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1. Optimal, near-optimal, and robust epidemic control

   https://doi.org/10.1038/s42005-021-00570-y  

   Morris, Dylan H.; Rossine, Fernando W.; Plotkin, Joshua B.; Levin, Simon A. (April 2021, Communications Physics)

   Abstract In the absence of drugs and vaccines, policymakers use non-pharmaceutical interventions such as social distancing to decrease rates of disease-causing contact, with the aim of reducing or delaying the epidemic peak. These measures carry social and economic costs, so societies may be unable to maintain them for more than a short period of time. Intervention policy design often relies on numerical simulations of epidemic models, but comparing policies and assessing their robustness demands clear principles that apply across strategies. Here we derive the theoretically optimal strategy for using a time-limited intervention to reduce the peak prevalence of a novel disease in the classic Susceptible-Infectious-Recovered epidemic model. We show that broad classes of easier-to-implement strategies can perform nearly as well as the theoretically optimal strategy. But neither the optimal strategy nor any of these near-optimal strategies is robust to implementation error: small errors in timing the intervention produce large increases in peak prevalence. Our results reveal fundamental principles of non-pharmaceutical disease control and expose their potential fragility. For robust control, an intervention must be strong, early, and ideally sustained. 

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2. Stochastic Optimal Control Matching

   Domingo-Enrich, Carles; Han, Jiequn; Amos, Brandon; Bruna, Joan; Chen, Ricky (December 2024, NeurIPS)
3. Stochastic Optimal Control Matching

   Domingo-Enrich, Carles; Han, Jiequn; Amos, Brandon; Bruna, Joan; Chen, Ricky (December 2024, Neural Information Processing Systems)
4. Kullback–Leibler-Quadratic Optimal Control

   https://doi.org/10.1137/21M1433654  

   Cammardella, Neil; Bušić, Ana; Meyn, Sean P. (October 2023, SIAM Journal on Control and Optimization)

   Editor-in-Chief: George Yin (Ed.)

   This paper presents approaches to mean-field control, motivated by distributed control of multi-agent systems. Control solutions are based on a convex optimization problem, whose domain is a convex set of probability mass functions (pmfs). The main contributions follow: 1. Kullback-Leibler-Quadratic (KLQ) optimal control is a special case, in which the objective function is composed of a control cost in the form of Kullback-Leibler divergence between a candidate pmf and the nominal, plus a quadratic cost on the sequence of marginals. Theory in this paper extends prior work on deterministic control systems, establishing that the optimal solution is an exponential tilting of the nominal pmf. Transform techniques are introduced to reduce complexity of the KLQ solution, motivated by the need to consider time horizons that are much longer than the inter-sampling times required for reliable control. 2. Infinite-horizon KLQ leads to a state feedback control solution with attractive properties. It can be expressed as either state feedback, in which the state is the sequence of marginal pmfs, or an open loop solution is obtained that is more easily computed. 3. Numerical experiments are surveyed in an application of distributed control of residential loads to provide grid services, similar to utility-scale battery storage. The results show that KLQ optimal control enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints. 

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5. Optimal Control of Active Nematics

   https://doi.org/10.1103/PhysRevLett.125.178005  

   Norton, Michael M.; Grover, Piyush; Hagan, Michael F.; Fraden, Seth (October 2020, Physical Review Letters)

   null (Ed.)