It　remains　a　formidable　challenge　to　accurately　recognize　motion　intentions　of　patients　thus　to　control　hand　exoskeletons　according　to　their　volition.　Current　methods　primarily　focus　on　recognition　of　limited　patient＇s　motion　intentions,　with　the　purpose　of　controlling　preconfigured　gestures　of　a　hand　exoskeleton　for　grasping　objects.　These　methods　exhibit　a　marked　shortfall　when　encountering　scenarios　that　are　unexpected　or　not　designed　in　advance,　such　as　non-preprogrammed　hand　movements　and　object　manipulation　tasks.　To　tackle　this　issue,　large　language　model　(LLM)　and　speech　recognition　technology　are　employed　in　this　study　to　allow　the　patient　to　control　a　hand　exoskeleton　at　will.　In　particular,　two　LLMs　are　tailored　to　formulate　codes　of　either　generating　non-preprogrammed　gestures　or　dealing　with　unencountered　objects.　Additionally,　an　incremental　learning　framework　is　proposed　to　enable　patients　to　perform　both　predefined　and　non-predefined　operation　tasks　by　integrating　a　natural　language　parser　with　the　two　LLM-based　learners.　The　natural　language　parser　can　directly　control　the　hand　exoskeleton　to　perform　predefined　operations　tasks　from　prestored　command　set,　while　the　LLM-based　learners　can　incrementally　expand　the　control　command　set　so　as　to　enhance　adaptability　of　the　hand　exoskeleton　to　complex　activities　over　daily　use.　This　study　is　a　pioneering　work　in　the　field　of　hand　exoskeletons,　which　will　revolutionize　the　way　to　control　hand　exoskeletons.　Furthermore,　the　proposed　framework　can　be　easily　generalized　to　any　other　robots　by　modifying　the　prompt　of　customized　LLMs,　which　provides　a　new　idea　to　achieve　autonomous　learning　in　robotics.