The dynamic behavior of a vehicle is predominantly controlled by the forces and moments generated at the contact patch between the tire and the road surface. As a result, tire characteristics can dramatically change vehicle response, especially during maneuvers that yields the tires to reach to the limits of its adhesion capacity. To assist the driver in such cases and to prevent other possible instability scenarios, various vehicle control systems e.g. anti-lock brakes (ABS), stability controllers (ESP, ESC) or rollover mitigation schemes are introduced, which are generally known as active vehicle safety systems. Based on the above facts, one can easily come to the conclusion that to improve upon the current control algorithms developed for the technology in use; a vehicle control system design requires accurate knowledge of the tire states. This study proposes the use of a smart tire system that can provide information on momentary variation of tire features through the sensor units attached directly on the tire and develops control algorithms based on this information to assure the match-up between tire and controller dynamics. A prototype smart tire system was developed for field testing and for detailed analysis of its potential. Based on the collected prototype data, novel observer and controller schemes were developed to obtain dynamic tire state information and to improve vehicle handling performance. The proposed algorithms were implemented and evaluated using numerical analysis in Matlab/SimulinkR environment. For a more realistic simulation environment, vehicle models were integrated from Mechanical Simulations CarSimR® software suite. / Ph. D.

This work describes a framework for simultaneous estimation and modeling (SEAM) of dynamic systems using non-Gaussian belief fusion by first presenting the relevant fundamental formulations, then building upon these formulations incrementally towards a more general and ubiquitous framework. Multi-Gaussian belief fusion (MBF) is introduced as a natural and effective method of fusing non-Gaussian probability distribution functions (PDFs) in arbitrary dimensions efficiently and with no loss of accuracy. Construction of some multi-Gaussian structures for potential use in MBF is addressed. Furthermore, recursive Bayesian estimation (RBE) is developed for linearized systems with uncertainty in model parameters, and a rudimentary motion model correction stage is introduced. A subsequent improvement to motion model correction for arbitrarily non-Gaussian belief is developed, followed by application to observation models. Finally, SEAM is generalized to fully nonlinear and non-Gaussian systems. Several parametric studies were performed on simulated experiments in order to assess the various dependencies of the SEAM framework and validate its effectiveness in both estimation and modeling. The results of these studies show that SEAM is capable of improving estimation when uncertainty is present in motion and observation models as compared to existing methods. Furthermore, uncertainty in model parameters is consistently reduced as these parameters are updated throughout the estimation process. SEAM and its constituents have potential uses in robotics, target tracking and localization, state estimation, and more. / Doctor of Philosophy / The simultaneous estimation and modeling (SEAM) framework and its constituents described in this dissertation aim to improve estimation of signals where significant uncertainty would normally introduce error. Such signals could be electrical (e.g. voltages, currents, etc.), mechanical (e.g. accelerations, forces, etc.), or the like. Estimation is accomplished by addressing the problem probabilistically through information fusion. The proposed techniques not only improve state estimation, but also effectively "learn" about the system of interest in order to further refine estimation. Potential uses of such methods could be found in search-and-rescue robotics, robust control algorithms, and the like. The proposed framework is well-suited for any context where traditional estimation methods have difficulty handling heightened uncertainty.

