A　data-based　value　iteration　algorithm　with　the　bidirectional　approximation　feature　is　developed　for　discounted　optimal　control.　The　unknown　nonlinear　system　dynamics　is　first　identified　by　establishing　a　model　neural　network.　To　improve　the　identification　precision,　biases　are　introduced　to　the　model　network.　The　model　network　with　biases　is　trained　by　the　gradient　descent　algorithm,　where　the　weights　and　biases　across　all　layers　are　updated.　The　uniform　ultimate　boundedness　stability　with　a　proper　learning　rate　is　analyzed,　by　using　the　Lyapunov　approach.　Moreover,　an　integrated　value　iteration　with　the　discounted　cost　is　developed　to　fully　guarantee　the　approximation　accuracy　of　the　optimal　value　function.　Then,　the　effectiveness　of　the　proposed　algorithm　is　demonstrated　by　carrying　out　two　simulation　examples　with　physical　backgrounds.　(C)　2021　Elsevier　Ltd.　All　rights　reserved.