Cyber-physical systems (CPS) have been increasingly deployed in many safety-critical industrial environments, where effective and efficient optimal control synthesis is vital for ensuring reliable system operation. The optimal control problem—aimed at synthesizing an optimal control solution for a given control task—remains a key challenge in CPS, particularly due to the intricate coupling of CPS’s continuous and discrete (hybrid) dynamics. This challenge is further compounded in multi-component industrial systems, where the space of control solutions, including both discrete paths (control mode sequences) and continuous control parameters, is prone to the well-known state explosion problem. In this paper, we propose an efficient path-encoding-based joint optimization method for the optimal control problem in multi-component hybrid systems. Our method jointly encodes paths and control parameters in a structured, integrated space, transforming the control synthesis problem into a well-defined optimization problem that can be efficiently solved by existing derivative-free optimization solvers. To further enhance efficiency, we introduce an optimized local path-encoding strategy, which decomposes the original one-dimensional path space into a multi-dimensional component-wise path space, enabling more effective exploration of paths. This strategy also reduces memory overhead and improves scalability. We implemented our method in a tool called PED, and experimental results show that it efficiently solves the optimal control problem in various complex multi-component hybrid systems. Moreover, the incorporation of our local path-encoding strategy further improves its performance.
Wang et al. (Mon,) studied this question.