Mechanical connectors always work well, go to a manufacturer's website, e.g. Simpson StrongTie, and browse their wood connectors, deck and patio connectors, and you will find products that will meet your needs. The framing seems undersized but I don't know if you have snow or wind loads you need to meet or what the dead load is. In most jurisdictions a building permit is required and part of that process is a plan review. It is always nice to have a second set of eyes review your plans. Good Luck with the project.