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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]
Even if the plant is linear, a nonlinear controller can often have attractive features such as simpler implementation, faster speed, more accuracy, or reduced control energy, which justify the more difficult design procedure. An example of a nonlinear control system is a thermostat-controlled heating system. A building heating system such as a ...
Some special cases of nonlinear programming have specialized solution methods: If the objective function is concave (maximization problem), or convex (minimization problem) and the constraint set is convex , then the program is called convex and general methods from convex optimization can be used in most cases.
The Hammerstein-Wiener model consists of a linear dynamic block sandwiched between two static nonlinear blocks. [10] The Urysohn model [11] [12] is different from other block models, it does not consists of sequence linear and nonlinear blocks, but describes both dynamic and static nonlinearities in the expression of the kernel of an operator. [13]
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
Another contrast is between linear and non-linear models. Most early models of communication are linear models. They present communication as a unidirectional process in which messages flow from the communicator to the audience. Non-linear models, on the other hand, are multi-directional: messages are sent back and forth between participants.
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.
Nonlinear algebra is the nonlinear analogue to linear algebra, generalizing notions of spaces and transformations coming from the linear setting. [1] Algebraic geometry is one of the main areas of mathematical research supporting nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity.