Nonlinear feedback systems perturbed by noise: steady-state probability distributions and optimal control

Abstract

Abstract-In this paper we describe a class of nonlinear feedback systems perturbed by white noise for which explicit formulas for steady-state probability densities can be found. We show that this class includes what has been called monotemperaturic systems in earlier work and establish relationships with Lyapunov functions for the corresponding deterministic systems. We also treat a number of stochastic optimal control problems in the case of quantized feedback, with performance criteria formulated in terms of the steady-state probability density.Index Terms-Nonlinear feedback system, quantizer, steady-state probability density, stochastic optimal control, white noise.

Multi-Mode Multi-Dimensional Systems with Poissonian Sequencing

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Stable Process Approach to Analysis of Systems Under Heavy-Tailed Noise: Modeling and Stochastic Linearization

“…In addition, we also study the effect of nonlinearity. Next, in [11] and [13], stochastic linearization of systems driven by the Wiener process is thoroughly investigated. It should be emphasized that the extension to our setting is not straightforward.…”

H_∞ controller design for linear systems with quantized feedback

“…Then, the quantizer range of q 1 (·) and the quantizer range of q 2 (·) can be chosen as M 1 = 193 > 192.0584, M 2 = 179 > 178.2810, respectively. According to (9), the range of the quantizer q 3 (·) can be chosen as M 3 = 169.1941. The system initial state is given as x 0 = [10, −10], the controller initial state is given as x c0 = [10, −10].…”