In this work, sampled-data iterative learning control (ILC) method is extended to a class of continuous-time nonlinear systems with iteration-varying trial lengths.In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled-data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant.To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases. KEYWORDSinitial state condition, iteration learning control, iteration-varying lengths, iteratively moving average operator, relative degree, sampled-data Int J Robust Nonlinear Control. 2018;28:3073-3091.wileyonlinelibrary.com/journal/rnc

Aim: Promoting walking activity is an effective way to improve the health of older adults. Walking frequency is a critical component of walking behavior and an essential determinant of daily walking levels. To decipher the association between the built environment and walking frequency among older adults, this study's aims are as follows: (1) to empirically test whether non-linear relationships between the two exist, and (2) to identify the thresholds of the built environment characteristics that promote walking.Methods: The walking frequency of old adults was derived from the Zhongshan Household Travel Survey (ZHTS) in 2012. The sample size of old adults aged 60 or over was 4784 from 274 urban and rural neighborhoods. A semi-parametric generalized additive model (GAMM) is used to analyze the non-linear or non-monotonic relationships between the built environment and the walking frequency among older adults.Results: We found that non-linear relationships exist among five out of the six built environment characteristics. Within certain thresholds, the population density, sidewalk density, bus stop density, land use mixture, and the percentage of green space are positively related to older adults' walking trips. Furthermore, the land use mixture and the percentage of green space show an inverse “V”-shaped relationship.Conclusions: Built environment features can either support or hinder the walking frequency among older adults. The findings in the current study contribute to effective land use and transport policies for promoting active travel among older adults.

Global aging has raised increasing concerns on the health and well-being of older adults. Public transport is a viable option to improve the mobility and quality of life among older adults. However, policies that promote the public transport use among older adults are rare. This study utilizes the eXtreme Gradient Boosting (XGBoost) decision tree to explore the non-linear associations of the built and social environment with bus use among older adults in China. The bus use of older adults was obtained from the Zhongshan Household Travel Survey (ZHTS) in 2012. Results show that non-linear relationships exist among all built environment and social environment characteristics. Within certain thresholds, the percentage of green space land use, land use mixture, bus-stop density, and dwelling unit density are positively related to bus use among older adults. Likewise, one social environment variable, the proportion of older adults in a neighborhood, is the key social environment variable. Furthermore, the dwelling unit density and proportion of older adults appear to have an inverse U-shaped relationship. Additionally, age, ownership of motorcycles, and distance from home to the nearest bus stop also show non-linearity. The findings presented in this paper facilitate effective planning interventions to promote bus use among older adults.

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