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Abstract-Evolutionary computations are naturally inspired stochastic algorithms that are capable of running perpetually. When deployed as optimization tools, it is imperative to prescribe a set of definitive stopping criteria that if satisfied, the evolutionary process could be brought to a halt. User specified limits on maximum evaluations or generations are the common measures used to stop the evolution due to resource constraints that might directly/indirectly be imposed on the system. Conversely, we propose a novel convergence detection mechanism that monitors the contribution of the genetic operators on the fitness progress and the diversity profile of the population via the ±σ crossover envelope. This adaptively terminates the evolution as convergence sets in. Extended Price's theorem is utilized to estimate the dynamical contributions of the individual genetic operators. Experimental results show that under standard parameter settings with binary tournament selection, the proposed technique is robust and could be a promising alternative to the conventional similarity measure-based methods for convergence detection.
An integral sliding mode controller (ISMC) which employs particle swarm optimization (PSO) algorithm to search for optimal values of the parameters of the integral sliding manifold as well as the gains of the controller is proposed in this work. We considered the swing-up and stabilization of the cart-inverted pendulum system which is assumed to be affected by uncertainties. First, we determined the swing-up and stabilization conditions of the control system by using the internal dynamics of the cart-inverted pendulum system and sliding mode dynamics. A PSO algorithm is then used to search for the optimal values of the ISMC design parameters that satisfy the stabilization condition with the aim of improving the transient performance of the control system. To mitigate the chattering phenomenon, a saturation function of the integral sliding variable was used in the discontinuous control law. Simulation results on swing-up and stabilization of the cart-inverted pendulum system revealed improvement in transient behaviour by reducing settling time (by 52.61%), overshoots (by 45.56%) and required track length for cart movement (by 68.34%).
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