This dissertation introduces advances in the Wiener path integral (WPI) technique for determining efficiently and accurately the stochastic response of diverse nonlinear dynamical systems. First, a novel, general, formalism of the WPI technique is developed to account, in a direct manner, also for systems with non-Markovian response processes. Specifically, the probability of a path and the associated transition probability density function (PDF) corresponding to the Wiener excitation process are considered. Next, a functional change of variables is employed, in conjunction with the governing stochastic differential equation, for deriving the system response joint transition PDF as a functional integral over the space of possible paths connecting the initial and final states of the response vector. In comparison to alternative derivations in the literature, the herein-developed formalism does not require the Markovian assumption for the system response process. Overall, the veracity and mathematical legitimacy of the WPI technique to treat also non-Markovian system response processes are demonstrated. In this regard, nonlinear systems with a history-dependent state, such as hysteretic structures or oscillators endowed with fractional derivative elements, can be accounted for in a direct manner—that is, without resorting to any ad hoc modifications of the WPI technique pertaining, typically, to employing additional auxiliary filter equations and state variables. Next, a reduced-order WPI formulation is introduced for efficiently determining the stochastic response of diverse nonlinear systems with fractional derivative elements. This formulation can be also construed as a dimension reduction approach that renders the associated computational cost independent of the total number of stochastic dimensions of the problem. In fact, the proposed technique can determine, directly, any lower-dimensional joint response PDF corresponding to a subset only of the response vector components. This is accomplished by utilizing an appropriate combination of fixed and free boundary conditions in the related variational, functional minimization, problem. Notably, the reduced-order WPI formulation is particularly advantageous for problems where the interest lies in, few only, specific degrees-of-freedom whose stochastic response is critical for the design and optimization of the overall system. Further, an extrapolation approach within the WPI technique is developed that significantly enhances the computational efficiency of the technique without, practically, affecting the associated degree of accuracy. Overall, the WPI technique treats the system response joint transition PDF as a functional integral over the space of all possible paths connecting the initial and the final states of the response vector. Next, the functional integral is evaluated, ordinarily, by considering the contribution only of the most probable path. This corresponds to an extremum of the functional integrand, and is determined by solving a functional minimization problem that takes the form of a deterministic boundary value problem (BVP). This BVP corresponds to a specific grid point of the response PDF domain. Remarkably, the BVPs corresponding to two neighboring grid points not only share the same equations, but also the boundary conditions differ only slightly. This unique aspect of the technique is exploited, and it is shown that solution of a BVP and determination of the response PDF value at a specific grid point can be used for extrapolating and estimating efficiently and accurately the PDF values at neighboring points without the need for considering additional BVPs. Last, a joint time-space extrapolation approach within WPI technique is developed for determining, efficiently and accurately, the non-stationary stochastic response of diverse nonlinear dynamical systems. The approach can be construed as an extension of the above space-domain extrapolation scheme to account also for the temporal dimension. Specifically, it is shown that information inherent in the time-history of an already determined most probable path can be used for evaluating points of the response PDF corresponding to arbitrary time instants, without the need for solving additional BVPs. In a nutshell, relying on the aforementioned unique and advantageous features of the WPI-based BVP, the complete non-stationary response joint PDF is determined, first, by calculating numerically a relatively small number of PDF points, and second, by extrapolating in the joint time-space domain at practically zero additional computational cost. Compared to an alternative brute-force implementation of the WPI technique, and to a standard Monte Carlo simulation (MCS) solution treatment, the developed extrapolation approach reduces the associated computational cost by several orders of magnitude. Several representative numerical examples are considered to demonstrate the reliability of the developed techniques. Juxtapositions with pertinent MCS data are included as well.

The Blood Oxygen Level Dependent (BOLD) signal provides indirect estimates of neural activity. The parameters of this BOLD signal can give information about the pathophysiological state of the brain. Most of the models for the BOLD signal are overparameterized which makes the unique identification of these parameters difficult. In this work, we use information from multiple neu- roimaging sources to get better estimates of these parameters instead of relying on the information from the BOLD signal only. The mulitmodal neuroimaging setup consisted of the information from Cerebral Blood Volume (CBV) ( VASO-Fluid-Attenuation-Inversion-Recovery (VASO-FLAIR)), and Cerebral Blood Flow (CBF) (from Arterial Spin Labelling (ASL)) in addition to the BOLD signal and the fusion of this information is achieved in a Particle Filter (PF) framework. The trace plots and the correlation coefficients of the parameter estimates from the PF reflect ill-posedness of the BOLD model. The means of the parameter estimates are much closer to the ground truth compared to the estimates obtained using only the BOLD information. These parameter estimates were also found to be more robust to noise and influence of the prior. / Master of Science

Traditional methods of analyzing functional Magnetic Resonance Images use a linear combination of just a few static regressors. This work demonstrates an alternative approach using a physiologically inspired nonlinear model. By using a particle filter to optimize the model parameters, the computation time is kept below a minute per voxel without requiring a linearization of the noise in the state variables. The activation results show regions similar to those found in Statistical Parametric Mapping; however, there are some notable regions not detected by that technique. Though the parameters selected by the particle filter based approach are more than sufficient to predict the Blood-Oxygen-Level-Dependent signal response, more model constraints are needed to uniquely identify a single set of parameters. This illposed nature explains the large discrepancies found in other research that attempted to characterize the model parameters. For this reason the final distribution of parameters is more medically relevant than a single estimate. Because the output of the particle filter is a full posterior probability, the reliance on the mean to estimate parameters is unnecessary. This work presents not just a viable alternative to the traditional method of detecting activation, but an extensible technique of estimating the joint probability distribution function of the Blood-Oxygen-Level-Dependent Signal parameters. / Master of Science

Yes / This paper presents a novel minimum entropy filter design for a class of stochastic nonlinear systems which are subjected to non-Gaussian noises. Motivated by stochastic distribution control, an output entropy model is developed using RBF neural network while the parameters of the model can be identified by the collected data. Based upon the presented model, the filtering problem has been investigated while the system dynamics have been represented. As the model output is the entropy of the estimation error, the optimal nonlinear filter is obtained based on the Lyapunov design which makes the model output minimum. Moreover, the entropy assignment problem has been discussed as an extension of the presented approach. To verify the presented design procedure, a numerical example is given which illustrates the effectiveness of the presented algorithm. The contributions of this paper can be included as 1) an output entropy model is presented using neural network; 2) a nonlinear filter design algorithm is developed as the main result and 3) a solution of entropy assignment problem is obtained which is an extension of the presented framework.

