The theory of optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations linear quadratic control pdf the cost is described by a quadratic function is called the LQ problem. Like the LQR problem itself, the LQG problem is one of the most fundamental problems in control theory. The cost function is often defined as a sum of the deviations of key measurements, desired altitude or process temperature, from their desired values.
The algorithm thus finds those controller settings that minimize undesired deviations. The magnitude of the control action itself may also be included in the cost function. The LQR algorithm reduces the amount of work done by the control systems engineer to optimize the controller.
However, the engineer still needs to specify the cost function parameters, and compare the results with the specified design goals. Often this means that controller construction will be an iterative process in which the engineer judges the “optimal” controllers produced through simulation and then adjusts the parameters to produce a controller more consistent with design goals. The LQR algorithm is essentially an automated way of finding an appropriate state-feedback controller.
As such, it is not uncommon for control engineers to prefer alternative methods, like full state feedback, also known as pole placement, in which there is a clearer relationship between controller parameters and controller behavior. Difficulty in finding the right weighting factors limits the application of the LQR based controller synthesis.
Note that one way to solve the algebraic Riccati equation is by iterating the dynamic Riccati equation of the finite-horizon case until it converges. Analysis and Control of Dynamic Economic Systems. Mathematical Control Theory: Deterministic Finite Dimensional Systems.
Quadratus is Latin for square. Quadratic programming, a special type of mathematical optimization problem.
Quadratic probing, a scheme in computer programming for resolving collisions in hash tables. This disambiguation page lists mathematics articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.