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Modeling for System Control
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
A deterministic system is a system without random parameters or inputs. In other words, the system is known exactly. On the other hand, a stochastic system is one in which at least one parameter or input is affected by random disturbances or noise. The external signals that influence a system also have to be modeled. They are also either deterministic or stochastic. These random disturbances affecting the system parameters or inputs could be known and measurable, known and nonmeasurable, or unknown. Smoothing, filtering, and estimation techniques are used to get an accurate response for a stochastic system.
Historical development of hydrological modelling
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
A system can be considered as deterministic or stochastic. A deterministic system defines a cause–effect relationship, and therefore predictions are possible if the cause is known. The cause is the driving function (input) and effect is the response function (output). A stochastic system, on the other hand, is non-deterministic and has one or more parts attributed to chance and therefore random. Unlike in a deterministic system, a stochastic system does not always produce the same output for a given input.
Modeling for Epilepsy
Published in Andrea Varsavsky, Iven Mareels, Mark Cook, Epileptic Seizures and the EEG, 2016
Andrea Varsavsky, Iven Mareels, Mark Cook
A model can be deterministic or contain stochastic components. It is rare to find a completely deterministic system where a set of mathematical equations determines dynamics exactly. Most models are a combination of deterministic and stochastic elements and it is important to understand the different types of random contributions: Model simplification: Using a simplified representation results in discrepancies between true and model behavior. The simplifications are necessary to make the problem tractable, but comparisons between model and real data reveal fluctuations that cannot be explained by the model. These may be accounted for by a stochastic component. If the simplifying assumptions are valid then these errors can be kept small.Stochastic activity: The mechanics of certain aspects of a system are sometimes not understood, either because suitable experimental data do not exist or because its complexity cannot, at present, be captured by analytical methods. Even though the underlying activity may be deterministic these components appear random and can be approximated as such. These random elements are part of the system itself and have particular properties (e.g., mean, variance, distribution) gathered from experimental data or assumed based on realistic constraints. An example is presented in Section 6.2 where a model based on the stochastic nature of action potential firing rates is presented.Stochastic inputs: The system equations can be deterministic but driven by a stochastic process, that is, the input to the system is somehow random. One example is presented in Section 6.3 where the model equations are deterministic (even though they are derived from stochastic observations) but the input to this model is stochastic. Again, the real input to this system could in actuality be deterministic, but is so complex that it is approximated as a random process.
Continuous-time Laguerre-based subspace identification utilising nuclear norm minimisation
Published in International Journal of Systems Science, 2021
Miao Yu, Ge Guo, Jianchang Liu
Note that the system (1) is the combined deterministic-stochastic system. It differs from the purely deterministic system with no measurement nor process noise and stochastic system with no external input. The deterministic system describes the influence of the deterministic input on the deterministic output, and the stochastic system depicts the influence of the measurement and process noise on the stochastic output (Lindquist & Picci, 2015).
A state-of-the-art review of an optimal sensor placement for contaminant warning system in a water distribution network
Published in Urban Water Journal, 2018
Oluwaseye S. Adedoja, Yskandar Hamam, Baset Khalaf, Rotimi Sadiku
An optimization-based approach has been widely adopted and can be categorized into: deterministic optimization, stochastic optimization, and robust optimization. Arithmetically, a deterministic system can be perceived as a system in which no randomness is to be considered when developing a future state of a system. Some studies (Kumar et al. 1999; Krause et al. 2008a) employed the deterministic algorithm for an optimal layout. An excessive computational burden and difficulty for a sub-optimal state, under certain scenarios, especially when a large network is considered was outlined as a setback of the method. The study by Rico-Ramirez et al. (2007) proposed a two-stage mixed-integer stochastic linear programming method for sensor placement in WDN. The results of the study revealed that uncertainties largely contributed to the consequences of the optimal solution. Also, Cozzolino et al. (2011) considered a random selection of water demands and time-varying hydraulic situations by using two stochastic methods. The study aimed to increase the probability of contaminant detections. The work of Comboul and Ghanem (2012) discussed stochastic method and analysis of uncertainty. In order to address the challenge of uncertainty in WDN, Monte Carlo sample is usually employed to produce initial contaminant occurrence in stochastic optimization. However, it is difficult to produce crucial contaminant occurrence by Monte Carlo sample. This is due to the fact that, ordinary Monte Carlo will produce random events with the use of a uniform distribution. As such, the probability to reveal a critical event is limited. In an effort to overcome this challenge, Perelman and Ostfeld (2009) discussed an importance-based sampling approach to expose critical events. The approach was derived from cross-entropy which originated from an intermittent simulation event. The proposed approach showed a positive result with a small probability of occurrence and an extreme impact of the whole set of possible contamination incidents. An entropy-based theory has also found its relevance in the sensor placement in a water distribution system. The study by Christodoulou et al. (2013) suggested an entropy-based method to address the sensor placement problems in a WDN. Furthermore, Weickgenannt et al. (2010a) employed an importance-based sampling to examine the relative importance of contaminant events. The results of their study did not only enhance the possibility to reveal the contaminant events but, also minimizes the computation burden. The studies by Liu and Auckenthaler (2014) and Ung et al. (2017b) discussed an optimal sensor placement in alliance with contaminant source identification. Liu and Auckenthaler (2014) assumed that contaminant events are randomly generated by an abridged Gaussian probability function. Nevertheless, stochastic techniques have been applied to some contamination schemes, but two major research gaps were identified. First, a specific probability of an individual contamination event is required. Secondly, the solution is optimal for an estimated value of objective function. Therefore, it cannot be used to rescue an awful condition. Hence, the robust optimization method was recommended to address these setbacks.