Laplace One-Step Controller For Linear Scalar Systems

Uncertainties in many physical systems have impulsive properties poorly modeled by Gaussian distributions. Building on work to develop Cauchy controllers, a Laplace controller is explored as a heavier-tailed alternative to the Gaussian. Whereas the Cauchy density has no moments, the Laplace density has finite moments of all orders as the Gaussian density. For a scalar discrete linear system with additive Laplace process and measurement noises, the one-step optimal control problem is considered, where the conditional expectation of the cost criterion is determined as a function of the measurements and the control in closed form. The optimal control is determined numerically for different values of noise parameters and cost criterion weightings, and its properties are examined.