Nonlinear system identification

Résumé

System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more. A nonlinear system is defined as any system that is not linear, that is any system that does not satisfy the superposition principle. This negative definition tends to obscure that there are very many different types of nonlinear systems. Historically, system identification for nonlinear systems has developed by focusing on specific classes of system and can be broadly categorized into five basic approaches, each defined by a model class:

Volterra series models,

Block-structured models,

Neural network models,

NARMAX models, and

State-space models.

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Source officielle

https://en.wikipedia.org/wiki/Nonlinear_system_identification

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Adaptive Control for Nonlinear Uncertain Systems with Actuator Amplitude and Rate Saturation Constraints

Yannick Morel

Wiley-Blackwell2008

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Event-based control is an alternative to traditional control where new measurements are sampled only if critical events occur. This not only allows to reduce the control effort but it satisfies nowadays application requirements, such for example reduction of information exchange, computational power, or energy consumption. The work in this field is, however, still sparse and only a few results are available. Properly choosing an event-detection logic can considerably improve the overall system's performance. We propose a control algorithm which makes use of a model-based triggering strategy to reduce the control effort (reduced-attention control), while guaranteeing robustness against bounded additive perturbations for nonlinear continuous time systems. In particular, we derive conditions which guarantee that asymptotic stability of the nominal system implies practical stability of the real one in a neighborhood of the origin. A continuous stirred tank reactor is used as a benchmark problem to show the effectiveness of the presented algorithm. © 2010 IEEE.

IEEE2010

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Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Tudor Ratiu

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 -245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear systems of hydrodynamic type is also recalled. Further, the criteria of skew-symmetry, derivation and Jacobi identity making this algebra into a Lie algebra are derived. The coboundary operators are defined and discussed. We deduce the hereditary operator and its generalization to the corresponding 3 ary bracket. Further, we derive the so-called rho compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.

Taylor & Francis Ltd2016

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