6,165 research outputs found
Homogeneity in the bi-limit as a tool for observer and feedback design
International audienceWe introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system
Stabilization via generalized homogeneous approximations
We introduce a notion of generalized homogeneous approximation at the origin and at infinity which extends the classical notions and captures a large class of nonlinear systems, including (lower and upper) triangular systems. Exploiting this extension and although this extension does not preserve the basic properties of the classical notion, we give basic results concerning stabilization and robustness of nonlinear systems, by designing a homogeneous (in the generalized sense) feedback controller which globally asymptotically stabilizes a chain of power integrators and makes it the dominant part at infinity and at the origin (in the generalized sense) of the dynamics. Stability against nonlinear perturbation follows from domination arguments
Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.
This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation.
In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems.
In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties
An Experimental Study of Research Self-Efficacy In Master’s Students
Engaging master’s counseling students in the research literature and facilitating an environment that strengthens their research identity development are necessities for counselor educators. This need is juxtaposed with over 20 years of research, which found that counseling students appeared to lack confidence and have low interest in this topic (Gelso, Baumann, Chui, & Savela, 2013; Phillips & Russell, 1994). Low research self-efficacy was presented as an important explanatory factor. Thus, this experimental study deployed a pedagogical intervention based on the work of Albert Bandura and his social learning theory. Two sections of the required research course in a southeastern university CACREP counseling program was taught at the same time and day by two instructors. One instructor facilitated the course curriculum to the intervention group based on an experimenter-created self-efficacy pedagogy. The other instructor taught the content to the comparison group using standard pedagogical methods. Students were assessed using two measures: a well-known research self-efficacy scale (RSE; Holden, Barker, Meenaghan, & Rosenberg, 1999) and a researcher-developed knowledge questionnaire. The researcher hypothesized that from pre- to post-test, the intervention would contribute to significantly increasing the research self-efficacy and knowledge scores of the experimental group over and above the scores of the comparison group. Group differences were tested using ANOVAs with repeated measures. Salient findings were: RSE was shown to be a reliable tool to measure research self-efficacy, a significant relationship existed between students’ research knowledge and self-efficacy, pedagogical techniques seemed to aid the process of students’ knowledge acquisition and increased self-efficacy, research experiences outside of the classroom influenced research self-efficacy scores, and when in matriculation students take a research course appeared to influence research self-efficacy. The results offer counseling departments suggestions of how to prepare professional counselors that are skilled to act ethically (ACA, 2014), and enact the 20/20 vision (Kaplan & Gladding, 2011), as they relate to research. Implications for theory and practice are discussed in Chapter 5
Control techniques for mechatronic assisted surgery
The treatment response for traumatic head injured patients can be improved by
using an autonomous robotic system to perform basic, time-critical emergency neurosurgery,
reducing costs and saving lives. In this thesis, a concept for a neurosurgical robotic system is proposed to perform three specific emergency neurosurgical procedures; they are the placement of an intracranial pressure monitor, external
ventricular drainage, and the evacuation of chronic subdural haematoma. The control
methods for this system are investigated following a curiosity led approach. Individual problems are interpreted in the widest sense and solutions posed that are general in nature. Three main contributions result from this approach: 1)
a clinical evidence based review of surgical robotics and a methodology to assist in their evaluation, 2) a new controller for soft-grasping of objects, and 3) new propositions and theorems for chatter suppression sliding mode controllers. These contributions directly assist in the design of the control system of the neurosurgical robot and, more broadly, impact other areas outside the narrow con nes of the target application. A methodology for applied research in surgical robotics is proposed. The methodology sets out a hierarchy of criteria consisting of three tiers, with the most important being the bottom tier and the least being the top tier. It is argued that
a robotic system must adhere to these criteria in order to achieve acceptability. Recent commercial systems are reviewed against these criteria, and are found to conform up to at least the bottom and intermediate tiers. However, the lack of
conformity to the criteria in the top tier, combined with the inability to conclusively
prove increased clinical benefit, particularly symptomatic benefit, is shown to be hampering the potential of surgical robotics in gaining wide establishment. A control scheme for soft-grasping objects is presented. Grasping a soft or fragile object requires the use of minimum contact force to prevent damage or deformation. Without precise knowledge of object parameters, real-time feedback
control must be used to regulate the contact force and prevent slip. Moreover, the controller must be designed to have good performance characteristics to rapidly modulate the fingertip contact force in response to a slip event. A fuzzy sliding mode controller combined with a disturbance observer is proposed for contact force control and slip prevention. The robustness of the controller is evaluated through
both simulation and experiment. The control scheme was found to be effective and robust to parameter uncertainty. When tested on a real system, however, chattering phenomena, well known to sliding mode research, was induced by the
unmodelled suboptimal components of the system (filtering, backlash, and time delays). This reduced the controller performance. The problem of chattering and potential solutions are explored. Real systems using sliding mode controllers, such as the control scheme for soft-grasping, have a tendency to chatter at high frequencies. This is caused by the sliding mode
controller interacting with un-modelled parasitic dynamics at the actuator-input
and sensor-output of the plant. As a result, new chatter-suppression sliding mode controllers have been developed, which introduce new parameters into the system. However, the effect any particular choice of parameters has on system performance
is unclear, and this can make tuning the parameters to meet a set of performance
criteria di cult. In this thesis, common chatter-suppression sliding mode control
strategies are surveyed and simple design and estimation methods are proposed.
