Chinese President Xi Jinping was greeted by Vice President Biden after landing in Maryland on Sept. 24, 2015. (AP)

President Obama has lavished more personal attention on Chinese President Xi Jinping than on any other world leader over the past several years.

But as Xi makes his first state visit to Washington, the romance is all but dead.

Observers said there is little personal warmth, and even less trust, between Xi and Obama as the White House prepares to roll out the red carpet with a pomp-filled arrival ceremony Friday.

Xi has aggressively sought to expand China’s influence in Asia, and his assertiveness has caught the Obama administration off guard, often making the White House appear indecisive in its responses.

Obama aides insist the president’s strategy of engagement over confrontation will pay long-term dividends. They point to a major climate pact with Beijing last year and China’s backing for the U.S.-led nuclear accord with Iran. White House officials said Xi will on Friday announce new plans to enact a cap-and-trade program to curtail carbon emissions starting in 2017, further evidence that Beijing is serious about curbing China’s carbon emissions.

If Xi has been more forceful on the world stage, the aides said, he has also provided evidence that China has the potential to be the kind of responsible global partner that the United States has sought.

At the same time, escalating tensions have led others to conclude that Xi has gotten the better of Obama, taking advantage of the U.S. president’s impulse for collaboration while Xi furthers his own ambitions to consolidate power in China and assert greater authority abroad.

“It’s not possible to deal with this approach without doing things that create risk,” said Aaron Friedberg, a former aide to President George W. Bush on Asian affairs. “China is taking risky actions believing that others will back away fearing confrontation. We’re going to have to take risks as well.”

The Obama administration has resisted calls in Washington to impose new economic sanctions on Chinese businesses over the cybertheft of U.S. trade secrets or to dispatch Navy ships into waters recently claimed by Beijing in the South China Sea, a crucial international shipping corridor.

Critics, including several Republican presidential candidates, have said Obama’s inaction has emboldened Xi, and foreign policy analysts said Beijing is intent on pushing the boundaries in Obama’s final years in office amid fears that the next U.S. admin­istration will be less friendly toward China.

Ruan Zongze, who served as a minister at China’s embassy in Washington from 2007 to 2011, said in a recent interview that calls for a tougher policy toward China are rooted in anxiety among U.S. officials “to prove they’re not in decline.”

In China, he said, the view is that U.S. relations with Russia and in the Middle East are “not in desirable shape” and that there is no upside for the Obama administration to pick a fight with Beijing.

If American political candidates have a favorite foreign punching bag, it is China. Wonkblog’s Ana Swanson explains why so many candidates change their tune once elected, and just how important the U.S.-China relationship really is. (Jorge Ribas/The Washington Post)

“China is not challenging American supremacy,” Ruan said.

White House officials said Obama will hold off on any punitive actions until after he meets with Xi. In a speech to business leaders in Seattle this week, Xi denied a role by his government in the cybertheft of trade secrets and said he would seek to strengthen cooperation with the United States on the issue.

“This summit will be an opportunity for us to hear directly from him what form that takes, and then we’ll be able to make a judgment based on those conversations,” said Ben Rhodes, a White House deputy national security adviser.

At the heart of those conversations is a relationship between leaders who have struggled to develop a personal rapport and enter Friday’s summit on different trajectories.

Obama, 54, is in the final stages of his presidency, having steered the United States onto firmer financial footing but still working to realize a foreign policy strategy aimed at lessening the United States’ focus on the Middle East and shifting attention to Asia.

Xi, 62, is in the third year of a 10-year term as head of China’s ruling Communist Party, a leader who has ambitions to return China to a central role in Asian affairs but has struggled to enact changes to modernize its economy.

In Xi, who assumed power in 2013, the White House saw a figure who was more dynamic than his predecessors, including Hu Jintao, with whom Obama had made little headway in his first term. Obama advisers viewed Xi, who had lived in the United States, as a potential reformer who would make China willing to shoulder more responsibility to solve global challenges, and the White House was determined to enlist Xi as an ally even before he became president.

In November 2011, Obama held an un­or­tho­dox introductory meeting with Xi, then China’s vice president, on the sidelines of a regional security summit in Bali. Three months later, Xi arrived for a cross-country U.S. tour, hosted by Vice President Biden, with stops in Iowa and California as well as Washington, D.C.

“I’m glad you will get an opportunity to get out of Washington . . . maybe even taking in a Lakers game,” Obama told Xi in the Oval Office during that visit. “I look forward to a future of improved dialogue and increased cooperation.”

When Xi became president, Obama invited him in June 2013 for a two-day summit at the Sunnylands estate in Southern California, a lush retreat favored by Ronald Reagan. At a working dinner, each man laid out his domestic agenda and the political challenges he faced at home — the better to understand how each other’s foreign policy aims might be affected by domestic concerns.

Rhodes said that because the United States and China have such a long bilateral agenda, the two sides are forced to plow through issues in face-to-face talks that get consumed by talking points.

The White House has sought to engage Xi in separate, more intimate settings to develop more rapport through franker exchanges. Obama and Xi met for a private dinner Thursday night, ahead of the formal summit meetings and state dinner Friday.

Obama told his aides that “the most constructive engagements were when they were able to talk for several hours over dinner without a formal agenda,” Rhodes said.

During those talks, Rhodes added, the two leaders would typically “give a vision for where they want to take their country, give a vision for how they think the U.S. and China should operate together in the world, and kind of put aside the talking points and actually get a window into one another’s worldview. And those worldviews are very different.”

White House aides credit the Sunnylands session with helping lay the groundwork for a landmark deal, announced during Obama’s visit to Beijing last year, to reduce China’s greenhouse gases by 2030.

But in other areas, Xi has repeatedly challenged the White House. At Sunnylands, they spent a significant amount of time discussing U.S. concerns over China’s hacking of American businesses, but the cybertheft problem has gotten significantly worse.

In 2013, China declared an Air Defense Identification Zone around a set of contested islands in the East China Sea that had long been administered by Japan. Though Obama announced during a visit to Tokyo in 2014 that the United States would defend its treaty ally, China has since moved aggressively to expand its control in another major maritime thoroughfare on the South China Sea.

And on economics, Xi has launched the Asian Infrastructure Investment Bank, a regional initiative backed by U.S. allies, including Germany and Britain, even as the Obama administration seeks to complete an expansive 12-nation Asia-Pacific trade pact that excludes China.

“Xi had some big ideas for this relationship, and he has tried to test American resolve,” said Minxin Pei, a China expert at the German Marshall Fund. “The United States has begun to respond firmly, but it could have been a lot more vigorous countering Chinese moves.”

White House officials say China’s recent economic woes, including a sharp drop in its stock market, have put Xi on the defensive to show his countrymen that he can maintain the breakneck economic growth that has propelled China’s rise over the past two decades.

The question is whether Xi’s weakened position will make him more or less averse to compromise with Obama.

“We reject reductive reasoning and lazy rhetoric that says conflict between the U.S. and China is inevitable, even as we’ve been tough with China where we disagree,” Susan E. Rice, the White House national security adviser, said in a speech Monday. “This isn’t a zero-sum game.”