Analysis of linear programming in model predictive control

Near time-optimal model predictive control using an L1-norm based cost functional

“…Idle control means in this context that even though a non-zero control error is present, the solution of the 1 -norm based optimization problem is zero control action [7]. Penalizing the rate of control input change ∆U instead of the absolute value U can reduce the size of the regions in the state-space where idle and deadbeat control occur [8]. Another reason for choosing ∆U instead of U is the intended dynamic control performance, as already discussed.…”

Experimental Application of Predictive Controllers

“…The model predictive control (MPC) theory was originated in the end of 1970s decade and developed considerably ever since [5][6][7][8][9][10]. MPC became an important control strategy of industrial applications, mainly due to great success of its implementations in the petrochemical industry.…”

A Microcontroller-Based Adaptive Model Predictive Control Platform for Process Control Applications

“…Model predictive control (MPC) schemes employ dynamic models of a process-in conjunction with the use of on-line optimization-to compute an optimal sequence of input moves that minimizes the predicted future values of an objective function [1][2][3]. Most modern MPC schemes utilize a quadratic (2-norm) objective function, with the optimization solved on-line by quadratic programming (QP) software; however, much of the original work on MPC algorithms utilized linear (1-norm) objective functions which were solved on-line by linear programming (LP) software [5,6]. This transition was principally due to a number of well-documented drawbacks to the use of LP in early formulations in MPC, including possible idle/deadbeat dichotomous behaviors, the need to use iterative schemes to obtain solutions even in the unconstrained case, and potentially poor scaling in the size of the MPC problem to the corresponding LP [1,5,6].…”

“…Most modern MPC schemes utilize a quadratic (2-norm) objective function, with the optimization solved on-line by quadratic programming (QP) software; however, much of the original work on MPC algorithms utilized linear (1-norm) objective functions which were solved on-line by linear programming (LP) software [5,6]. This transition was principally due to a number of well-documented drawbacks to the use of LP in early formulations in MPC, including possible idle/deadbeat dichotomous behaviors, the need to use iterative schemes to obtain solutions even in the unconstrained case, and potentially poor scaling in the size of the MPC problem to the corresponding LP [1,5,6]. MPC generally employs the receding-horizon approach, in which the first control in this sequence is applied, and the optimization is again carried out at the next time step with accurate knowledge of the new state that the process has evolved into.…”

“…The potential benefits that adaptive and predictive control schemes can bring to industrial control applications have been well documented in recent years [1][2][3][4][5]. Model predictive control (MPC) schemes employ dynamic models of a process-in conjunction with the use of on-line optimization-to compute an optimal sequence of input moves that minimizes the predicted future values of an objective function [1][2][3].…”