Block Oriented Nonlinear System Identification Using Semidenite Programming

Identification of block-oriented nonlinear systems has been an active research area for the last several decades. A block-oriented nonlinear system represents a nonlinear dynamical system as a combination of linear dynamic systems and static nonlinear blocks. In block-oriented nonlinear systems, each block (linear dynamic systems and static nonlinearity) can be connected in many different ways (series, parallel, feedback) and this flexibility provides the block-oriented modeling approach with an ability to capture a large class of nonlinear systems. However, intermediate signals in such block-oriented systems are not measurable and the inaccessibility of such measurements is the main difficulty in block-oriented nonlinear system identification. Recently a system identification method using rank minimization has been introduced for linear system identification. Finding the simplest model within a feasible model set restricted by convex constraints can often be formulated as a rank minimization problem. In this research, the rank minimization approach is extended to block-oriented nonlinear system identification. The system parameter estimation problem is formulated as a rank minimization problem or the combination of prediction error and rank minimization problems by constraining a finite dimensional time dependency of a linear dynamic system and by using the monotonicity of static nonlinearity. This allows us to reconstruct non-measurable intermediate signals and once the intermediate signals have been reconstructed, the identification of each block can be solved with the standard Prediction Error method or Least Squares method. The research work presented in this dissertation proposes a new approach for block-oriented system identification by tackling the inaccessibility of measurement of intermediate signals in block-oriented nonlinear systems via rank minimization. Since the rank minimization problem is non-convex, the rank minimization problem is relaxed to a semidefinite programming problem by minimizing the nuclear norm instead of the rank. The research contributes to advances in block-oriented nonlinear system identification.