In the era of Industry 4.0 and smart manufacturing, process systems engineering must adapt to digital transformation. While reinforcement learning offers a model-free approach to process control, its applications are limited by the dependence on accurate digital twins and well-designed reward functions. To address these limitations, this paper introduces a novel framework that integrates inverse reinforcement learning (IRL) with multi-task learning for data-driven, multi-mode control design. Using historical closed-loop data as expert demonstrations, IRL extracts optimal reward functions and control policies. A latent-context variable is incorporated to distinguish modes, enabling the training of mode-specific controllers. Case studies on a continuous stirred tank reactor and a fed-batch bioreactor validate the effectiveness of this framework in handling multi-mode data and training adaptable controllers.