technology, cooperative ramp merging has become one of the popular solutions to this problem. In a mixed traffic situation, CAVs will not only interact with each other, but also handle complicated situations with human-driven vehicles involved. In this paper, a game theory-based ramp merging strategy has been developed for the optimal merging coordination of CAVs in the mixed traffic, which determines dynamic merging sequence and corresponding longitudinal/lateral control. This strategy improves the safety and efficiency of the merging process by ensuring a safe inter-vehicle distance among the involved vehicles and harmonizing the speed of CAVs in the traffic stream. To verify the proposed strategy, mixed traffic simulations under different penetration rates and different congestion levels have been carried out on an innovative Unity-SUMO integrated platform, which connects a game engine-based driving simulator with a traffic simulator. This platform allows the human driver to participate in the simulation, and also equip CAVs with more realistic sensing systems. In the traffic flow level simulation test, Unity takes over the sensing and control of all CAVs in the simulation, while SUMO handles the behavior of all legacy vehicles. The results show that the average speed of traffic flow can be increased up to 110%, and the fuel consumption can be reduced up to 77%, respectively.
Many populations in nature are fragmented: they consist of local populations occupying separate patches. A local population is prone to extinction due to the shot noise of birth and death processes. A migrating population from another patch can dramatically delay the extinction. What is the optimal migration rate that minimizes the extinction risk of the whole population? Here we answer this question for a connected network of model habitat patches with different carrying capacities.
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