Computational complexity analysis of set membership identification of a class of nonlinear systems

This paper analyzes the computational complexity of set membership identification of a class of nonlinear systems consisting of the interconnection of a linear time invariant plant and a static nonlinearity. Its main result shows that, even in cases where a portion of the plant is known, the problem is generically NP-hard both in the number of experimental data points and in the number of inputs or outputs of the nonlinearity. These results provide new insight into the reasons underlying the high computational complexity of several recently proposed algorithms and point out to the need for developing computationally tractable relaxations.