President Obama and his new Chinese counterpart, Xi Jinping, will retreat to the California desert this weekend for an unusual series of meetings that could help define one of the world’s most important relationships for years to come.

The timing and informality of the encounter — beginning Friday on the Annenberg estate in Rancho Mirage, Calif. — distinguish it from a typical ­heads-of-state summit. So does the broad agenda, which is designed to take a longer view of the security, economic and strategic challenges that unite and divide the nations.

The issues facing the two remain largely the same as they’ve been throughout Obama’s tenure, defined by economic rivalry, mounting cybersecurity threats to U.S. businesses, an assertive Chinese nationalism and an expanded American military presence in the Asia-Pacific region.

Only the Chinese leader has changed, and Obama intends to discover what, if anything, that might mean. Their time together on the 200-acre estate, free of the stiff pageantry that Chinese leaders typically expect in a U.S. visit, is a test of how the two leaders get along and whether a personal relationship can influence policy in the years ahead.

“There’s a lot of talk about strategic distrust,” said Jeffrey A. Bader, a senior fellow at the Brookings Institution, who served as Obama’s chief adviser on East Asia early in the administration.

“That’s not a phrase, frankly, I’d use, and I don’t believe it’s all that easy to overcome strategic distrust between countries,” he continued. “But trust between individuals is real, and they don’t have to have the same ideology.”

American presidents traditionally wait at least a year for a major meeting with a new Chinese leader, who often needs time to consolidate his hold over the institutions that comprise political authority in Beijing.

But Obama saw no reason to wait that long with Xi, who was given control of the presidency, the Communist Party and the military simultaneously when he took office in March. His predecessor, Hu Jintao, had to wait almost two years before all three sources of Chinese power were under his command.

The Obama administration had also been cultivating Xi for two years before he took office. Vice President Biden traveled to China two years ago to meet with him, and Xi was accompanied by Biden last year during a tour of the United States.

During that visit, Xi — the son of a Chinese revolutionary imprisoned for his political views — also spent more than 90 minutes with Obama at the White House, rare for a visiting vice president.

“Through these contacts and others, Xi has demonstrated what to Western eyes and ears looks and feels like a capacity to engage substantively a little more along the lines of what politicians might do,” said a senior administration official, who spoke on the condition of anonymity to discuss the summit.

Since taking office, Obama has made Asia a priority after a general lull during the Bush administration, which was preoccupied with the Iraq and Afghanistan wars. Obama has regularly attended meetings of ­Asian-Pacific countries, joined regional security forums and strengthened the U.S. military presence.

Many Asian leaders worried about Chinese ambitions have welcomed Obama’s interest in a larger American role in the region. At the same time, it has raised concerns within the Chinese leadership that Obama’s ambitions are designed in large part to blunt China’s.

Obama last hosted a Chinese leader in January 2011, when Hu, after nearly a decade in power, looked more to his legacy than to new ambitions.

The images of Xi and Obama, strolling in casual clothes, could help the Chinese leader send a signal home that he intends a close relationship with the United States at a time of mounting economic concerns.

Cheng Li, a U.S.-China expert at Brookings, said many in China view Xi as a “political conservative and an economic liberal,” a perception that has exacerbated frustrations over the slow pace of democratic reform.

Xi’s focus on economic growth comes as domestic employment lags. Li said as many as half of China’s 7­ million college graduates this year might not be able to find a job.

“The summit is essential for Xi to consolidate his power back home, and for Obama to help Xi to choose the right path for China and to be on the right side of history,” Li said.

During a news briefing in Beijing last month, Assistant Foreign Minister Zheng Zeguang said the summit is a chance for the two powers to follow “a new path that is different from traditional superpower confrontations, a new path under which big powers can live in harmony, cooperating with mutual benefit.”

Shi Yinhong, director of American studies at Renmin University in Beijing, said the challenge for Obama and Xi will be to bridge the gap in expectations over how quickly and on what terms the nations might work together.

“There is such a large distance between China’s proposal for a new, big power relationship and the U.S. attitude toward it,” Shi said. “China wants to sit down and talk first, but the U.S. wants to see immediate results.”

One area where that is true is in cybersecurity, particularly how it affects American intellectual property rights. Experts describe the issue as “asymmetric,” especially in the area of hacking — that is, China does it and the United States does not.

“To U.S. companies, it represents an existential threat,” said Patrick Chovanec, a former economics professor at Tsinghua University who is now chief strategist for Silvercrest Asset Management. “The Chinese do not seem to realize how serious this issue has become.”

U.S. officials have made cybersecurity a regular item in their meetings with Chinese officials. But little progress has been made in curbing the practice, which goes well beyond government-against-government espionage.

“This is not a ‘deliverables’ kind of meeting, but I don’t want to leave the impression it will be a touchy-feely boys weekend in Palm Springs,” the senior administration official said. “This is one of those cases that only over time will one be able to look back and say this meeting affected the trend lines, the vector, of Chinese behavior and interaction.”