Monte Carlo Statistical Prediction Method for Optimal Control of Linear Hybrid Systems

2009 ◽  
Vol 34 (8) ◽  
pp. 1028-1032
Author(s):  
Chun-Yue SONG
Author(s):  
Austin Rogers ◽  
Fangzhou Guo ◽  
Bryan Rasmussen

Abstract Many fault detection, optimization, and control logic methods rely on sensor feedback that assumes the system is operating at steady state conditions, despite persistent transient disturbances. While filtering and signal processing techniques can eliminate some transient effects, this paper proposes an equilibrium prediction method for first order dynamic systems using an exponential regression. This method is particularly valuable for many commercial and industrial energy system, whose dynamics are dominated by first order thermo-fluid effects. To illustrate the basic advantages of the proposed approach, Monte Carlo simulations are used. This is followed by three distinct experimental case studies to demonstrate the practical efficacy of the proposed method. First, the ability to predict the carbon dioxide level in classrooms allows for energy efficient control of the ventilation system and ensures occupant comfort. Second, predicting the optimal time to end the cool-down of an industrial sintering furnace allows for maximum part throughput and worker safety. Finally, fault detection and diagnosis methods for air conditioning systems typically use static system models; however, the transient response of many air conditioning signals may be approximated as first order, and therefore, the prediction model enables the use of static fault detection methods with transient data. In this paper, the equilibrium prediction method's performance will be quantified using both Monte Carlo simulations and case studies.


2007 ◽  
Vol 1 (2) ◽  
pp. 264-279 ◽  
Author(s):  
Shangming Wei ◽  
Kasemsak Uthaichana ◽  
Miloš Žefran ◽  
Raymond A. DeCarlo ◽  
Sorin Bengea

Author(s):  
Ajay Jasra ◽  
Arnaud Doucet

In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high- and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging.


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