Stochastic Linearization of Feedback Systems With Multivariate Nonlinearities and Systems With State-Multiplicative Noise

• 成果类型: Article
• 署名作者: Brahma, Sarnaduti; Ossareh, Hamid R.
• 署名单位: University of Vermont
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3096802
• 发表日期: 2022
• 页码: 3141-3148
• 关键词: stochastic systems; Covariance matrices; Aggregates; actuators; Nonlinear systems; STANDARDS; probability distribution; Multivariate nonlinearities; quasilinear control (QLC); saturation; state-multiplicative noise; stochastic linearization (SL)

摘要

Quasilinear control (QLC) theory provides a set of methods intended for the analysis and design of stochastic feedback systems with static nonlinearities. QLC leverages the method of stochastic linearization (SL), which linearizes the nonlinear functions by utilizing the statistical properties of the inputs to the nonlinearities. In the traditional QLC literature, SL has been thoroughly applied to systems having nonlinearities with only a single input. This article investigates the case of SL applied to feedback systems with nonlinear functions of multiple inputs. More specifically, the formulas for the SL gains and bias are derived for multivariate functions and then employed to explore SL of a trivariate saturation nonlinearity and study the SL of control systems with feedback loops. The developed theory is then applied to the analysis and optimal controller design of stochastic systems having randomly varying parameters or state-multiplicative noise. Finally, a recipe for investigating the robustness of SL is provided.