Thesis (M.Eng.)(Chemical)--University of Pretoria, 2004. / Includes summary. Includes bibliographical references.

Minimum invasive surgery is based on bilateral teleoperation in which surgeon interacts with the master side to the slave side that is located at a distance. The synchronization in between the two ends is through a communication channel. The primary objective in the telesurgery is the position and force tracking providing the surgeon with high fidelity. The presence of time delays in the communication channels makes the realization more difficult, and sometimes it may even destabilize the system. The work focuses on a design of the force control system by using Model Predictive Control to compensate for the effects of the time delay related to the use of surgical arms. Another vital issue of minimum impact velocity during contact with the environment has been tried to achieve by using the prediction from the Model Predictive Control to prevent accidental tissue damage. This work also addresses a problem of the developing a simple delayed free predictive kinematic imaging to understand the type of behavior of the system during contact with the environment when no perception is available.

With the help of rapidly advancing communication technology, control systems are increasingly integrated via communication networks. Networked control systems (NCSs) bring significant advantages such as flexible and scalable structures, easy implementation and maintenance, and efficient resources distribution and allocation. NCSs empowers to finish some complicated tasks using some relatively simple systems in a collaborated manner. However, there are also some challenges and constraints subject to the imperfection of communication channels. In this thesis, the stabilization problems and the performance limitation problems of control systems subject to networked-induced constraints are studied. Overall, the thesis mainly includes two parts: 1) Consensus and consensusability of multi-agent systems (MASs); 2) Delay margins of NCSs. Chapter 2 and Chapter 3 deal with the consensus problems of MASs, which aim to properly design the control protocols to ensure the state convergence of all the agents. Chapter 4 and Chapter 5 focus on the consensusability analysis, exploring how the dynamics of the agents and the networked induced constraints impact the overall systems for achieving consensus. Chapter 6 pays attention to the delay margins of discrete-time linear time-invariant (LTI) systems, studying how the dynamics of the plants limit the time delays that can be tolerated by LTI controllers. In Chapter 2, the leader-following consensus problem of MASs with general linear dynamics and arbitrary switching topologies is considered. The MAS with arbitrary switching topologies is formulated as a switched system. Then the leaderfollowing consensus problem is transformed to the stability problem of the corresponding switched system. A necessary and sufficient consensus condition is derived. The condition is also extended to MASs with time-varying delays. In Chapter 3, the consensus problem of MASs with general linear dynamics is studied. Motivated by the multiple-input multiple-output (MIMO) communication technique, a general framework is considered in which different state variables are exchanged in different independent communication topologies. This novel framework could improve the control system design flexibility and potentially improve the system performance. Fully distributed consensus protocols are proposed and analyzed for the settings of fixed and switching multiple topologies. The protocols can be applied using only local information. And the control gains can be designed depending on the dynamics of the individual agent. By transforming the overall MASs into cascade systems, necessary and sufficient conditions are provided to guarantee the consensus under fixed and switching state-variables-dependent topologies, respectively. Chapter 4 investigates the consensusability problem for MASs with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. Considering general linear dynamics under average state protocols, the consensus problem is then transformed into a robust control problem. Sufficient frequency domain criteria are established in terms of small-gain theorem by analyzing the delay dependent gains for both continuoustime and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. The consensusablity problem of general linear MASs considering directed topologies are explored from a frequency domain perspective in Chapter 5. By investigating the properties of Laplacian spectra, a consensus criterion is established based on the stability of several complex weighted closed-loop systems. Furthermore, for singleinput MASs, frequency domain consensusability criteria are proposed on the basis of the stability margins, which depend on the H∞ norm of the complementary sensitivity function determined by the agents’ unstable poles. The corresponding design procedure is also developed. Chapter 6 studies the delay margin problem of discrete-time LTI systems. For general LTI plants with multiple unstable poles and nonminimum phase zeros, we employ analytic function interpolation and rational approximation techniques to derive bounds on delay margins. Readily computable and explicit lower bounds are found by computing the real eigenvalues of a constant matrix, and LTI controllers can be synthesized based on the H∞ control theory to achieve the bounds. The results can be also consistently extended to the case of systems with time-varying delays. For first-order unstable plants, we also obtain bounds achievable by proportionalintergral- derivative (PID) controllers, which are of interest to PID control design and implementation. It is worth noting that unlike its continuous-time counterpart, the discrete-time delay margin problem being considered herein constitutes a simultaneous stabilization problem, which is known to be rather difficult. While previous work on the discrete-time delay margin led to negative results, the bounds developed in this chapter provide instead a guaranteed range of delays within which the delayed plants can be robustly stabilized, and in turn solve the special class of simultaneous stabilization problems in question. Finally, in Chapter 7, the thesis is summarized and some future research topics are also presented. / Graduate

