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Quadratic and linear optimization with analog circuits

  • Author(s): Vichik, Sergey
  • Advisor(s): Borrelli, Francesco
  • et al.

In this work we propose and investigate a new method of solving quadratic and linear optimization problems using analog electrical circuits instead of digital computation.

We present the design of an analog circuit which solves Quadratic Programming (QP) or Linear Programming (LP) problems.

In particular, the steady-state circuit voltages are the components of the QP (LP) optimal solution.

The thesis shows how to construct the circuit and provides a proof of equivalence between the circuit

and the QP (LP) problem.

We study the stability of the analog optimization circuit. The circuit dynamics are modeled as a switched affine system. A piece-wise quadratic Lyapunov function and the KYP lemma are used to derive the stability criterion. The stability criterion characterizes the range of critical circuit parameters for which the QP circuit is globally asymptotically stable.

The proposed method is used to build a printed circuit board (PCB) using programmable components to allow solution of various QP problems. The board supports implementation of an MPC controller for buck DC-DC converter. We conduct an experimental study to evaluate the performance of the analog optimization circuit.

We study the feasibility of very high speed implementation of the optimization circuit using Analog Very Large Scale Integration (AVLSI) technology. In AVLSI, all the required circuit components are built on top of a silicon substrate using advanced photo-lithographic technologies. AVLSI circuits are fast, small and cheap. Thus, AVLSI implementation is paramount to make the proposed technology commercially competitive.

We discuss the possible usage of the proposed method to make fast MPC controllers, image processors, communication decoders and analog co-processors. In fact, any application that requires a repeating solution of related optimization problems can benefit from this technology. Besides being faster than the digital computers, analog computers are more power efficient, may occupy smaller area on silicon and may be more resilient in harsh environments.

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