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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 branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback ...
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.
Nonlinear control theory – This covers a wider class of systems that do not obey the superposition principle, and applies to more real-world systems because all real control systems are nonlinear. These systems are often governed by nonlinear differential equations .
Controllability is an important property of a control system and plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem.
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 mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting.
The phrase H ∞ control comes from the name of the mathematical space over which the optimization takes place: H ∞ is the Hardy space of matrix-valued functions that are analytic and bounded in the open right-half of the complex plane defined by Re(s) > 0; the H ∞ norm is the supremum singular value of the matrix over that space.
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.