In　this　paper,　Lyapunov　theory　is　used　firstly　to　analyze　the　motion　characteristics　of　the　tractor-trailer　system.　Then,　a　novel　mixed　logical　dynamics　(MLD)　model　is　proposed　to　describe　the　kinematic　of　the　tractor-trailer　system.　For　the　resulting　MLD　model,　an　extended　cost　function　with　quadratic　form　is　addressed,　in　which　the　steering　angle　of　the　tractor,　as　well　as　two　errors　combining　the　position　and　the　orientation　of　the　trailer　are　considered.　To　minimize　the　tracking　error　of　the　trailer,　and　smooth　the　steering　angle　behavior　of　the　tractor,　an　equivalent　linear　quadratic　tracking　problem　is　presented.　In　view　of　this　problem,　an　explicit　model　predictive　control　(MPC)　controller　is　designed,　by　employing　the　multi-parametric　mixedinteger　quadratic　programming　(mp-MIQP)　technique.　Finally,　the　controller　performance　is　evaluated　through　simulation,　and　achieves　the　asymptotical　stability,　accurate　tracking　feature　and　the　constraint　fulfillment　properties,　even　in　the　case　of　the　nonsmooth　tracking　reference　path.