Model order reduction is a common practice to reduce large order systems so that their simulation and control become easy. Nonlinearity aware trajectory piecewise linear is a variation of trajectory piecewise linearization technique of order reduction that is used to reduce nonlinear systems. With this scheme, the reduced approximation of the system is generated by weighted sum of the linearized and reduced sub-models obtained at certain linearization points on the system trajectory. This scheme uses dynamically inspired weight assignment that makes the approximation nonlinearity aware. Just as weight assignment, the process of linearization points selection is also important for generating faithful approximations. This article uses a global maximum error controller based linearization points selection scheme according to which a state is chosen as a linearization point if the error between a current reduced model and the full order nonlinear system reaches a maximum value. A combination that not only selects linearization points based on an error controller but also assigns dynamic inspired weights is shown in this article. The proposed scheme generates approximations with higher accuracies. This is demonstrated by applying the proposed method to some benchmark nonlinear circuits including RC ladder network and inverter chain circuit and comparing the results with the conventional schemes.

Mathematical modelling of physical systems results into large order dynamical system. Such systems are computationally heavy to simulate. It is even difficult to design controller for such systems. To overcome such problems model order reduction of large order dynamical systems is performed. Model order reduction not only reduces computational burden but also makes control feasible. Nonlinearity aware trajectory piecewise linear technique is one of the model order reduction techniques that is used for reduction of nonlinear systems. This method is an improvement to the trajectory piecewise linear approximation. This paper adds another feature to nonlinearity aware trajectory piecewise linear approximation that further enhances its performance and produces approximations with better accuracy and much less number of sub-models thereby reducing the online computation cost. This modified algorithm is applied to a large order transmission line circuit with different nonlinearity cases and reduced models are obtained. A comparison between the simulation results obtained from the nonlinearity aware trajectory piecewise linear approximation with adaptive sampling, nonlinearity aware trajectory piecewise linear approximation and trajectory piecewise linear approximation are also shown in this paper.

Model order reduction techniques are often used to reduce the order of large order systems so that they get easy to simulate and control. Trajectory piecewise linear is a model order reduction technique that is used to reduce the order of nonlinear systems. Nonlinearity aware trajectory piecewise linear approximation is a modification of trajectory piecewise linear method that uses dynamically inspired weight assignment. Such weight assignment scheme makes the approximation more sensitive to the nonlinearities involved. This paper uses the nonlinearity aware trajectory piecewise linear approximation to reduce the order of chain of inverter circuit that forms a large order nonlinear system.

It is commonly observed that in order to understand various biological phenomenon and operation of medical devices, mathematical modelling is done that usually give rise to large order dynamical system. Such large order dynamical system becomes computationally heavy and creates storage problems too. These problems can be tackled if the order of large order system is reduced such that the input/output characteristics are nearly preserved. The reduced order models make the simulation possible and their control practically feasible. This paper shows reduction of pacemaker electrode problem that forms a large order system. A pacemaker electrode forms a part of an artificial pacemaker that is actually responsible for transmitting the electrical impulses to the heart tissue and regulates the beating of the heart. Being very large order problem, it gets difficult to carry out multiple simulations to find out optimum design parameters such as the electrode tip radius and the input excitation that plays an important role in current and voltage distribution on and around the pacemaker electrode. Reduced order model presented in this paper enables multiple simulations at reduced computational cost.

The trajectory piece-wise linear (TPWL) method is a popular technique for nonlinear model order reduction (MOR). Though widely studied, it has primarily been restricted to applications modeled by nonlinear systems with linear input operators. This paper is an effort to bridge this gap. We illustrate problems in the TPWL method in creating reduced order models for nonlinear systems with nonlinear input operators. We also propose a solution based on a quasi-linear formulation of the nonlinear system at approximation points. This results in a method for nonlinear MOR, called the trajectory piece-wise quasi-linear (TPWQ) method. TPWQ is formulated, numerically validated and a new technique to reduce the computational costs associated with simulating the quasi-linear systems is also demonstrated.