Search results for "nonlinear systems"
showing 10 items of 26 documents
Two optimizing procedures for the solution of complex systems of equations: a powerful tool for modelling and simulation of metabolism
2000
Introduction Standard calculations for the evaluation of indirect calorimetry (IC) are based on two-dimensional nonlinear systems of equations. For a more sophisticated evaluation metabolic models can be used, which are described by complex systems of equations. Since the solutions are multidimensional, a concrete result must be selected by means of constraints, using optimizing procedures. These multidimensional optimizations are critical concerning processing time and reproducibility of minimum detection. Methods In order to simulate the status of metabolism of ICU patients on the basis of IC data, a complex model of metabolism was developed. The model was described by a system of equatio…
Isotropic p-harmonic systems in 2D Jacobian estimates and univalent solutions
2016
The core result of this paper is an inequality (rather tricky) for the Jacobian determinant of solutions of nonlinear elliptic systems in the plane. The model case is the isotropic (rotationally invariant) p-harmonic system ...
Assessment of qualitative judgements for conditional events in expert systems
1991
Adaptive high-gain extended kalman filter and applications
2010
The work concerns the ``observability problem” --- the reconstruction of a dynamic process's full state from a partially measured state--- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc… We propose a solution to these problems, the Adaptive High-Gain (EKF). Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations…
On the Stability of the Soft Pendulum With Affine Curvature: Open-Loop, Collocated Closed-Loop, and Switching Control
2022
This letter investigates the stability properties of the soft inverted pendulum with affine curvature - a template model for nonlinear control of underactuated soft robots. We look at how changes in physical parameters affect stability and equilibrium. We give conditions under which zero dynamics corresponding to a collocated choice of the output is (locally or globally) stable or unstable. We leverage these results to design a switching controller that stabilizes a class of nonlinear equilibria of the pendulum, which can drive the system from one equilibrium to another.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
A short survey on nonlinear models of the classic Costas loop: rigorous derivation and limitations of the classic analysis
2015
Rigorous nonlinear analysis of the physical model of Costas loop --- a classic phase-locked loop (PLL) based circuit for carrier recovery, is a challenging task. Thus for its analysis, simplified mathematical models and numerical simulation are widely used. In this work a short survey on nonlinear models of the BPSK Costas loop, used for pre-design and post-design analysis, is presented. Their rigorous derivation and limitations of classic analysis are discussed. It is shown that the use of simplified mathematical models, and the application of non rigorous methods of analysis (e.g., simulation and linearization) may lead to wrong conclusions concerning the performance of the Costas loop ph…
Identification of Nonlinear Systems Described by Hammerstein Models
2004
This paper deals with a method for identification of nonlinear systems suitable to be described by Hammerstein models consisting of a static nonlinearity followed by an ARX linear model. The estimation of the static nonlinearity is carried out supplying the system with a sequence of step signals of various amplitude and determining the corresponding steady-state responses. The estimation of the parameters of the ARX linear system is carried out by means of a least square estimator using data generated supplying the system with a Pseudorandom Binary Sequence (PRBS). The method in question is able to identify static nonlinearities of general type, also with hysteresis and/or discontinuities. …
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.
Approximation of the Feasible Parameter Set in worst-case identification of Hammerstein models
2005
The estimation of the Feasible Parameter Set (FPS) for Hammerstein models in a worst-case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidic uncertainties. It consists in the projection of the FPS of the extended parameter vector onto suitable subspaces and in the solution of convex optimization problems which provide Uncertainties Intervals of the model parameters. The bounds obtained are tighter than in the previous approaches. hes.