Fully Probabilistic Design for Stochastic Discrete System with Multiplicative Noise

Zhou

2022

Sci Rep

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This paper proposes a unified probabilistic control framework for a class of stochastic systems with both control input and state time delays. Both of the stochastic nature and time delays in the system dynamics are considered simultaneously, thus providing a comprehensive and rigorous control methodology. The problem is formulated in a fully probabilistic framework, where the system dynamics and its controller are fully characterised by arbitrary probabilistic models. In this framework, the Kullback–Leibler Divergence between the actual joint probability density function of the system dynamics and controller and a predefined ideal joint probability density function is used to characterise the discrepancy between the two distributions and derive the randomised controller. Time delays in the control input and system state are taken into consideration in the optimisation process for the derivation of the optimal randomised controller. Besides, the analytic control solution of the time delay fully probabilistic control problem for a class of linear Gaussian stochastic systems is derived while the successive approximation approach is implemented to deal with the time-advanced components in the control law that result from the existence of time delays. The effectiveness of the proposed control framework is then illustrated on a numerical example and a real-world example.

Section: Review Of Current Approachesmentioning

confidence: 99%

A fully probabilistic control framework for stochastic systems with input and state delay

Zhou

2022

Sci Rep

Self Cite

“…For other classes of stochastic systems where the noise affecting the system is dependent on the state or input values, the covariance of the ideal distribution can be specified to be different than the covariance of the system innovations with the aim of designing controllers that reduce the effect of the noise on the dynamics of the system. This has been addressed in our recent work on the development of FPD control methods for stochastic systems with multiplicative noise [Zhou et al, 2019].…”

Section: B Analytic Solution To the Linear Gaussian Tdfpdmentioning

confidence: 99%

A fully probabilistic design for stochastic systems with input delay

International Journal of Control

2020

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This paper is concerned with the regulation problem of discrete time stochastic systems involving input delays. This problem has attracted resurgent interests in recent years due to its relevance to networked control systems. The problem is formulated in a fully probabilistic framework and the control solution is obtained by minimising the Kullback-Leibler Divergence (KLD), as a performance function, between the actual and desired joint probability density functions of the system dynamics. A closed form solution for the randomised controller is obtained for stochastic systems that can be described by arbitrary probability density functions. Furthermore, the analytic solution for a class of linear Gaussian stochastic systems is obtained. It is shown that the optimal randomised controller for this class of linear Gaussian stochastic systems is state feedback controller which is modified by an extra linear term that is related to the lagged and future control inputs. The developed method is demonstrated on a simulation example and the results are compared with the standard fully probabilistic design control method.

“…This approach considers the full distribution of the stochastic system dynamics for the derivation of randomized controllers. This approach has then been further developed to consider various aspects of stochastic and uncertain systems [3,[9][10][11]. In FPD, the Kullback-Leibler divergence (KLD), defined in (1), is implemented to measure the distance between the actual and ideal joint probability density functions.…”

Section: Introductionmentioning

confidence: 99%

Fully probabilistic control for uncertain nonlinear stochastic systems

Zafar

Asian Journal of Control

2022

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This paper develops a novel probabilistic framework for stochastic nonlinear and uncertain control problems. The proposed framework exploits the Kullback-Leibler divergence to measure the divergence between the distribution of the closed-loop behavior of a dynamical system and a predefined ideal distribution. To facilitate the derivation of the analytic solution of the randomized controllers for nonlinear systems, transformation methods are applied such that the dynamics of the controlled system becomes affine in the state and control input. Additionally, knowledge of uncertainty is taken into consideration in the derivation of the randomized controller. The derived analytic solution of the randomized controller is shown to be obtained from a generalized state-dependent Riccati solution that takes into consideration the stateand control-dependent functional uncertainty of the controlled system. The proposed framework is demonstrated on an inverted pendulum on a cart problem, and the results are obtained.