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An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a furnace has a nonlinear response to changes in temperature; it is either "on" or "off", it does not have the fine control in response to temperature differences that a proportional (linear) device would have.
This made ISS the dominating stability paradigm in nonlinear control theory, with such diverse applications as robotics, mechatronics, systems biology, electrical and aerospace engineering, to name a few. The notion of ISS was introduced for systems described by ordinary differential equations by Eduardo Sontag in 1989. [7]
Nonlinear systems are often analyzed using numerical methods on computers, for example by simulating their operation using a simulation language. If only solutions near a stable point are of interest, nonlinear systems can often be linearized by approximating them by a linear system using perturbation theory, and linear techniques can be used. [16]
Block diagram illustrating the feedback linearization of a nonlinear system. Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form
In control systems, sliding mode control (SMC) is a nonlinear control method that alters the dynamics of a nonlinear system by applying a discontinuous control signal (or more rigorously, a set-valued control signal) that forces the system to "slide" along a cross-section of the system's normal behavior.
Here is a characteristic example of applying a Lyapunov candidate function to a control problem. Consider the non-linear system, which is a mass-spring-damper system with spring hardening and position dependent mass described by (+) ¨ + ˙ + + =
In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic, and others [1] [2] for designing stabilizing controls for a special class of nonlinear dynamical systems. These systems are built from subsystems that radiate out from an irreducible subsystem that can be stabilized using some other method.
In mathematics and science, 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. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]