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
Genetic diversity as an objective in multi-objective evolutionary algorithms
Evolutionary Computation
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)
Engineering Applications of Artificial Intelligence
Engineering Applications of Artificial Intelligence
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In this paper, fuzzy threshold values, instead of crisp threshold values, have been used for optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a single inverted pendulum having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the normalized summation of rising time and overshoot of cart (S"R"O-C) and the normalized summation of rising time and overshoot of pendulum (S"R"O-P) in the deterministic approach. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for single inverted pendulum problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic single inverted pendulum using the conflicting objective functions in time domain. Such Pareto front is then obtained for single inverted pendulum having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA with fuzzy threshold values includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.