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Uncertainty quantification of model predictive control for nonlinear systems with parametric uncertainty using hybrid pseudo-spectral method

Ali Namadchian, Mehdi Ramezani, Yuanyuan Zou
2019 Cogent Engineering  
In this paper, a hybrid pseudo-spectral (hPS) method is utilized to analyze the uncertainty of the model predictive control (MPC) for nonlinear systems with stochastic parameter uncertainty.  ...  Simulation results demonstrate that the proposed method can approximate the two first moments of the states and control inputs under MPC much faster and computationally more efficient than MC simulations  ...  control for nonlinear systems with parametric uncertainty using hybrid pseudo-spectral method, Ali Namadchian & Mehdi Ramezani, Cogent Engineering (2019), 6: 1691803.  ... 
doi:10.1080/23311916.2019.1691803 fatcat:koxrigefjbda3czxxynm335kri

Subjective Equilibria under Beliefs of Exogenous Uncertainty [article]

Gürdal Arslan, Serdar Yüksel
2021 arXiv   pre-print
We present a subjective equilibrium notion (called "subjective equilibrium under beliefs of exogenous uncertainty (SEBEU)" for stochastic dynamic games in which each player chooses its decisions under  ...  the (incorrect) belief that a stochastic environment process driving the system is exogenous whereas in actuality this process is a solution of closed-loop dynamics affected by each individual player.  ...  At such an equilibrium, to be called a subjective equilibrium under be- liefs of exogenous uncertainty (SEBEU), if players are given the full distribution of the stochastic environment process as if it  ... 
arXiv:2005.01640v2 fatcat:l3lw6aik3jbijm6a4zdy3sm4tq

Adaptive Estimation and Control for Systems with Parametric and Nonparametric Uncertainties [chapter]

Hongbin Ma, Kai-Yew Lum
2009 Adaptive Control  
is established under some conditions.  ...  And in this example we can establish the asymptotic convergence of tracking error under some mild conditions, althouth these conditions required are not as perfect as in the first example in sense that  ...  section, we can only establish stability of the closed-loop system under condition 5 . 0 0 < < L for the parametric part, which is much stronger than the condition 2 2 3 0 + < ≤ L .  ... 
doi:10.5772/6500 fatcat:alcdaegnb5bbjmdqb7kcb6evem

Robust Model Predictive Control of Irrigation Systems with Active Uncertainty Learning and Data Analytics [article]

Chao Shang, Wei-Han Chen, Abraham Duncan Stroock, Fengqi You
2019 arXiv   pre-print
The fundamental idea is to integrate both mechanistic models, which describe dynamics in soil moisture variations, and data-driven models, which characterize uncertainty in forecast errors of evapotranspiration  ...  As for precipitation forecast errors, we analyze the dependence of their distribution on forecast values, and further design a tailored uncertainty set based on the properties of this type of uncertainty  ...  UNCERTAINTY SET FORMULATIONS The uncertainty set W of stochastic disturbance sequence w plays an important role in RMPC, since it exerts direct influence on the conservatism of control decisions.  ... 
arXiv:1810.05947v2 fatcat:re26rhdxjzboxbnu44hk7qcyk4

Uncertainty, information and complexity in identification and control

Le Yi Wang
2000 International Journal of Robust and Nonlinear Control  
The relationship between information acquisition (identi"cation) and information processing (control) in their capability of dealing with uncertainty is studied.  ...  A notion of information-based complexity is hence introduced, "rst in its generality, and then in its special applications to metric spaces in feedback control systems.  ...  By Reference [34] , a necessary and su$cient condition for +kG : k3[ H , H ), to be robustly stabilizable by a "xed controller in !  ... 
doi:10.1002/1099-1239(200009/10)10:11/12<857::aid-rnc529>;2-j fatcat:oqxz5e5cozaxpl2i7cbytb6vqy

Scaling of gain bounds for switched adaptive control with large uncertainties

Dominic Buchstaller, Mark French
2007 2007 46th IEEE Conference on Decision and Control  
A wide class of MMAC with a finite lp (1 ≤ p ≤ ∞) closed loop gain are shown to have an unboundedly increasing lp closed loop gain for a simple set of plants under increasing parametric uncertainty.  ...  A modification is proposed which achieves a quadratic closed loop gain function which is independent of the size of the uncertainty set.  ...  This motivates the need to examine the behaviour of such a closed loop gain for multiple model adaptive control (MMAC).  ... 
doi:10.1109/cdc.2007.4434330 dblp:conf/cdc/BuchstallerF07 fatcat:y7dig4tzfbdsxkc7uw3av5rqlu

Mean Square Stability Analysis of Stochastic Continuous-time Linear Networked Systems [article]

Sai Pushpak, Amit Diwadkar, Umesh Vaidya
2018 arXiv   pre-print
The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output channels of the plant.  ...  For a special case of single input channel uncertainty, we also prove a fundamental limitation result that arises in the mean square exponential stabilization of the continuous-time linear system.  ...  The nominal part of this stochastic closed-loop system (G) is the deterministic part of the stochastic closed-loop system which consists of MIMO plant (P), controller (K) and the mean part of the uncertainties  ... 
arXiv:1602.02857v6 fatcat:2i3uhhjdbvgqnduikjvriiogsa

Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

Isaac E. Elishakoff, Vladik Kreinovich, Wolfram Luther, Evgenija D. Popova, Marc Herbstritt
2011 Dagstuhl Reports  
The major emphasis of the seminar lies on modeling and analyzing uncertainties and propagating them through application systems by using, for example, interval arithmetic.  ...  This report documents the program and the results of Dagstuhl Seminar 11371 "Uncertainty modeling and analysis with intervals -Foundations, tools, applications", taking place September 11-16, 2011.  ...  Thanks go to Martin Fuchs for his help in collecting abstracts of the talks and other related materials for these proceedings.  ... 
doi:10.4230/dagrep.1.9.26 dblp:journals/dagstuhl-reports/ElishakoffKLP11 fatcat:7e3wkeju6zhfdcy6n7o2kdz7py

Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities

Zidong Wang, Biao Huang, K.J. Burnbam
2001 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
This paper investigates the robust reliable control problem for a class of nonlinear time-delay stochastic systems.  ...  The system under study involves stochastics, state time-delay, parameter uncertainties, possible actuator failures and unknown nonlinear disturbances, which are often encountered in practice and the sources  ...  Corollary 1: Under the conditions of Theorem 2, the state feedback control law (21) almost surely exponentially stabilizes the uncertain time-delay system (1) and (2) , independent of the unknown delay  ... 
doi:10.1109/81.922470 fatcat:b6f33sxnibgb3de4qxg5tvvmim

Online Robust Control of Nonlinear Systems with Large Uncertainty [article]

Dimitar Ho, Hoang M. Le, John C. Doyle, Yisong Yue
2021 arXiv   pre-print
We present an online approach that robustly controls a nonlinear system under large model uncertainty.  ...  To the best of our knowledge, this is the first approach for online robust control of nonlinear systems with such learning theoretic and safety guarantees.  ...  Here we expand on the desired conditions of π and SEL. Required conditions on procedure π Online control with oracle under idealized conditions.  ... 
arXiv:2103.11055v2 fatcat:ofakkysmtrdydg44nwqfm6g4ya

Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise [article]

Junhui Li, Jieying Lu, Weizhou Su
2021 arXiv   pre-print
This paper addresses the mean-square optimal control problem for \a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback.  ...  A necessary and sufficient condition for the existence of the stabilizing solution to the MARE is explicitly presented.  ...  In [4] , fundamental conditions for mean-square stabilizability of generic linear systems with structured i.i.d. multiplicative noise were developed.  ... 
arXiv:2109.01358v1 fatcat:6ondsodzcrgbhdbcegwc26dflu

On Feedback Capability in a Class of Nonlinearly Parameterized Uncertain Systems

Chanying Li, Lei Guo
2011 IEEE Transactions on Automatic Control  
with multiple unknown parameters.  ...  suitable decomposition of the family of the nonlinearly parameterized functions in question turns out to be necessary.  ...  This shows that the stabilizability set s in Theorem 2.1 cannot be expanded anymore under the general condition f (1; 1) 2 F(b).  ... 
doi:10.1109/tac.2011.2160599 fatcat:bdthl4op3nbb3eakfrimlc7a3m

Page 7407 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
We show, under a rather weak assumption, that when a family of systems is not robustly stabilizable by any linear time- invariant feedback controller, then no nonlinear time-varying con- troller can robustly  ...  Under some additional conditions it is stated that J(u,0) = J {t, 0}, where w,% are optimal feedback controls and 0 = {U¢} is the optimal program control, which can be found a priori.  ... 

Output Regulation of Linear Stochastic Systems: the Full-Information Case

Giordano Scarciotti
2018 2018 European Control Conference (ECC)  
A general class of linear systems is considered, namely systems in which the state, control variable and exogenous variable may appear simultaneously in the drift term and in the diffusion term of the  ...  The full information output regulation problem for linear stochastic systems is addressed.  ...  I. INTRODUCTION The problem of output regulation is a fundamental problem in control theory.  ... 
doi:10.23919/ecc.2018.8550527 dblp:conf/eucc/Scarciotti18 fatcat:5xqh26n4gnfwvone734fgnbpt4

Stabilization of Discrete-Time Nonlinear Uncertain Systems by Feedback Based on LS Algorithm

Chanying Li, James Lam
2013 SIAM Journal of Control and Optimization  
This result thus provides an answer to the question of what are the fundamental limitations of the discrete-time adaptive nonlinear control.  ...  In fact, as pointed out by [4] , fundamental difficulties arise for adaptive control of discrete-time parametric nonlinear systems.  ...  In this paper, we will see that the polynomial rule (3) does indeed provide a necessary and sufficient condition of stabilizability for system (2) in the stochastic framework.  ... 
doi:10.1137/110852875 fatcat:wglvqzqombfunb4gemo26usjy4
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