a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems...
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types of nonlinear systems. Historically, system identification for nonlinear systems has developed by focusing on specific classes of system and can be...
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Dynamical Systems, Caltech. Laboratory of Nonlinear Systems, Ecole Polytechnique Fédérale de Lausanne (EPFL). Center for Dynamical Systems, University...
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Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary...
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a nonlinear system is a system that is not linear—i.e., a system that does not satisfy the superposition principle. Less technically, a nonlinear system...
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Consistent and inconsistent equations (redirect from Inconsistent system)
In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values...
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Control theory (section Nonlinear systems control)
applies to more real-world systems because all real control systems are nonlinear. These systems are often governed by nonlinear differential equations....
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Chaos theory (redirect from Chaotic system)
chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning there is...
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Butterfly effect (section In physical systems)
conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely...
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Jacobian matrix J+ = (JTJ)−1JT instead of the inverse of J. If the nonlinear system has no solution, the method attempts to find a solution in the non-linear...
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Model predictive control (section Nonlinear MPC)
the nonlinearity. The process can be controlled with nonlinear MPC that uses a nonlinear model directly in the control application. The nonlinear model...
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nonlinear system of differential equations is the Navier–Stokes equations. Unlike the linear case, the existence of a solution of a nonlinear system is...
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symmetric. Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by...
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State-space representation (section Nonlinear systems)
to the functions can be dropped if the system is unforced (i.e., it has no inputs). A classic nonlinear system is a simple unforced pendulum m ℓ 2 θ ¨...
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In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs...
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and nonlinear systems. A linear observer structure is described in the following sections. The state of a linear, time-invariant discrete-time system is...
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In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. In nonlinear resonance the system behaviour – resonance frequencies...
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Data analysis (section Nonlinear analysis)
Stem-and-leaf displays Box plots Nonlinear analysis is often necessary when the data is recorded from a nonlinear system. Nonlinear systems can exhibit complex dynamic...
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In time series modeling, a nonlinear autoregressive exogenous model (NARX) is a nonlinear autoregressive model which has exogenous inputs. This means that...
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properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic...
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differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the...
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will just select linear terms if the system under study is linear, and nonlinear terms if the system is nonlinear, which allows a great deal of flexibility...
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(link) B.H. Dayton, T.-Y. Li and Z. Zeng (2011). "Multiple zeros of nonlinear systems". Mathematics of Computation. 80 (276): 2143–2168. arXiv:2103.05738...
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Flatness in systems theory is a system property that extends the notion of controllability from linear systems to nonlinear dynamical systems. A system that...
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a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different physical systems, ranging...
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Cross-correlation (section Nonlinear systems)
nonlinear systems. In certain circumstances, which depend on the properties of the input, cross correlation between the input and output of a system with...
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Signal processing (section Nonlinear)
and Kalman filters. Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time...
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solution for nonlinear systems. This is enabled by utilizing a homotopy-Maclaurin series to deal with the nonlinearities in the system. The HAM was first...
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Observability (section Nonlinear systems)
observability criteria for nonlinear time-varying systems. Observability may also be characterized for steady state systems (systems typically defined in terms...
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in many scientific areas. Nonlinear ones are of particular interest for their commonality in describing real-world systems and how much more difficult...
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