Combined simple cautious and robust control for parameter and disturbance bounded distributions

The qualities and drawbacks of two control methods to cope with process uncertainty are considered: cautious control which only uses statistics, and robust control which only uses the bounds of the process uncertainty. On the basis of results obtained for new simple methods for both, two new performance measures are introduced which use statistics as well as bounds of process parameters and disturbances, and therefore combine the qualities of cautious and robust control. These controllers are shown to outperform cautious and robust contro

Min–max MPC using a tractable QP problem

Min–max model predictive controllers (MMMPC) suffer from a great computational burden that is often circumvented by using approximate solutions or upper bounds of the worst possible case of a performance index. This paper proposes a computationally efficient MMMPC control strategy in which a close approximation of the solution of the min–max problem is computed using a quadratic programming problem. The overall computational burden is much lower than that of the min–max problem and the resulting control is shown to have a guaranteed stability. A simulation example is given in the paper

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

Min-Max MPC (MMMPC) controllers [P.J. Campo, M. Morari, Robust model predictive control, in: Proc. American Control Conference, June 10–12, 1987, pp. 1021–1026] 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(n3) 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

A Study in function optimization with the breeder genetic algorithm

Optimization is concerned with the finding of global optima (hence the name) of problems that can be cast in the form of a function of several variables and constraints thereof. Among the searching methods, {em Evolutionary Algorithms} have been shown to be adaptable and general tools that have often outperformed traditional {em ad hoc} methods. The {em Breeder Genetic Algorithm} (BGA) combines a direct representation with a nice conceptual simplicity. This work contains a general description of the algorithm and a detailed study on a collection of function optimization tasks. The results show that the BGA is a powerful and reliable searching algorithm. The main discussion concerns the choice of genetic operators and their parameters, among which the family of Extended Intermediate Recombination (EIR) is shown to stand out. In addition, a simple method to dynamically adjust the operator is outlined and found to greatly improve on the already excellent overall performance of the algorithm.Postprint (published version