Monte Carlo methods. Vol. 1: basics
Monte Carlo methods. Vol. 1: basics
Stochastic optimal control: theory and application
Stochastic optimal control: theory and application
A Monte Carlo approach to the analysis of control system robustness
Automatica (Journal of IFAC) - Special issue on robust control
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Evolutionary Algorithms for Solving Multi-Objective Problems
Evolutionary Algorithms for Solving Multi-Objective Problems
Inverse multi-objective robust evolutionary design optimization in the presence of uncertainty
GECCO '05 Proceedings of the 7th annual workshop on Genetic and evolutionary computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
Brief Robust control of nonlinear systems with parametric uncertainty
Automatica (Journal of IFAC)
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A robust approach for the Pareto optimum design of PI controllers for systems with probabilistic uncertainty is presented. In this way, some non-dominated optimum PI controllers in the Pareto sense are found using three non-commensurable objective functions both in time and frequency domains based on stochastic behaviour of a system with parametric uncertainties. Such conflicting objective functions are, namely, the probability of instability, the probability of failure to a desired time response and its variance, and the degree of stability from the Nyquist diagram's percentiles. The first two objective functions have to be minimized whilst the last one to be maximized simultaneously. It is shown that multi-objective Pareto optimization of such robust PI controllers using a recently developed diversity preserving mechanism genetic algorithm unveils some very important and informative trade-offs among these objective functions. Consequently, some optimum PI controllers can be compromised and chosen from the Pareto frontiers.