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Jan M. Maciejowski is a British electrical engineer. He is professor emeritus of control engineering at the University of Cambridge . He is notable for his contributions to system identification and control .
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s.
The idea is to substitute the constraint into the objective function to create a composite function that incorporates the effect of the constraint. For example, assume the objective is to maximize f ( x , y ) = x ⋅ y {\displaystyle f(x,y)=x\cdot y} subject to x + y = 10 {\displaystyle x+y=10} .
Optimal control is a particular control technique in which the control signal optimizes a certain "cost index": for example, in the case of a satellite, the jet thrusts needed to bring it to desired trajectory that consume the least amount of fuel. Two optimal control design methods have been widely used in industrial applications, as it has ...
A particular form of the LQ problem that arises in many control system problems is that of the linear quadratic regulator (LQR) where all of the matrices (i.e., , , , and ) are constant, the initial time is arbitrarily set to zero, and the terminal time is taken in the limit (this last assumption is what is known as infinite horizon). The LQR ...
Uplift modelling uses a randomised scientific control not only to measure the effectiveness of an action but also to build a predictive model that predicts the incremental response to the action. The response could be a binary variable (for example, a website visit) [ 1 ] or a continuous variable (for example, customer revenue). [ 2 ]
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]
As a result, the constraint satisfaction problem can be used to set a constraint whose relation is the table on the right, which may not be in the constraint language. As a result, if a constraint satisfaction problem has the table on the left as its set of solutions, every relation can be expressed by projecting over a suitable set of variables.