Search results
Results from the WOW.Com Content Network
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 problem benchmark (Luus) with an integral objective, inequality, and differential constraint. 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]
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide ... Continuum theory; Control theory;
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.
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 .
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.
Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. [2] Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian. [3]
Modern control theory, instead of changing domains to avoid the complexities of time-domain ODE mathematics, converts the differential equations into a system of lower-order time domain equations called state equations, which can then be manipulated using techniques from linear algebra. [2]