Agri-food supply chains have experienced notable changes in recent decades, with tomatoes (Solanum lycopersicum) maintaining their status as a key global crop in terms of both production and consumption. These supply chains comprise a complex network of stakeholders—including producers, processors, distributors, and retailers—who collectively ensure the delivery of tomatoes from farms to consumers. This study develops mathematical models of agri-food tomato supply chains (AFTSCs) and examines their behavior through stability analysis and dynamic simulations based on a compartmental approach. Furthermore, the environmental impact is evaluated using a sustainability index, to which the waste diversion rate is introduced. This metric is defined as the proportion of diverted waste (i.e., materials recycled, reused, or composted) relative to the total waste generated, thereby enabling the quantification of sustainability performance within the system. Finally, a sensitivity analysis is conducted on the proposed dynamical models to validate and reinforce the findings.

This technical note aims to present a theoretical analysis for cybertronics engineering (CE) for a class of dynamic supply chains for artificial intelligence (AI)-based products, services or hybrid solutions. The cybertronics-based analysis encompasses three classes of supply chains: (1) energy-based dynamic supply chains (DSC); (2) semiconductor manufacturing and quantum supply chains; and (3) retailing of the AI-based DSC solutions generated. Considering the nonlinear nature of DSC, to provide solutions for products and services based on AI-chained supply chains, novel robust control is addressed via sliding mode control (SMC) with proper stability analysis for the DSC.