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In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, [citation needed] a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs ...
Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. [1] It has numerous applications in science, engineering and operations research.
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory
In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations.
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 ...
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.
In a discrete-time context, the decision-maker observes the state variable, possibly with observational noise, in each time period. The objective may be to optimize the sum of expected values of a nonlinear (possibly quadratic) objective function over all the time periods from the present to the final period of concern, or to optimize the value of the objective function as of the final period ...
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. [1] Some particular properties of real-valued sequences and functions that real analysis studies include convergence , limits , continuity , smoothness , differentiability and integrability .