Gradient-based optimization methods for sensor & actuator placement in LTI systems

This paper develops efficient techniques for calculating gradient information which may be used to optimize the placement of sensors & actuators of a given precision for the effective estimation and control of high-dimensional discretizations of infinite-dimensional linear time-invariant (LTI) systems. The necessary gradients are determined in this setting via adjoint analyses which quantify the effects of small variations of the observation and control operators. The approach can be modified appropriately to fit a variety of specific objectives within the Linear Quadratic Gaussian (LQG) estimation/control framework. Unlike other work in this area, we work directly with the covariance of the estimation error P, rather than working with the Fischer information matrix M, which is, in a sense, a best-case estimate of P−1 that neglects the impact of the state disturbances on the evolution of the state estimation error. The method is tested by optimizing the placement of two sensors and two actuators in a 1D complex Ginzburg-Landau system.