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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 ...
A Carathéodory-π solution can be applied towards the practical stabilization of a control system. [ 6 ] [ 7 ] It has been used to stabilize an inverted pendulum, [ 6 ] control and optimize the motion of robots, [ 7 ] [ 8 ] slew and control the NPSAT1 spacecraft [ 3 ] and produce guidance commands for low-thrust space missions.
If, in addition, all eigenvalues of have negative real parts (is stable), and the unique solution of the Lyapunov equation + = is positive definite, the system is controllable. The solution is called the Controllability Gramian and can be expressed as W c = ∫ 0 ∞ e A τ B B T e A T τ d τ {\displaystyle {\boldsymbol {W_{c}}}=\int _{0 ...
Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory
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.
H ∞ (i.e. "H-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H ∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization.
One of the main results in the theory is that the solution is provided by the linear–quadratic regulator (LQR), a feedback controller whose equations are given below. LQR controllers possess inherent robustness with guaranteed gain and phase margin , [ 1 ] and they also are part of the solution to the LQG (linear–quadratic–Gaussian) problem .
A control given as a function of time only is referred to as an open-loop control. In contrast, a control that gives optimal solution during some remainder period as a function of the state variable at the beginning of the period is called a closed-loop control .