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Research Papers

Probabilistic Control for Uncertain Systems

[+] Author and Article Information
Randa Herzallah

 FET, Al-Balqa’ Applied University, P.O. Box 15008 Amman 11134 Jordanherzallah.r@gmail.com

J. Dyn. Sys., Meas., Control 134(2), 021018 (Jan 12, 2012) (7 pages) doi:10.1115/1.4005370 History: Received May 01, 2010; Revised September 11, 2011; Accepted September 13, 2011; Published January 12, 2012; Online January 12, 2012

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Architecture of forward and inverse MDNs: (a) The architecture of the system output MDN. (b) The architecture of the inverse controller MDN.

Grahic Jump Location
Figure 2

Control results of nonlinear stochastic system with additive noise: output and tracking error (a) the actual and reference model outputs of MDN. (b) Tracking error of MDN. (c) The actual and reference model outputs of standard MLPN. (d) Tracking error of standard MLPN.

Grahic Jump Location
Figure 3

Control results of nonlinear stochastic system with multiplicative noise: output and tracking error (a) the actual and reference model outputs of MDN. (b) Tracking error of MDN. (c) The actual and reference model outputs of standard MLPN. (d) Tracking error of standard MLPN.

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