Local modal participation analysis of nonlinear systems using Poincar\xe9 linearization

International audience

Reachability of Black-Box Nonlinear Systems after Koopman Operator Linearization

A copula-based Gaussian mixture closure method for stochastic response of nonlinear dynamic systems

Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet existing approaches either require knowledge about the underlying system equations or large data sets as they rely on phase space methods. In this work we propose a novel and fully data driven scheme relying on machine learning (ML), which generalizes control techniques of chaotic systems without requiring a mathematical model for its dynamics. Exploiting recently developed ML-based prediction capabilities, we demonstrate that nonlinear systems can be forced to stay in arbitrary dynamical target states coming from any initial state. We outline and validate our approach using the examples of the Lorenz and the Rössler system and show how these systems can very accurately be brought not only to periodic, but even to intermittent and different chaotic behavior. Having this highly flexible control scheme with little demands on the amount of required data on hand, we briefly discuss possible applications ranging from engineering to medicine.

An adaptive system for linear systems with unknown parameters is a nonlinear system. The analysis of such adaptive systems requires similar techniques to analyse nonlinear systems. Therefore it is natural to treat adaptive control as a part of nonlinear control systems. Nonlinear and Adaptive Control Systems treats nonlinear control and adaptive control in a unified framework, presenting the major results at a moderate mathematical level, suitable for MSc students and engineers with undergraduate degrees. Topics covered include introduction to nonlinear systems; state space models; describing functions for common nonlinear components; stability theory; feedback linearization; adaptive control; nonlinear observer design; backstepping design; disturbance rejection and output regulation; and control applications, including harmonic estimation and rejection in power distribution systems, observer and control design for circadian rhythms, and discrete-time implementation of continuous-time nonlinear control laws.

Theory of nonlinear control

Inelastic analysis of flexible bars using simplified nonlinear equivalent systems

Non-intrusive frequency response analysis of nonlinear systems with interval uncertainty: A comparative study

Nonlinear Sampled-data Systems—A lifting framework

In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

A comparison between Sobol’s indices and Shapley’s effect for global sensitivity analysis of systems with independent input variables

Modal analysis of non-conservative systems with friction-induced strong nonlinear damping by using response-controlled testing

A state-space characterization of robustness analysis and synthesis for nonlinear uncertain systems is proposed. The robustness of a class of nonlinear systems subject to L/sub 2/-bounded structured uncertainties is characterized in terms of a nonlinear matrix inequality (NLMI), which yields a convex feasibility problem. As in the linear case, scalings are used to find a Lyapunov or storage function that give sufficient conditions for robust stability and performances. Sufficient conditions for the solvability of robustness synthesis problems are represented in terms of NLMIs as well. With the proposed NLMI characterizations, it is shown that the computation needed for robustness analysis and synthesis is not more difficult than that for checking Lyapunov stability; the numerical solutions for robustness problems are approximated by the use of finite element methods or finite difference schemes, and the computations are reduced to solving linear matrix inequalities. Unfortunately, while the development in this paper parallels the corresponding linear theory, the resulting computational consequences are, of course, not as favourable.

On linear models for nonlinear systems

VIRTUAL DECOMPOSITION AND TIME SCALE DECOUPLING CONTROL OF NONLINEAR SYSTEMS