Laplace controller for linear scalar systems

The conditional probability density function given the measurement history for linear scalar systems with additive noises described by Laplace densities is used to construct a controller. By defining the cost criterion to be in a functional form consistent with the Laplace densities, the conditional expectation of this cost criterion can be obtained in closed form. Since the expected value of the cost criterion can be shown to be log-concave, this criterion is unimodal, allowing rapid extremization for real-time performance. Since the argument of the cost criterion is in terms of weighted absolute values of the control and state, the optimal control performance is quite different from that of the LQG controller. A 50-step numerical example is presented to demonstrate the noise rejection and hedging behavior of the controller in steady-state.