Towards Fully Probabilistic Control Design

Kárný, Miroslav

doi:10.1016/b978-0-08-042375-3.50045-7

Cited by 30 publications

(69 citation statements)

References 1 publication

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“…Note that only the first term in (4) depends on the desired states and KL divergence can be interpreted as "weight" of a control action, [6].…”

Section: A Kl-optimal Control Problemmentioning

confidence: 99%

“…In order to evaluate the performance of a control algorithm, we introduce a quadratic loss (100, 100, 1, 1, 1), (1, 1). The values of the matrices has been taken with respect to some preliminary simulations and the well known interpretation of the penalization which states that the true values are kept on the desired ones with precision given by Q −1 t using zero control with precision R −1 t , [6].…”

Section: A Robot Model and Cost Index Specificationmentioning

confidence: 99%

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Extended Rauch-Tung-Striebel controller

Zima

Armesto

Girbés

et al. 2013

52nd IEEE Conference on Decision and Control

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This paper presents a novel controller for nonlinear unconstrained systems, coined as Extended Rauch-TungStriebel (ERTS) controller. The controller is derived from a general framework based on the duality between optimal control and estimation established by Todorov. The proposed controller uses Rauch-Tung-Striebel smoother that predicts (filters) future states by linearizing the nonlinear system around predicted states and then applies a backward smoothing. The new controller is applied to solve path following problems of non-holonomic vehicles and compared with the standard LQR controller linearizing the model around the desired trajectory and the iterative LQR (iLQR) controller. The main advantages of ERTS controller with respect to the alternative techniques are good control performance and computational efficiency.

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“…Note that only the first term in (4) depends on the desired states and KL divergence can be interpreted as "weight" of a control action, [6].…”

Section: A Kl-optimal Control Problemmentioning

confidence: 99%

Section: A Robot Model and Cost Index Specificationmentioning

confidence: 99%

Extended Rauch-Tung-Striebel controller

Zima

Armesto

Girbés

et al. 2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

show abstract

“…Hence for more details on their evaluation the interested reader is referred to [23]. Now according to (6) the function (x t−1 ) has to satisfy the following identity,…”

Section: Generalised Probabilistic Control Lawmentioning

confidence: 99%

“…Proof. The optimal control law of the fully probabilistic control problem is defined in (6), repeated here…”

Section: Generalised Probabilistic Control Lawmentioning

confidence: 99%

“…However, in contrast to earlier discussed approaches the design process in this article will be based on the minimisation of the Kullback-Leibler divergence distance between the joint distribution of the system dynamics and a predefined ideal joint distribution. This method of control is known as Fully Probabilistic Design (FPD) [6]. The objective of FPD is to determine the pdf of a randomised optimal control law, c(u t | x t−1 ) that minimises the following explicit performance function derived from the Kullback-Leibler divergence:…”

Section: Introductionmentioning

confidence: 99%

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Generalised Probabilistic Control Design for Uncertain Stochastic Control Systems

Herzallah

2018

Asian Journal of Control

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In this paper a novel generalised fully probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented for a linear Gaussian uncertain class of stochastic systems. A single layer neural network is used to approximate the probability density function of the system dynamics. The generalised probabilistic control law is obtained by solving the recurrence equation of dynamic programming to the fully probabilistic design control problem while taking into consideration the dependency of the parameters of the estimated probability density function of the system dynamics on the input values. It is shown to be of the class of cautious type controllers which accurately minimises the value of the Kullback-Leibler divergence without disregarding the variance of the model prediction as an element to be minimised. Comparison of theoretical and numerical results obtained from the F-16 fighter aircraft application with existing state-of-the-art demonstrates the effectiveness of the proposed method.

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A probabilistic indirect adaptive control for systems with input‐dependent noise

Herzallah

2010

Adaptive Control & Signal

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SUMMARYA probabilistic indirect adaptive controller is proposed for the general nonlinear multivariate class of discrete time system. The proposed probabilistic framework incorporates input-dependent noise prediction parameters in the derivation of the optimal control law. Moreover, because noise can be nonstationary in practice, the proposed adaptive control algorithm provides an elegant method for estimating and tracking the noise. For illustration purposes, the developed method is applied to the affine class of nonlinear multivariate discrete time systems and the desired result is obtained: the optimal control law is determined by solving a cubic equation and the distribution of the tracking error is shown to be Gaussian with zero mean. The efficiency of the proposed scheme is demonstrated numerically through the simulation of an affine nonlinear system.

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Towards Fully Probabilistic Control Design

Cited by 30 publications

References 1 publication

Extended Rauch-Tung-Striebel controller

Extended Rauch-Tung-Striebel controller

Generalised Probabilistic Control Design for Uncertain Stochastic Control Systems

A probabilistic indirect adaptive control for systems with input‐dependent noise

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