In　this　paper,　a　new　stabilizing　value　iteration　Q-learning　(SVIQL)　algorithm　is　presented　to　achieve　the　online　evolving　control　for　unknown　nonlinear　systems.　To　achieve　this,　we　aim　to　establish　the　data-driven　evolving　control　framework,　ensure　the　stability　of　iterative　policies　derived　from　SVIQL,　and　reduce　the　computational　cost　in　online　learning.　First,　by　using　an　admissible　policy　for　initialization,　the　monotonicity　and　stability　properties　of　SVIQL　are　theoretically　analyzed.　It　is　highlighted　that　under　this　SVIQL　framework,　the　iterative　Q-function　sequence　is　monotonically　nonincreasing　and　all　iterative　policies　are　admissible.　Second,　we　compare　the　convergence　speed,　computational　complexity,　and　evolving　control　results　of　SVIQL　and　policy　iteration　Q-learning　methods.　The　results　shows　that　SVIQL　has　faster　policy　update　speed　with　smaller　computational　complexity.　Third,　in　the　online　evolving　control　stage,　the　offline　and　online　data　are　combined　to　learn　the　new　iterative　policy,　which　is　used　to　regulate　the　nonlinear　system　over　time.　For　implementing　the　SVIQL　algorithm,　the　critic　and　action　networks　are　constructed　to　approximate　the　iterative　Q-function　and　control　policy,　respectively.　Moreover,　the　convergence　of　two　network　weights　is　analyzed.　Finally,　numerical　simulations　are　conducted　to　confirm　the　effectiveness　of　the　online　evolving　control　under　the　SVIQL　scheme.