Min-Max MPC based on a computationally efficient upper bound of the worst case cost

Abstract

Min-Max MPC (MMMPC) controllers [1] suffer from a great computational burden which limits their applicability in the industry. Sometimes upper bounds of the worst possible case of a performance index have been used to reduce the computational burden. This paper proposes a computationally efficient MMMPC control strategy in which the worst case cost is approximated by an upper bound based on a diagonalization scheme. The upper bound can be computed with O(n 3 ) operations and using only simple matrix operations. This implies that the algorithm can be coded easily even in non mathematical oriented programming languages such as those found in industrial embedded control hardware. A simulation example is given in the paper.

An LMI approach for robust Iterative Learning Control with Quadratic performance criterion

“…We first employ the technique in [13] to find an upper bound of (12). Suppose that there exists a diagonal matrix such that .…”

“…Recently, in [13], Ramirez et al have proposed an efficient strategy to solve min-max problem with quadratic performance index for linear systems with bounded additive uncertainties. An upper bound of the worst-case performance has been derived, then the solution of min-max problem has been given by solving minimization problem.…”

“…The technique to find an upper bound of maximization problem [13] can be applied to min-max problem of robust Q-ILC design. Therefore, our paper aims to solve min-max optimization problem in robust Q-ILC design and derive an explicit algorithm to get the update formula for iterative control input.…”

Online artificial neural network model‐based nonlinear model predictive controller for the meridian UAS

“…This imposes a severe restriction in its utility. Although Min-max design targets robustness optimally in its design (see for example [33] and [34]), where minimization of a cost function is jointly performed with the maximization of the external disturbance effect, it becomes quickly unfeasible in numerical solutions. Another approach, as is the case for LQG, H 2 or H 1 and nonlinear designs (see Ref.…”

“…where the subscript i D 1, 2, , j indicates the number of iterations and s the number of inequality constraints valid at iteration i, and where u i 1 I u i N I I i 1 I I i s is a column vector in R mN Cs . As a main feature of the SQP method, the constraints need to be checked every iteration to remove the inactive ones or add the new active ones, updating (33). The corrections are obtained by solving the following system of equations…”