We introduce and analyze a class of generalized trust region sequential quadratic programming (GTRSQP) algorithms for equality constrained optimization. Unlike in standard trust region SQP (TRSQP) algorithms, the optimization subproblems arising in our GTRSQP algorithm can be generated from models of the objective and constraint functions that are not necessarily based on Taylor approximations. The need for such generalizations is motivated by optimal control problems for which model problems can be generated using, e.g., different discretizations. Several existing TRSQP algorithms are special cases of our GTRSQP algorithm. Our first order global convergence result for the GTRSQP algorithm applied to TRSQP allows one to relax the condition that the so-called tangential step lies in the null-space of the linearized constraints. The application of the GTRSQP algorithm to an optimal control problem governed by Burgers equation is discussed.