user: Problem: Article: Closing the first night of the Democratic convention, Mrs Obama spoke of the vision and values that guided him as president.
She said it was an "extraordinary privilege" to serve as first lady.
President Obama will formally accept the nomination on Thursday, and face Republican Mitt Romney in November.
A recent opinion poll suggests Mr Obama maintains a thin lead over Mr Romney.
But an ABC News/Washington Post poll released as the convention got under way in Charlotte, North Carolina, showed Mr Obama with the lowest pre-convention favourability for an incumbent president since the 1980s.
The president is aiming to recapture the political spotlight over the next few days, after last week's Republican convention.
By Mark MardellNorth America editor
Mrs Obama said that four years ago she "believed deeply" in her husband's "vision for this country", but worried about how a run for president would change their life and the life of their daughters.
In a speech well received by a hyped-up crowd, she shared memories from their 23-year relationship, and noted that she had found a "kindred spirit" in a man whose values were similar to hers.
"Barack and I were both raised by families who didn't have much in the way of money or material possessions but who had given us something far more valuable - their unconditional love, their unflinching sacrifice, and the chance to go places they had never imagined for themselves."
She added: "Barack knows what it means when a family struggles. He knows what it means to want something more for your kids and grandkids.
"Barack knows the American Dream because he's lived itâ€¦ and he wants everyone in this country to have that same opportunity, no matter who we are, or where we're from, or what we look like, or who we love."
The first lady's speech connected their shared background to the values she said guided Mr Obama as president.
"As president, you can get all kinds of advice from all kinds of people," she said, "but at the end of the day, when it comes time to make that decision, as president, all you have to guide you are your values and your vision and the life experiences that make you who you are."
She said Mr Obama was inspired by his own background when advocating for laws involving fair pay for women, healthcare and student debt.
He had not been changed by the White House, she said, and was "still the same man I fell in love with all those years ago".
"He's the same man who started his career by turning down high-paying jobs and instead working in struggling neighbourhoods where a steel plant had shut down, fighting to rebuild those communities."
In the toughest moments, she added, "he just keeps getting up and moving forwardâ€¦ with patience and wisdom, and courage and grace."
Earlier, the chair of the Democratic National Committee, Debbie Wasserman Schultz, brought the gala into session with a strike of the gavel.
Shortly after the convention opened, delegates cheered their backing for the party's new platform in an open voice vote.
Among the changes found in the text of the party's 2012 platform was the removal of language from the Middle East section referring to Jerusalem as the capital of Israel.
That message was replaced with a passage referring to the party's "unshakeable commitment to Israel's security" and Mr Obama's "steadfast opposition to any attempt to delegitimize Israel".
The change prompted criticism from Republicans and Mitt Romney, who accuse Mr Obama of "selling out" a key US ally.
According to the New York Times' Alessandra Stanley, Michelle Obama's speech was a reminder that the role of president's wife "seems pretty much frozen in the template set by Jacqueline Kennedy and Pat Nixon".
Writing in the The Washington Post, EJ Dionne said the speech was "thoroughly apolitical on the surface" and that it "carried multiple political messages".
Paul West, in the Los Angeles Times, said Mrs Obama set out "to humanise a candidate who often comes across as aloof and remote from the lives of ordinary Americans".
Politico's Jennifer Epstein said Mrs Obama's message was simple: "We are you."
Tuesday's first session saw a series of Democratic governors, members of Congress, mayors and electoral candidates speak in support of Mr Obama and his policies, most notably his much-criticised healthcare reform law.
A video tribute to the late Senator Edward Kennedy included clips from his 1994 Senate debate with Mr Romney, and independent Rhode Island Governor Lincoln Chafee argued that his former party - the Republicans - had lost their way and had forfeited the label of conservative.
Former White House Chief of Staff Rahm Emanuel said the next president would set the tone for the next 40 years.
"It will be the president's leadership that determines how we as a nation meet the challenges that face the middle class. It is the president's values that shape a future in which the middle class has hope," he said.
Julian Castro, the Latino Mayor of San Antonio, Texas, gave the keynote address immediately before Mrs Obama.
The Democratic gathering will see Mr Obama and Vice-President Joe Biden formally re-nominated as the party's presidential and vice-presidential candidates on Wednesday.
Later that evening, there will be speeches from Elizabeth Warren, who is fighting Republican incumbent Scott Brown in a high-profile race for a Massachusetts Senate seat, and former President Bill Clinton.
The convention culminates on Thursday with speeches from Mr Obama and Mr Biden.
Republican nominee Mitt Romney is expected to spend the week preparing for a series of debates with Mr Obama.
The gala also offers the Democrats the chance to make a high-profile pitch to voters in North Carolina, a state that narrowly voted for Mr Obama in 2008, but is now firmly up for grabs.
Answer: [[US First Lady Michelle Obama has made an impassioned speech backing her husband, President Barack Obama, for another four-year White House term.]]

Problem: Article: They are contained in correspondence between US firm PIMCO and the finance committee at Stormont.
The committee is investigating the £1.2bn sale by the National Asset Management Agency (Nama) - the Irish bad bank - amid claims of fixer fees.
The meeting took place at Stormont on 22 May, 2013.
It was also attended by then finance minister Sammy Wilson, Frank Cushnahan - who was at the time a Nama adviser - and solicitor Ian Coulter.
Nama: The key figures and background you need to know
Timeline of Nama's NI property deal
The Democratic Unionist Party (DUP) had previously stated that its leader Mr Robinson met with PIMCO, but few details were provided.
In its letter, PIMCO states an unsolicited approach was made to it by US law firm Brown Rudnick, which introduced it to "two other parties which it appeared to be working with".
It does not name the other parties.
It goes on to state it "was advised by these parties that the Northern Ireland government was concerned to ensure that there would not be a fire sale of homes and businesses".
Instead, it wanted "a longer term approach to investment and development of the assets" by a purchaser.
PIMCO states having expressed an interest, "it was explained the Northern Ireland Executive wanted to meet".
It said it attended the Stormont meeting "so that an assessment could be made as to PIMCO's suitability".
The letter adds: "It is our understanding PIMCO was not the only firm invited to meet with the representatives of the Northern Ireland Executive at that time."
The Irish government was made aware of buyer interest in the Nama portfolio the following month.
Mr Cushnahan resigned as a Nama adviser in November 2013 and has strongly denied any wrongdoing.
The Sinn Féin chairman of the Finance Committee, Daithí McKay, described details of the meeting as "a very significant development".
He said PIMCO "mistakenly believed" the meeting was "taking place under the auspices of the executive."
Mr McKay added: "It is the first time that any of the players in the sale of Nama's northern portfolio have put anything on the record about this secret meeting.
"This letter raises further questions about the Nama sale and I will be asking why no record of this meeting has been made available to date by the Department of Finance."
Answer:

assistant: [[Details have emerged of a meeting between First Minister Peter Robinson and a potential buyer of Nama's Northern Ireland loan book in 2013.]]