Analog Optimization Circuit for Embedded Model Predictive Control

Embedded Model Predictive Control (MPC) has taken on new significance, especially in resource-constrained applications, due to recent advances in software and hardware implementation technologies. In this paper, we exploit analog circuit techniques for embedded control implementation. We first interpret the traditional MPC problem as a continuous-time emulation of projected-gradient dynamics. Then the dynamics are implemented on an array of analog circuit processors, also known as Field Programmable Analog Arrays (FPAAs). Using an appropriately constructed Lyapunov function, we establish exponential stability of the ensuing circuit for a fixed input. We prove finite gain $\mathcal{L}_2$ stability when the analog circuit is in feedback interconnection with a physical system. We consider a broad range of control approaches to showcase the flexibility and the ease of implementation when the proposed analog optimization circuit is applied to a quadruple water tank system.