Solving Linear and Quadratic Programs with an Analog Circuit

We present the design of an analog circuit which solves linear programming (LP) or Quadratic Programming (QP) problems. In particular, the steady-state circuit voltages are the components of the LP (QP) optimal solution. The paper shows how to construct the circuit and provides a proof of equivalence between the circuit and the LP (QP) problem. The proposed method is used to implement an LP-based Model Predictive Controller by using an analog circuit. Simulative and experimental results show the effectiveness of the proposed approach.