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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.

Bilinear systems are a class of nonlinear dynamical systems that arise in a variety of applications. In order to obtain a sufficiently accurate representation of the underlying physical phenomenon, these models frequently have state-spaces of very large dimension, resulting in the need for model reduction. In this work, we introduce two new methods for the model reduction of bilinear systems in an interpolation framework. Our first approach is to construct reduced models that satisfy multipoint interpolation constraints defined on the Volterra kernels of the full model. We show that this approach can be used to develop an asymptotically optimal solution to the H_2 model reduction problem for bilinear systems. In our second approach, we construct a solution to a bilinear system realization problem posed in terms of constructing a bilinear realization whose kth-order transfer functions satisfy interpolation conditions in k complex variables. The solution to this realization problem can be used to construct a bilinear system realization directly from sampling data on the kth-order transfer functions, without requiring the formation of the realization matrices for the full bilinear system. / Ph. D.

The author proposes a novel functional regression method for parameter estimation and adaptive control in this dissertation. In the functional regression method, the regressors and a signal which contains the information of the unknown parameters are either determined from raw measurements or calculated as the functions of the measurements. The novel feature of the method is that the algorithm maps the regressors to the functionals which are represented in terms of customized test functions. The functionals are updated continuously by the evolution laws, and only an infinite number of variables are needed to compute the functionals. These functionals are organized as the entries of a matrix, and the parameter estimates are obtained using either the generalized inverse method or the transpose method. It is shown that the schemes of some conventional adaptive methods are recaptured if certain test function designs are employed. It is proved that the functional regression method guarantees asymptotic convergence of the parameter estimation error to the origin, if the system is persistently excited. More importantly, in contrast to the conventional schemes, the parameter estimation error may be expected to converge to the origin even when the system is not persistently excited. The novel adaptive method are also applied to the Model Reference Adaptive Controller (MRAC) and adaptive observer. It is shown that the functional regression method ensures asymptotic stability of the closed loop systems. Additionally, the studies indicate that the transient performance of the closed loop systems is improved compared to that of the schemes using the conventional adaptive methods. Besides, it is possible to analyze the transient responses a priori of the closed loop systems with the functional regression method. The simulations verify the theoretical analyses and exhibit the improved transient and steady state performances of the closed loop systems. / Ph. D.

The automation of scientific discovery has been an active research topic for many years. The promise of a formalized approach to developing and testing scientific hypotheses has attracted researchers from the sciences, machine learning, and philosophy alike. Leveraging the concept of dynamical symmetries a new paradigm is proposed for the collection of scientific knowledge, and algorithms are presented for the development of EUGENE – an automated scientific discovery tool-set. These algorithms have direct applications in model validation, time series analysis, and system identification. Further, the EUGENE tool-set provides a novel metric of dynamical similarity that would allow a system to be clustered into its dynamical regimes. This dynamical distance is sensitive to the presence of chaos, effective order, and nonlinearity. I discuss the history and background of these algorithms, provide examples of their behavior, and present their use for exploring system dynamics. / Master of Science / Determining why a system exhibits a particular behavior can be a difficult task. Some turn to causal analysis to show what particular variables lead to what outcomes, but this can be time-consuming, requires precise knowledge of the system’s internals, and often abstracts poorly to salient behaviors. Others attempt to build models from the principles of the system, or try to learn models from observations of the system, but these models can miss important interactions between variables, and often have difficulty recreating high-level behaviors. To help scientists understand systems better, an algorithm has been developed that estimates how similar the causes of one system’s behaviors are to the causes of another. This similarity between two systems is called their ”dynamical distance” from each other, and can be used to validate models, detect anomalies in a system, and explore how complex systems work.

A parametric identification procedure is proposed that combines the method of multiple scales and higher-order statistics to efficiently and accurately model nonlinear systems. A theoretical background for the method of multiple scales and higher-order statistics is given. Validation of the procedure is performed through applying it to numerical simulations of two nonlinear systems. The results show how the procedure can successfully characterize the system damping and nonlinearities and determine the corresponding parameters. The procedure is then applied to experimental measurements from two structural systems, a cantilevered beam and a three-beam frame. The results show that quadratic damping should be accounted for in both systems. Moreover, for the three-beam frame, the parametric excitation is much more important than the direct excitation. To show the flexibility of the procedure, numerical simulations of ship motion under parametric excitation are used to determine nonlinear parameters govening the relation between pitch, heave, and roll motions. The results show a high level of agreement between the numerical simulation and the mathematical model with the identified parameters. / Master of Science

A promising approach to treat patients with vocal fold paralysis using electrical stimulation is investigated throughout this research work. Functional Electrical Stimulation works by stimulating the atrophied muscle or group of muscles directly by current when the transmission lines between the central nervous system are disrupted. This technique helps maintain muscle mass and promote blood flow in the absence of a functioning nervous system. The goal of this work is two-fold: develop control techniques for muscle contraction to optimize muscle stimulation and develop a small-scale electromagnetic system to provide stimulation to the laryngeal muscles for patients with vocal fold paralysis. These studies; therefore, focus on assessing a linear Proportional-Integral (PI) controller and two nonlinear controllers: Model Reference Adaptive Controller (MRAC) and an Adaptive Augmented PI (ADP-PI) system to identify the most appropriate controller providing effective stimulation of the muscle. Direct stimulation is applied to mouse skeletal muscle in vitro to test the controllers along with numerical simulations for validation of these experimental tests. The experiments included muscle contractions following four distinct trajectories: a step, sine, ramp, and square wave. Overall, the closed-loop controllers followed the stimulation trajectories set for all the simulated and tested muscles. When comparing the experimental outcomes of each controller, we concluded that the ADP-PI algorithm provided the best closed-loop performance for speed of convergence and disturbance rejection. Next, the focus of the research work was on the implementation of an electromagnetic system to generate appropriate currents of stimulation using the aforementioned controllers. For this study, Nickel-Titanium shape memory alloys were used to assess activation (contraction) through a two-coil system guided by the controllers. The application of the two-coil system demonstrated the effectiveness of the approach and a main effect was observed between the PI, MRAC, and ADP-PI controllers when following the trajectories. Lastly, a small scale two-coil system is developed for animal testing in the muscle-mass-spring setup. Experiments were successful in generating the appropriate stimulation controlled by the output-based algorithms for muscle contraction. Trials conducted for this study were compared to the muscle contractions observed in the first study. The controllers were able to provide appropriate stimulation to the muscle system to follow the set trajectories: a step, ramp, and sinusoidal input. More trials are required to draw statistical conclusions about the performance of each controller. Regardless, the small-scale two-coil system along with the applied controllers can be reconfigured to be an implantable system and tested for appropriate stimulation of the laryngeal muscles. / Ph. D.