A fully probabilistic design for stochastic systems with input delay

Herzallah, Randa

doi:10.1080/00207179.2020.1742386

Cited by 7 publications

(14 citation statements)

References 26 publications

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“…See e.g. [136,91], which extends the result to the case where, at each k, the dynamics of the system are conditioned on data prior to k − 1.…”

Section: Fully Probabilistic Designmentioning

confidence: 83%

Probabilistic design of optimal sequential decision-making algorithms in learning and control

Emiland¹,

Russo²

2022

Preprint

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This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that combines a problem formulation and a set of resolution methods. The formulation consists of an infinite-dimensional optimization problem. The methods come from approaches to search optimal solutions in the space of probability functions. Through the lenses of this overarching framework we revisit popular learning and control algorithms, showing that these naturally arise from suitable variations on the formulation mixed with different resolution methods. A running example, for which we make the code available, complements the survey. Finally, a number of challenges arising from the survey are also outlined.

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“…See e.g. [136,91], which extends the result to the case where, at each k, the dynamics of the system are conditioned on data prior to k − 1.…”

Section: Fully Probabilistic Designmentioning

confidence: 83%

Probabilistic design of optimal sequential decision-making algorithms in learning and control

Emiland¹,

Russo²

2022

Preprint

View full text Add to dashboard Cite

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“…Noting that − ln(γ(e t )) = 0.5(e T t M t e t +g t e t +ω t ), it can be seen that the identity is satisfied for M t , g t and ω t as defined in Equations ( 16), (17), and ( 18) respectively. This proves the claimed quadratic nature of the performance function.…”

Section: Solution To the Mrfpd For Linear Stochastic Systems With No Delaysmentioning

confidence: 99%

“…However, in its original form [16] the FPD method insists on zero delay between the input and the state of the system. On account of this, we recently extended the FPD method such that it considers a class of stochastic systems that involves a lagged and an unlagged control inputs [17]. This recent development considers the problem of designing randomised controllers that shape the joint probability density function of the system state.…”

Section: Introductionmentioning

confidence: 99%

“…Concequently, the objective of the current paper is to develop a general probabilistic framework to obtain the tracking control solution to the stochastic control problems with input delay where the system state is required to track a predefined desired state as obtained from a reference model. The formulation in this paper aims at designing a randomised controller that shapes the pdf of the tracking error distribution as opposed to original formulation of the FPD method that considers designing randomised controllers that shape the pdf of the system state [15]- [17]. This method will be referred to as model reference fully probabilistic design control (MRFPD) method.…”

Section: Introductionmentioning

confidence: 99%

“…To reemphasise, the formulation of the control problem in this paper will be based on shaping the pdf of the tracking error, where the considered class of stochastic systems is assumed to be controlled by a lagged control input. This new formulation means that the solution methodology developed in [17], which considers shaping the pdf of the system state and assumes that stochastic systems are affected by lagged and unlagged control inputs, is not appropriate for the considered model reference tracking problem where the stochastic system is controlled by a lagged control input only. Thus, a different approach which is based on probabilistic inference for evaluating the predictive distributions of the tracking error and randomised controller will be followed in the current paper.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fully Probabilistic Design for Tracking Control for Stochastic Systems With Input Delay

Herzallah

2021

IEEE Trans. Automat. Contr.

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This paper studies model reference adaptive control (MRAC) for a class of stochastic discrete time control systems with time delays in the control input. In particular, a unified fully probabilistic control framework is established to develop the solution to the MRAC, where the controller is the minimiser of the Kullback-Leibler Divergence (KLD) between the actual and desired joint probability density functions of the tracking error and the controller. The developed framework is quite general, where all the components within this framework, including the controller and system tracking error, are modelled using probabilistic models. The general solution for arbitrary probabilistic models of the framework components is first obtained and then demonstrated on a class of linear Gaussian systems with time delay in the main control input, thus obtaining the desired results. The contribution of this paper is twofold. First, we develop a fully probabilistic design framework for MRAC, referred to as MRFPD, for stochastic dynamical systems. Second, we establish a systematic pedagogic procedure that is based on deriving explicit forms for the required predictive distributions for obtaining the causal form of the randomised controller when input delays are present.

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Fully probabilistic control for uncertain nonlinear stochastic systems

Zafar

Herzallah

2022

Asian Journal of Control

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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.

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A fully probabilistic design for stochastic systems with input delay

Cited by 7 publications

References 26 publications

Probabilistic design of optimal sequential decision-making algorithms in learning and control

Probabilistic design of optimal sequential decision-making algorithms in learning and control

A Fully Probabilistic Design for Tracking Control for Stochastic Systems With Input Delay

Fully probabilistic control for uncertain nonlinear stochastic systems

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