The estimation methods predict convergence, chattering amplitude, settling time,
and maximum output bounds (overshoot) using harmonic linearizations and invariant
ellipsoid sets
ESTIMATION AND CONTROL OF NONLINEAR SYSTEMS: MODEL-BASED AND MODEL-FREE APPROACHES
State estimation and subsequent controller design for a general nonlinear system is an
important problem that have been studied over the past decades. Many applications,
e.g., atmospheric and oceanic sampling or lift control of an airfoil, display strongly nonlinear
dynamics with very high dimensionality. Some of these applications use smaller
underwater or aerial sensing platforms with insufficient on-board computation power to
use a Monte-Carlo approach of particle filters. Hence, they need a computationally efficient
filtering method for state-estimation without a severe penalty on the performance.
On the other hand, the difficulty of obtaining a reliable model of the underlying system,
e.g., a high-dimensional fluid dynamical environment or vehicle flow in a complex
traffic network, calls for the design of a data-driven estimation and controller when abundant
measurements are present from a variety of sensors. This dissertation places these
problems in two broad categories: model-based and model-free estimation and output
feedback.
In the first part of the dissertation, a semi-parametric method with Gaussian mixture
model (GMM) is used to approximate the unknown density of states. Then a Kalman
filter and its nonlinear variants are employed to propagate and update each Gaussian
mode with a Bayesian update rule. The linear observation model permits a Kalman
filter covariance update for each Gaussian mode. The estimation error is shown to be
stochastically bounded and this is illustrated numerically. The estimate is used in an
observer-based feedback control to stabilize a general closed-loop system. A transferoperator-
based approach is then proposed for the motion update for Bayesian filtering
of a nonlinear system. A finite-dimensional approximation of the Perron-Frobenius (PF)
operator yields a method called constrained Ulam dynamic mode decomposition (CUDMD).
This algorithm is applied for output feedback of a pitching airfoil in unsteady
flow.
For the second part, an echo-state network (ESN) based approach equipped with an
ensemble Kalman filter is proposed for data-driven estimation of a nonlinear system from
a time series. A random reservoir of recurrent neural connections with the echo-state
property (ESP) is trained from a time-series data. It is then used as a model-predictor for
an ensemble Kalman filter for sparse estimation. The proposed data-driven estimation
method is applied to predict the traffic flow from a set of mobility data of the UMD
campus. A data-driven model-identification and controller design is also developed for
control-affine nonlinear systems that are ubiquitous in several aerospace applications. We
seek to find an approximate linear/bilinear representation of these nonlinear systems from
data using the extended dynamic mode decomposition algorithm (EDMD) and apply Liealgebraic
methods to analyze the controllability and design a controller. The proposed
method utilizes the Koopman canonical transform (KCT) to approximate the dynamics
into a bilinear system (Koopman bilinear form) under certain assumptions. The accuracy
of this approximation is then analytically justified with the universal approximation
property of the Koopman eigenfunctions. The resulting bilinear system is then subjected
to controllability analysis using the Myhill semigroup and Lie algebraic structures, and a
fixed endpoint optimal controller is designed using the Pontryagin’s principle
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