In　this　article,　a　novel　value　iteration　scheme　is　developed　with　convergence　and　stability　discussions.　A　relaxation　factor　is　introduced　to　adjust　the　convergence　rate　of　the　value　function　sequence.　The　convergence　conditions　with　respect　to　the　relaxation　factor　are　given.　The　stability　of　the　closed-loop　system　using　the　control　policies　generated　by　the　present　VI　algorithm　is　investigated.　Moreover,　an　integrated　VI　approach　is　developed　to　accelerate　and　guarantee　the　convergence　by　combining　the　advantages　of　the　present　and　traditional　value　iterations.　Also,　a　relaxation　function　is　designed　to　adaptively　make　the　developed　value　iteration　scheme　possess　fast　convergence　property.　Finally,　the　theoretical　results　and　the　effectiveness　of　the　present　algorithm　are　validated　by　numerical　examples.