Related papers: Nonlinear system identification employing automati…
The Newmark/Newton-Raphson (NNR) method is widely employed for solving nonlinear dynamic systems. However, the current NNR method exhibits limited applicability in complex nonlinear dynamic systems, as the acquisition of the Jacobian matrix…
Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets.…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that…
In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
Broyden's method is a general method commonly used for nonlinear systems of equations, when very little information is available about the problem. We develop an approach based on Broyden's method for nonlinear eigenvalue problems. Our…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
From implicit differentiation to probabilistic modeling, Jacobian and Hessian matrices have many potential use cases in Machine Learning (ML), but they are viewed as computationally prohibitive. Fortunately, these matrices often exhibit…