Abstract: From the point of view of dominating the model structure and improving the identification accuracy, a new modelling method to construct optimal upper boundary regression model (UBRM) is proposed. Firstly, quadratic programming-support vector regression (QP-SVR) is converted to the optimization of l₁-norm to obtain the sparsity of the UBRM. Secondly, constraints corresponding to the UBRM and l₁-norm on approximation errors are constructed to improve the identification accuracy. Finally, a new optimization problem combined the structural risk of l₁-norm with l₁-norm on approximation errors is thus formulated and it is solved by linear programming to derive an optimal UBRM. The optimal UBM has the following remarkable features: 1)modelling accuracy of UBRM can be guaranteed by the l₁-norm minimization on approximation error; 2) model structural complexity is under control by introducing l₁-norm on structural risk within the framework of support vector regression (SVR) to guarantee the model sparsity; 3)the generalization performance of the proposed method adopts the equilibrium between the modelling accuracy and sparseness. The rationalities and superiorities of the proposed optimal UBRM is demonstrated by experiments derived from uncertain measurements and uncertain parameters of nonlinear system.