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This article provides an introduction to the theory of mechanism design and its application to engineering problems. Our aim is to provide the fundamental principles of mechanism design for control engineers and theorists, along with state-of-the-art methods in engineering applications. We start our exposition with a brief overview of game theory, highlighting the fundamental notions necessary to introduce mechanism design. Then, we offer a comprehensive discussion of the principles of mechanism design. Finally, we explore four key applications in engineering, that is, communication networks, power grids, transportation, and security systems. 

As we move to increasingly complex cyber–physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal control problems for a class of CPS with nonlinear dynamics. We exploit the property of differential flatness to simplify the Euler–Lagrange equations that arise during optimization, and this simplification eliminates the numerical instabilities that plague optimal control in general. We also present an explicit differential equation that describes the evolution of the optimal state trajectory, and we extend our results to consider both the unconstrained and constrained cases. Furthermore, we demonstrate the performance of our approach by generating the optimal trajectory for a planar manipulator with two revolute joints. We show in simulation that our approach is able to generate the constrained optimal trajectory in 4.5 ms while respecting workspace constraints and switching between a ‘left’ and ‘right’ bend in the elbow joint.