Abstract
We present the design of an analog circuit which solves linear programming (LP) or quadratic programming (QP) problem. 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.
Highlights
Analog circuits for solving optimization problems have been extensively studied in the past [1, 2, 3]
When the model is linear and the performance index is based on two-norm, one-norm or ∞-norm, the resulting optimization problem can be cast as a linear program (LP) or a quadratic program (QP), where the state enters the right hand side of the constraints
In this paper we presented an approach to design an electric analog circuit that is able to solve feasible Linear and Quadratic Programs
Summary
Analog circuits for solving optimization problems have been extensively studied in the past [1, 2, 3]. In MPC at each sampling time, starting at the current state, an open-loop optimal control problem is solved over a finite horizon. At the time step a new optimal control problem based on new measurements of the state is solved over a shifted horizon. When the model is linear and the performance index is based on two-norm, one-norm or ∞-norm, the resulting optimization problem can be cast as a linear program (LP) or a quadratic program (QP), where the state enters the right hand side (rhs) of the constraints. The proposed analog circuit can be used to repeatedly solve LPs or QPs with varying rhs and is suited for linear MPC controller implementation.
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