Linear Time-invariant Problems Research Articles

Solving of Linear Time Invariance Quadratic Optimal Control Systems using Chebyshev Scaling Function

In this paper we have studied the linear time invariance optimal control problems with quadratic performance index, and approximated control variable, state variable and performance index using Chebyshev scaling function method with unknown coefficients. The linear time invariant problems were parameterized based on control-state parameterization technique such that the objective function and the constraints are casted in terms of state variable and control variable. This method was converting the linear time invariance quadratic optimal control problems into quadratic programming problems and the converted problems were solved using MATLAB. Hence we increase the order of polynomial (M), and then the computational results of the proposed methods gave better results. Keywords: Optimal control, Chebyshev scaling function, operational matrix integration. DOI : 10.7176/MTM/9-7-01 Publication date : July 31 st 2019

The real Schur decomposition estimates Lyapunov characteristic exponents with multiplicity greater than one

Lyapunov characteristic exponents are indicators of the nature and of the stability properties of solutions of differential equations. The estimation of Lyapunov exponents of algebraic multiplicity greater than 1 is troublesome. In this work, we intuitively derive an interpretation of higher multiplicity Lyapunov exponents in forms that occur in simple linear time invariant problems of engineering relevance. We propose a method to determine them from the real Schur decomposition of the state transition matrix of the linear, nonautonomous problem associated with the fiducial trajectory. So far, no practical way has been found to formulate the method as an algorithm capable of mitigating over- or underflow in the numerical computation of the state transition matrix. However, this interesting approach in some practical cases is shown to provide quicker convergence than usual methods like the discrete QR and the continuous QR and Singular Value Decomposition (SVD)methods when Lyapunov exponents with multiplicity greater than one are present.

State-Based Adjoint Method for Reduced Order Modeling

Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.

Using Frequency Response Coherent Structures for Model-Order Reduction in Microwave Applications

An effective practical technique for model-order reduction of large-scale linear time-invariant problems in microwave applications is presented. The reduction is performed as the Galerkin projection onto a subspace of frequency response coherent structures that contain the spectrum of the system multiinput impulse response. The subspace basis is created by the proper orthogonal decomposition of the system transfer characteristics sampled at discrete frequency points. A reduced-order modeling of an integrated planar spiral transformer is used for practical verification and comparison to the standard moment matching subspace approach.

An algorithm for time series analysis of linear time-invariant differential equations

For linear time-invariant problems an algorithm is presented that enables fast and accurate time series analysis. The method is based on the assumption that the forcing functions can be expressed by a polygonal course. As a result an exact and therefore unconditional stable numerical procedure is derived.