  In this paper, we study the parameter synthesis problem for a class of
parametric timed automata. The problem asks to construct the set of valuations
of the parameters in the parametric timed automa- ton, referred to as the
feasible region, under which the resulting timed automaton satisfies certain
properties. We show that the parameter syn- thesis problem of parametric timed
automata with only one parametric clock (unlimited concretely constrained
clock) and arbitrarily many pa- rameters is solvable when all the expressions
are linear expressions. And it is moreover the synthesis problem is solvable
when the form of con- straints are parameter polynomial inequality not just
simple constraint and parameter domain is nonnegative real number.
