Search results for "Nonlinear system"
showing 10 items of 1446 documents
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.
Numerical methods for a nonlinear impact model: A comparative study with closed-form corrections
2011
A physically based impact model-already known and exploited in the field of sound synthesis-is studied using both analytical tools and numerical simulations. It is shown that the Hamiltonian of a physical system composed of a mass impacting on a wall can be expressed analytically as a function of the mass velocity during contact. Moreover, an efficient and accurate approximation for the mass outbound velocity is presented, which allows to estimate the Hamiltonian at the end of the contact. Analytical results are then compared to numerical simulations obtained by discretizing the system with several numerical methods. It is shown that, for some regions of the parameter space, the trajectorie…
Multimode Representation of the Magnetic Field for the Analysis of the Nonlinear Behavior of Solar Activity as a Driver of Space Weather
2022
ISSP UL as the Center of Excellence is supported through the Framework Program for European universities Union Horizon 2020, H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under Grant Agreement No. 739508, CAMART2 project; Internal Foundation of University of Maryland.
Stability of stochastic nonlinear systems with state-dependent switching
2013
In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…
A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
2020
The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Sliding mode exponential H<inf>&#x221E;</inf> synchronization of Markovian jumping master-slave systems with time-delays and nonlinea…
2011
This paper investigates the problem of exponential H ∞ synchronization for a class of master-slave systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H ∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. A numerical examp…
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Stochastic Response on Non-Linear Systems under Parametric Non-Gaussian Agencies
1992
The probabilistic response characterization of non-linear systems subjected to non-normal delta correlated parametric excitation is obtained. In order to do this an extension of both Ito’s differential rule and the Fokker-Planck equation is presented, enabling one to account for the effect of the non-normal input. The validity of the approach reported here is confirmed by results obtained by means of a Monte Carlo simulation.
A novel approach to nonlinear variable-order fractional viscoelasticity.
2020
This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear superposition principle, i.e. the theoretical basis on which linear viscoelastic fractional operators are formulated, does not apply in standard form because the fractional order is not constant with time. Moving from this consideration, the paper proposes a novel approach where the system response is derived by a consistent application of the Boltzmann principle to an equivalent system, built at every time instant based on the fractional order at that instant and the response at all the previous ones. The ap…