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COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show—as proof of concept grounded on rigorous mathematical evidence—that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn—while not eliminating the virus—this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github at https://github.com/V4p1d/FPSP%5fCovid19. A software tool has also been developed so that interested parties can explore the proof-of-concept system. Author summary: Why? The design of post-lockdown mitigation policies while vaccines are still not available is pressing now as new secondary waves of the virus have emerged in many countries (for example, in Spain, France, UK, Italy, Israel, and others), and as several of these countries grapple with the reintroduction of full lockdown measures. What do we do and find? We propose efficacious and realisable methods based on control theory to tame the complex behaviour of COVID-19 in well mixed populations. We achieve this through a policy of fast intermittent lockdown intervals with regular period. We illustrate how our approach offers a fundamentally new perspective on ways to design COVID-19 exit strategies from policies of total lockdown. Our theoretical results are also very general and apply to a wide range of epidemiological models. What do these findings mean? Unlike many other proposed abatement strategies, which have risks and uncertainties possibly leading to multiple waves of infection, we demonstrate that our proposed policies have the potential to suppress the virus outbreak, while at the same time allowing continued economic activity. These policies, while of practical significance, are built on rigorous theoretical results, which are to the best of our knowledge, new in mathematical epidemiology. An extensive validation is carried out using a detailed epidemic model validated on real COVID-19 data from Italy and published very recently in Nature Medicine. [ABSTRACT FROM AUTHOR]