Fault detection and diagnosis presents a big challenge within the petrochemical industry. The annual economic impact of unexpected shutdowns is estimated to be $20 billion. Assistive technologies will help with the effective detection and classification of the faults causing these shutdowns. Clustering analysis presents a form of unsupervised learning which identifies data with similar properties. Various algorithms were used and included hard-partitioning algorithms (K-means and K-medoid) and fuzzy algorithms (Fuzzy C-means, Gustafson-Kessel and Gath-Geva). A novel approach to the clustering problem of time-series data is proposed. It exploits the time dependency of variables (time delays) within a process engineering environment. Before clustering, process lags are identified via signal cross-correlations. From this, a least-squares optimal signal time shift is calculated. Dimensional reduction techniques are used to visualise the data. Various nonlinear dimensional reduction techniques have been proposed in recent years. These techniques have been shown to outperform their linear counterparts on various artificial data sets including the Swiss roll and helix data sets but have not been widely implemented in a process engineering environment. The algorithms that were used included linear PCA and standard Sammon and fuzzy Sammon mappings. Time shifting resulted in better clustering accuracy on a synthetic data set based on than traditional clustering techniques based on quantitative criteria (including Partition Coefficient, Classification Entropy, Partition Index, Separation Index, Dunn’s Index and Alternative Dunn Index). However, the time shifted clustering results of the Tennessee Eastman process were not as good as the non-shifted data. Copyright / Dissertation (MEng)--University of Pretoria, 2009. / Chemical Engineering / unrestricted

abstract: Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space using a mathematical approach. Chapter 1 presents a detailed review of literature on cancer modeling. Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b). In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a). Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

We investigate the dynamics and stability of nonlinear time-delayed one-degree-of-freedom systems possessing quadratic and cubic nonlinearities and subjected to external and parametric disturbances. Due to the time-delay terms, the trivial solution of the unforced system undergoes Hopf bifurcations. We use the method of multiple scales to determine the normal forms of the Hopf bifurcations and hence determine whether they are locally supercritical or subcritical. Then, we use a combination of a path following scheme, the normal forms, and the method of harmonic balance to calculate and trace small- and large-amplitude limit cycles and use Floquet theory to ascertain their stability and hence generate global bifurcation diagrams. We validate these diagrams using numerical simulations. We apply the results to two important physical problems: machine-tool chatter in lathes and control of the sway of container cranes using time-delayed position feedback. We find that the Hopf bifurcations in machine tools are globally subcritical even when they are locally supercritical. We find multiple large-amplitude solutions coexisting with the linearly stable trivial solution. Consequently, there are three operating regions for machine tools: an unconditionally stable region, an unconditionally unstable region, and a conditionally stable region. In the latter region, the multiple responses lead to hysteresis. Then, we investigate the use of bifurcation control to transform the subcritical bifurcations into supercritical ones. We find that cubic-velocity feedback with appropriate gains can shrink or even eliminate the conditionally stable region. Then, we find that time-delayed acceleration feedback with an appropriate gain can completely eliminate the linear instability region. In contrast, we find that the Hopf bifurcations in controlled cranes are locally and globally supercritical. Finally, we investigate the effectiveness of time-delayed position feedback in rejecting external and parametric disturbances in ship-mounted cranes. / Ph. D.

In order to predict the linear stability of combustion systems in industrial-scale gas turbines, a stability analysis was completed using models generated for each of the major dynamic components. Changes in the combustion process of gas turbines to reduce emissions has resulted in large amplitude pressure oscillations associated with a coupling between the natural acoustic modes of the combustor and the unsteady heat release from the flame. Detailed models of the acoustics and the heat release processes were created and assembled, with a time delay element and the appropriate scaling, into a system block diagram to investigate the stability of the system using linear system theory. Wherever possible the analytical models were validated with experimental data. The main goal of this work was to create a design methodology which could be used by industry to predict where instabilities were likely to occur during the design phase. Results show that the system based stability analysis can predict some of the instability frequencies seen in the experimental data, but more refined models are needed to predict every instability. Future work will involve designing experiments to validate and refine the dynamic models already developed. / Master of Science

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19237号 / 工博第4072号 / 新制||工||1628(附属図書館) / 32236 / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 泉田 啓, 教授 藤本 健治, 教授 松野 文俊 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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