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Nonlinear Model-based Predictive Control (NMPC) is a relevant research area having applications in the industrial sector. Traditionally, in this technique, gradient descent algorithms have been used to solve the related optimization problem. More recently, bio-inspired meta-heuristics have also been applied to this problem. However, only a few works have been devoted to testing solvers that use parameter control with self-adaptive traits, which allows mitigating the problem of offline parameter tuning in bioinspired approaches. In this paper, we propose the novel Adaptive Modified Grey Wolf Optimization (AMGWO) and the Adaptive Moth-Flame Optimization (AMFO), for solving Nonlinear Model-based Predictive Control (NMPC) problems. To achieve this, a mechanism for individual leaders weighting and a crossover operator are introduced in AMGWO, and a simple self-adaptive parameter technique is applied in both meta-heuristics. The improved solvers are tested to perform the swing-up of a single inverted pendulum and attitude control of a satellite, which are nonlinear problems relevant for assessing control performance. Nonparametric statistical tests are applied to compare the improved meta-heuristics optimization outcomes with other five meta-heuristics, which shows that the self-adaptive parameter technique can significantly improve the performance when applied as an NMPC solver, as the AMFO and AMGWO statistically outperform or performs as well as all algorithms compared in both the pendulum and satellite control, respectively. This is important as improving the optimizer efficiency will lead to more accurate control and enable rapid hardware implementation.

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The purpose of this study was to investigate the effects of different vertical positions of an asymmetrical load on the anticipatory postural adjustments phase of gait initiation. Sixty-eight college students (32 males, 36 females; age: 23.65 ± 3.21 years old; weight: 69.98 ± 8.15 kg; height: 1.74 ± 0.08 m) were enrolled in the study. Ground reaction forces and moments were collected using two force platforms. The participants completed three trials under each of the following random conditions: no-load (NL), waist uniformly distributed load (WUD), shoulder uniformly distributed load (SUD), waist stance foot load (WST), shoulder stance foot load (SST), waist swing foot load (WSW), and shoulder swing foot load (SSW). The paired Hotelling’s T-square test was used to compare the experimental conditions. The center of pressure (COP) time series were significantly different for the SUD vs. NL, SST vs. NL, WST vs. NL, and WSW vs. NL comparisons. Significant differences in COP time series were observed for all comparisons between waist vs. shoulder conditions. Overall, these differences were greater when the load was positioned at the shoulders. For the center of mass (COM) time series, significant differences were found for the WUD vs. NL and WSW vs. NL conditions. However, no differences were observed with the load positioned at the shoulders. In conclusion, only asymmetrical loading at the waist produced significant differences, and the higher the extra load, the greater the effects on COP behavior. By contrast, only minor changes were observed in COM behavior, suggesting that the changes in COP (the controller) behavior are adjustments to maintain the COM (controlled object) unaltered.