Analog circuits for linear-quadratic optimal control

Abstract

Analog circuits are developed for solving quadratic programs arising from Model Predic-tive Control (MPC) problems. The steady-state voltages measured at the circuit nodes approximate the optimal solution to the problem. Different approaches were considered to high-light the benefits and challenges associated with analog programming circuits. Analog circuits allow for virtually instantaneous computations when compared to the high latency of iterations associated with digital approaches. Implementing MPC problems through analog cir-cuits allows for rapid solution convergence which is highly valuable in MPC. Through analog cir- cuits, the time taken in computation and iteration using digital methods is avoided, thus ex-pediting the solution. Most methods utilize the Karush Kuhn Tucker (KKT) conditions to simulate a given problem through the use of resistors, operational amplifiers, and diodes such that the circuit’s optimal solutions are enforced at the nodes. Different approaches were implemented and their differences were observed to highlight the benefits and detriments of each. The circuit can be realized for specific matrices with a combination of a passive resistive network, diodes, and sources. In many other instances, negative resistance must be included; hence the passivity of the entire circuit is complicated.