# Control-Based 4D Printing: Adaptive 4D-Printed Systems
## 4 Adaptive 4D-Printed Systems Design
However, closed-loop controllers are preferred here to make the most of the integrated 3D-printed sensors in handling uncertainties for wide frequency bandwidths [127; 128; 129; 130; 131; 122]. Indeed, in order to increase the efficiency of control strategies in terms of time and computational costs, model-based ML [131] in conjunction with self-learning controllers [132; 133] are preferred compared to the model-free controllers to deal with the complexity involved in diverse scenarios [134; 135; 136; 66; 129]. A forward dynamics model using recurrent or convolutional neural networks could be employed to implement a model-based feedback controller for an adaptive 4D-printed system [137]. Then, a policy-based reinforcement-learning feedback controller can be used to learn the nonlinear model of a 4D-printed soft robot through experiments and simulation data to compensate for the uncertainties. The self-learning algorithms play a significant role in adaptive 4D-printed systems to optimise the controller commands based on the information acquired from the interaction with the environment via the 3D-printed sensors [138; 139; 140; 141; 142]. Model-based ML algorithms, however, require a large pool of data containing different scenarios of environmental changes to be trained to represent the 4D-printed system model with time-variable properties and multi-dimensional control states [143; 144]. The training process could be repetitious and expensive if it merely relies on experimental tests, therefore, the FEM (Figure 4) can be used in the offline loop for constructing a comprehensive and reliable model exploring the various possible scenarios [143; 144; 145; 146; 147; 148; 149]. Figure 3: Adaptive 4D-printed systems composition. Recent advancements in control-based 4D printing with integrating the sensors, ML models trained by FEM results and controlling the entire 4D-printed systems are gathered in Table 2. To the best of the knowledge of the authors, there has yet to be an entirely adaptive 4D-printed system, as defined in this paper. However, there are some promising studies in integrated 3D-printed sensors in 4D printing [7, 16, 38, 39, 40, 67, 150], the application of the FEM [151] and ML-based controllers in 4D-printed systems [34, 66, 135]. These relevant research results support the possibility of realizing the proposed adaptive 4D-printed systems. Figure 4: Finite element model (FEM) of 4D-printed systems (**a**) A reversible energy absorbing metastructure (reproduced from [27] with the permission of Elsevier); (**b**) A dielectric elastomer (DE) soft gripper (reproduced from [65] with the permission of Elsevier). Additionally, there have been several studies on the design and fabrication of 4D-printed compliant mechanisms promoting controlled self-management and self-actuation without needing sensors [34; 56; 63; 152; 153; 154]. Further investigations on equipping such mechanisms with controllers to provide more flexibility and adaptability are envisaged, allowing for their wider ranges of autonomous operations. It is interesting to note that, there have been only a few studies on the use of the FEM to design and optimize controllers in 4D-printed systems. This will certainly increase the robustness and repeatability of 4D-printed systems in diverse applications with variable unstructured environments.