Automated scheme for linearisation points selection in TPWL method applied to non-linear circuits

Abstract

Trajectory piecewise linear (TPWL) approximation is a well-known model order reduction technique for non-linear systems. It involves weighted summation of the dimensionally reduced linear systems obtained at certain points on the system trajectory. The points at which the linearised systems are produced are called linearization points (LP). The LPs are important as they decide the quality and the complexity of the approximation. The criterion of selecting LPs play a crucial role as the fidelity of the reduced model depends upon it. According to the previous methods, a new linearised model is formed whenever the distance of the linear model being simulated from all the previously selected LPs is greater than some chosen distance. This distance is heuristically chosen in the conventional LP selection schemes. This article proposes a new criterion of selecting the distance and the LPs that not only removes the ambiguity but also enhances the performance of the approximation. With the proposed scheme, much smaller number of LPs are needed and the distances are computed automatically, instead of being arbitrarily selected. A number of relevant examples are presented, showing the advantages of the method, both in the number of LPs and in the error of the TPWL approximation.

Keywords

• reduced order systems
• computational complexity
• linear systems
• state-space methods
• piecewise linear techniques
• approximation theory
• error analysis
• nonlinear dynamical systems
• linearisation techniques
• well-known model order reduction technique
• nonlinear systems
• weighted summation
• dimensionally reduced linear systems
• nonlinear system trajectory
• linearised systems
• reduced model
• linearised model
• linear model
• selected lps
• chosen distance
• conventional lp selection schemes
• tpwl approximation
• automated scheme
• linearisation points selection
• tpwl method
• nonlinear circuits
• trajectory piecewise linear approximation