Yes / This note presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing st

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Yes / In this technical note, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

An important issue in the design and operation of assembly systems is the coordination of part deliveries and processing operations. These decisions can have a significant impact on inventory cost and customer service. The problem is especially complex when actual delivery and processing times are stochastic in nature, as is the case in small lot manufacturing. In this research a new methodology is developed for determining optimal part delivery dates in stochastic small lot assembly systems. This methodology is based on the descriptive model that comprises of taking the maximum of several random variables. The part arrival and processing times are assumed to follow various known probability distributions. The model includes consideration of limited buffers between stations. The overall objective is to minimize the expected total of part and subassembly inventory cost, makespan cost and tardiness cost. An approach based on the optimization of individual stations in isolation is used to obtain the part delivery dates at each station. Comparison of the approach with the nonlinear programming based approach to the problem indicates that it generates almost as good solutions in a fraction of the computation time. This approach is then used to study system behavior under various operating conditions. Results indicate that the Iognormal and gamma distributions result in higher total costs than the normal distribution. However, the normal distribution can be used to determine part delivery dates even if the actual distribution is Iognormal or gamma, with relatively small errors compared to the solutions obtained using the correct distribution. Variability is the most important factor in the design of the system, and affects the determination of due dates, buffer capacity requirements, choice of distribution, and estimates of system performance. The role of buffer capacities, however, is not very critical in the design of small lot unbalanced lines. / Ph. D.

This dissertation presents a new method of simultaneous parameter and state estimation for linear, stochastic, discrete—time, multiple-input, multiple-output (MIMO) (B systems. This new method is called pseudo-Iinear identification (PLID), and extends an earlier method to the more general case where system input and output measurements are corrupted by noise. PLID can be applied to completely observable, completely controllable systems with known structure (i.e., known observability indexes) and unknown parameters. No assumptions on pole and zero locations are required; and no assumptions on relative degree are required, except that the system transfer functions must be strictly proper. Under standard gaussian assumptions on the various noises, for time-invariant systems in the class described above, it is proved that PLID is the optimal estimator (in the mean-square-error sense) of the states and the parameters, conditioned on the output measurements. It is also proved, under a reasonable assumption of persistent excitation, that the PLID parameter estimates converge a.e. to the true parameter values of the unknown system. For deterministic systems, it is proved that PLID exactly identifies the states and parameters in the minimum possible time, so0called deadbeat identification. The proof brings out an interesting relation between the estimate error propagation and the observability matrix of the time-varying extended system (the extended system incorporates the unknown parameters into the state vector). This relation gives rise to an intuitively appealing notion of persistent excitation. Some results of system identification simulations are presented. Several different cases are simulated, including a two-input, two-output system with non-minimum-phase zeros, and an unstable system. A comparison of PLID with the widely used extended Kalman filter is presented for a single-input, single-output system with near cancellation of a pole-zero pair. Results are also presented from simulations of the adaptive control of an unstable. two-input, two-output system In these simulations, PLID is used in a se1f—tuning regulator to identify the parameters needed to compute the feedback gain matrix, and (simultaneously) to estimate the system states, for the state feedback / Ph. D.

An improved method for designing controllers for nonlinear stochastic systems is developed and analyzed. The resulting controller consists of a nonlinear control law coupled with an adaptive state estimator. The nonlinear control law is developed first. Using Taylor series expansion, linear approximations to the nonlinear systems are generated at selected points in the operating region. Then a control law which will produce the desired response is developed for each linearized configuration using conventional techniques for linear systems. The resulting control law parameters are treated as tabulated values from a set of unknown continuous functions of the nonlinear system parameters. These unknown functions are approximated at all points in the operating region by fitting curves to the tabulated data. The stability and convergence aspects of this nonlinear control law are analyzed in detail, with several derivations given and theorems proved. Two examples are given to illustrate the design procedure and evaluate its performance. The design procedure is extended to stochastic systems by incorporating a suitable state estimator. Two members of the class known as partitioned adaptive estimators (PAE's) are evaluated and their performance compared. The formulation known as the modified semi-Markov PAE is shown to be superior. The design, execution, and analysis of the experiments comprising the evaluation are discussed in detail, with particular attention given to correlating the performance of the estimators with the behavior of the weighting coefficients. Numerous figures and tables which amplify the discussions, along with some suggestions for further research, are also included. / Ph. D.

A Dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the Degree of Masters in Engineering by research only and to the Stochastic Mine Planning Laboratory, McGill University as part of the COSMO scholarship in Mine Planning under uncertainty Johannesburg, 2017 / This dissertation discusses the use of stochastic orebody modelling techniques for assessing geological uncertainty associated with gold mineralisation at Geita Gold Mine in Tanzania, and proposes a practical methodology that can be applied to similar studies. As part of the pre-feasibility stage studies for underground mining at Geita, stochastic simulations were required to assess the geological uncertainty associated with isolating (modelled) high grade lenses that occur within the known low grade mineralisation currently targeted for underground mining. Two different simulation techniques are applied in this research: Sequential Indicator Simulation to generate lithofacies realisations from which to assess ore category boundaries and shapes for use in quantifying volumetric uncertainty; and Direct Block Simulations to simulate gold grade realisations from which to assess grade uncertainty. This study identified potential upside and downside mine planning scenarios for volumes and total metal content from the ore category and grade simulations respectively. The findings of the results demonstrated that the high grade zones are much more broken up and discontinuous than the currently modelled high grade shape. The current business case uses a probabilistic high grade shape based on a single grade indicator and a probability choice of 50 percent as the threshold for high grade. The results of the study consider a simulation of possible outcomes based on the same threshold grade indicator and hence quantify the uncertainty or total geological risk. This geological risk may be introduced to mine designs, production schedules and NPV predictions The stochastic workflow developed can be applied to analogous deposit types to assess the risk related to geological uncertainty. The work includes a description of practical considerations to be accounted for when applying the techniques. / MT 2017

To understand the phenomena associated with such stochastic processes and to predict, at least qualitatively, the behavior of mechanical systems within environments which are completely random in time, new mechanical tools are necessary. Fortunately, the derivation of these tools does not necessitate a complete departure from existing theories. In fact, they may be considered as an extension of the well-defined theory of the integral transform, in particular, the exponential Fourier integral transform.

Stochastic models, in particular Continuous Time Markov Chains, are a commonly employed mathematical abstraction for describing natural or engineered dynamical systems. While the theory behind them is well-studied, their specification can be problematic in a number of ways. Firstly, the size and complexity of the model can make its description difficult without using a high-level language. Secondly, knowledge of the system is usually incomplete, leaving one or more parameters with unknown values, thus impeding further analysis. Sophisticated machine learning algorithms have been proposed for the statistically rigorous estimation and handling of this uncertainty; however, their applicability is often limited to systems with finite state-space, and there has not been any consideration for their use on high-level descriptions. Similarly, high-level formal languages have been long used for describing and reasoning about stochastic systems, but require a full specification; efforts to estimate parameters for such formal models have been limited to simple inference algorithms. This thesis explores how these two approaches can be brought together, drawing ideas from the probabilistic programming paradigm. We introduce ProPPA, a process algebra for the specification of stochastic systems with uncertain parameters. The language is equipped with a semantics, allowing a formal interpretation of models written in it. This is the first time that uncertainty has been incorporated into the syntax and semantics of a formal language, and we describe a new mathematical object capable of capturing this information. We provide a series of algorithms for inference which can be automatically applied to ProPPA models without the need to write extra code. As part of these, we develop a novel inference scheme for infinite-state systems, based on random truncations of the state-space. The expressive power and inference capabilities of the framework are demonstrated in a series of small examples as well as a larger-scale case study. We also present a review of the state-of-the-art in both machine learning and formal modelling with respect to stochastic systems. We close with a discussion of potential extensions of this work, and thoughts about different ways in which the fields of statistical machine learning and formal modelling can be further integrated.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 215-218. / by Leon K. Ekchian. / M.S.