Cities around the world will invest a total of about $41 trillion over the next 20 years to upgrade their infrastructure and benefit from the network of connected devices known as the Internet of Things, experts at the Smart America Challenge forecast.

"This is really a new way of thinking about how we better utilize technology to support the quality-of-life issues that citizens both want and need," said Alan Shark, executive director of the Public Technology Institute.

As cities invest in air-quality sensors, solar-powered trash compactors, self-healing power grids and more, the opportunities for private industry are huge. Experts say there is just one problem: It's virtually impossible to measure the return on investment for many leading-edge technologies first being put to use by the public sector.

One study has shown that every $1 spent on government tech saves $3.50, but analysts say there are few other reports to back it up, even at the federal level.

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Estimates of the size of the municipal technology market vary greatly because terms like "smart cities" and "innovative technology" have no universally accepted definitions. They can cover everything from bike-sharing programs to electric buses, from a city councilor's tweet to an app that lets citizens search through public records. But experts seem to agree on one point: The market will continue to expand for years.

Analysts estimates on the urban innovation trend are eye-popping — but right now it's as much for how greatly they vary as for how big the market may ultimately grow to be. Some analysts peg the smart-cities market to be worth about $27.5 billion annually by 2023, while others say the market could reach as much as $757 billion by 2020.

Population dynamics should support the continued adoption of technology by cities. In urban centers around the world, population numbers are skyrocketing and putting an unprecedented demand on city infrastructure and resources. Fifty-four percent of the world's population lives in urban areas, a proportion that is expected to increase to 66 percent by 2050, when another 2.5 billion people could be living in cities.

Urbanization has prompted national and local governments to realize the importance of leveraging technology to make cities as efficient as possible. The White House announced a smart cities initiative in 2015that will invest more than $160 million in federal research to help local communities reduce traffic congestion, fight crime, manage the effects of climate change and improve city services.

But local governments, which will be hit hardest by the consequences of urbanization, are outpacing their federal counterpart. The Center for Digital Government estimates U.S. cities will spend about $52.4 billion on technology in 2016. That is a 2.5 percent increase over their spending in 2015. The federal government will spend about $89.8 billion on technology in 2016, just a 1.5 percent increase over its spending last year.