Yes / In this paper, a novel control algorithm is presented to enhance the performance of the tracking property for a class of nonlinear and dynamic stochastic systems subjected to non-Gaussian noises. Although the existing standard PI controller can be used to obtain the basic tracking of the systems, the desired tracking performance of the stochastic systems is difficult to achieve due to the random noises. To improve the tracking performance, an enhanced performance loop is constructed using the EKF-based state estimates without changing the existing closed loop with a PI controller. Meanwhile, the gain of the enhanced performance loop can be obtained based upon the entropy optimization of the tracking error. In addition, the stability of the closed loop system is analyzed in the mean-square sense. The simulation results are given to illustrate the effectiveness of the proposed control algorithm. / This work was supported in part by the PNNL Control of Complex Systems Initiative and in part by the National Natural Science Foundation of China under Grants 61621004,61573022 and 61333007.

Yes / This paper presents a novel minimum entropy control algorithm for a class of stochastic nonlinear systems subjected to non-Gaussian noises. The entropy control can be considered as an optimization problem for the system randomness attenuation, but the mean value has to be considered separately. To overcome this disadvantage, a new representation of the system stochastic properties was given using the cumulant-generating function based on the moment-generating function, in which the mean value and the entropy was reflected by the shape of the cumulant-generating function. Based on the samples of the system output and control input, a time-variant linear model was identified, and the minimum entropy optimization was transformed to system stabilization. Then, an optimal control strategy was developed to achieve the randomness attenuation, and the boundedness of the controlled system output was analyzed. The effectiveness of the presented control algorithm was demonstrated by a numerical example. In this paper, a data-driven minimum entropy design is presented without pre-knowledge of the system model; entropy optimization is achieved by the system stabilization approach in which the stochastic distribution control and minimum entropy are unified using the same identified structure; and a potential framework is obtained since all the existing system stabilization methods can be adopted to achieve the minimum entropy objective.

Trial and error and the use of highly time-consuming methods are often necessary for modeling, simulating and characterizing nonlinear dynamical systems. However, for the rather common special case when a nonlinear system has linear relations between many of its degrees of freedom there are particularly interesting opportunities for more efficient approaches. The aim of this thesis is to develop and validate new efficient methods for the theoretical and experimental study of mechanical systems that include significant zero-memory or hysteretic nonlinearities related to only small parts of the whole system. The basic idea is to take advantage of the fact that most of the system is linear and to use much of the linear theories behind forced response simulations. This is made possible by modeling the nonlinearities as external forces acting on the underlying linear system. The result is very fast simulation routines where the model is based on the residues and poles of the underlying linear system. These residues and poles can be obtained analytically, from finite element models or from experimental measurements, making these forced response routines very versatile. Using this approach, a complete nonlinear model contains both linear and nonlinear parts. Thus, it is also important to have robust and accurate methods for estimating both the linear and nonlinear system parameters from experimental data. The results of this work include robust and user-friendly routines based on sinusoidal and random noise excitation signals for characterization and description of nonlinearities from experimental measurements. These routines are used to create models of the studied systems. When combined with efficient simulation routines, complete tools are created which are both versatile and computationally inexpensive. The developed methods have been tested both by simulations and with experimental test rigs with promising results. This indicates that they are useful in practice and can provide a basis for future research and development of methods capable of handling more complex nonlinear systems.

<p>Nonlinear systems occur in industrial processes, economical systems, biotechnology and in many other areas. The thesis treats methods for system identification and control of such nonlinear systems, and applies the proposed methods to a solar heating/cooling plant. </p><p>Two applications, an anaerobic digestion process and a domestic solar heating system are first used to illustrate properties of an existing nonlinear recursive prediction error identification algorithm. In both cases, the accuracy of the obtained nonlinear black-box models are comparable to the results of application specific grey-box models. Next a convergence analysis is performed, where conditions for convergence are formulated. The results, together with the examples, indicate the need of a method for providing initial parameters for the nonlinear prediction error algorithm. Such a method is then suggested and shown to increase the usefulness of the prediction error algorithm, significantly decreasing the risk for convergence to suboptimal minimum points. </p><p>Next, the thesis treats model based control of systems with input signal dependent time delays. The approach taken is to develop a controller for systems with constant time delays, and embed it by input signal dependent resampling; the resampling acting as an interface between the system and the controller.</p><p>Finally a solar collector field for combined cooling and heating of office buildings is used to illustrate the system identification and control strategies discussed earlier in the thesis, the control objective being to control the solar collector output temperature. The system has nonlinear dynamic behavior and large flow dependent time delays. The simulated evaluation using measured disturbances confirm that the controller works as intended. A significant reduction of the impact of variations in solar radiation on the collector outlet temperature is achieved, though the limited control range of the system itself prevents full exploitation of the proposed feedforward control. The methods and results contribute to a better utilization of solar power.</p>