Dual control for stochastic systems with multiple uncertainties

Uncertainties commonly exist in stochastic systems, and they may seriously affect control quality of the stochastic system. In this paper, a novel dual control is proposed, where the uncertainties caused by uncontrolled excitations, model parameter fluctuations and system noises are all taken into consideration. First, an online outlier detection algorithm is proposed and integrated in the control scheme to find the outliers in the uncontrolled excitations. Second, based on the model with uncontrolled excitations, two cost functions showing the dual properties are used to derive the control signal: one cost function represents the system output tracking performance, the other one represents the unknown parameter estimation performance. The minimization of the two cost functions forms a double-objective optimization problem and is solved by a designed perturbation domain around the nominal value. Experiments are carried out, and the results show that the proposed controller bears better performance, especially in cases where outliers exist.

[1]  Bjarne A. Foss,et al.  Dual adaptive model predictive control , 2017, Autom..

[2]  Vladimír Havlena,et al.  MPC‐based approximate dual controller by information matrix maximization , 2013 .

[3]  R. Padilla,et al.  An innovations approach to dual control , 1982 .

[4]  Hui Cao,et al.  An outlier detection scheme for dynamical sequential datasets , 2019, Commun. Stat. Simul. Comput..

[5]  Jay H. Lee,et al.  Energy supply planning and supply chain optimization under uncertainty , 2014 .

[6]  Heinz Unbehauen,et al.  Adaptive Dual Control: Theory and Applications , 2004 .

[7]  Bengt Lindoff,et al.  Analysis of approximations of dual control , 1999 .

[8]  Fucai Qian,et al.  Optimal nominal dual control for discrete-time linear-quadratic Gaussian problems with unknown parameters , 2008, Autom..

[9]  Peilin Fu,et al.  Variance minimization approach for a class of dual control problems , 2002, IEEE Trans. Autom. Control..

[10]  M. B. Zarrop,et al.  A suboptimal dual controller for stochastic systems with unknown parameters , 1985 .

[11]  D. Bayard,et al.  Implicit dual control for general stochastic systems , 1985 .

[12]  Bjarne A. Foss,et al.  MPC-based dual control with online experiment design , 2015 .

[13]  Kailash Birmiwal.  A new adaptive LQG control algorithm , 1994 .

[14]  Tansu Alpcan,et al.  An Information-Based Learning Approach to Dual Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Tamer Basar,et al.  Dual Control Theory , 2001 .

[16]  Björn Wittenmark,et al.  Adaptive Dual Control Methods: An Overview , 1995 .