$Web = Get-SPWeb http://yoursite/
$libName = "LibraryName"
$lib = $Web.Lists |? {$_.Title -eq $libName}
foreach ($item in $lib.Items)
{
    $File = $item.File
    if( $File.CheckOutStatus -ne "None" -And $File.Versions.Count -eq 0)
    {
        $File.CheckIn("CheckIn")
  Write-Host "$($File.Name) has been Checked In" -ForeGroundColor    yellow
    }
}
$Web.Dispose()

#Force check-in of all documents
$webUrl = "https://sharepoint/SiteCollection"
$libraryTitle = "Shared Documents"

Try
{
    $web = Get-SPWeb $webUrl
    if($web -ne $null)
    {

    ForEach($list in ($web.Lists | ? {$_ -is [Microsoft.SharePoint.SPDocumentLibrary]}))
    {

        If($list.Title -eq $libraryTitle)
        {
            Write-Host "Evalating documents in " $list.Title
            # first get checked out files

            $fileIds = @()
            $Kount = 0
            Write-Host " Checking for files without a checked in version"
            ForEach($file in $list.CheckedOutFiles)
            {
                write-Host $file.LeafName
                $file.TakeOverCheckOut()  # to retrieve item i have to do this before
                $doc = $list.getItemById($file.ListitemId)
                $itemFile = $doc.File
                if($itemFile -ne $null){
                    $itemFile.CheckIn("Checked In By Administrator for achive")
                    write-Host " Checked In" -ForeGroundColor Green
                }
              $Kount ++
            }
            Write-Host " Found $Kount files that have no checked in version"
            Write-Host "  Evaluating files with checked in versions"

            ForEach($item in $list.Items)
            {
            Write-Host "   " $item.Folder "" $item.File.Name
            if($item.File.CheckOutStatus -ne "None")
            {
                try
                {
                    $fileName = $item.File.Name
                    $userName = $item.File.CheckedOutByUser.Name;
                    Write-Host "Document $fileName is checked out by $userName" -f
                    $item.File.CheckIn("CheckIn by Administrator")
                }
                catch
                {
                    Write-Host "Unable to check-in " $item.Url -ForegroundColor Red
                }
            }
            }
            $list.Update()
    }
}
}
}
Catch
{
     Write-Host ($Error[0].Exception)
}