An investigation of techniques for nonlinear state observation

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 Master of Science in Engineering. Johannesburg, 2016An investigation and analysis of a collection of different techniques, for estimating the states of nonlinear systems, was undertaken. It was found that most of the existing literature on the topic could be organized into several groups of nonlinear observer design techniques, of which each group follows a specific concept and slight variations thereof. From out of this investigation it was discovered that a variation of the adaptive observer could be successfully applied to numerous nonlinear systems, given only limited output information. This particular technique formed the foundation on which a design procedure was developed in order to asymptotically estimate the states of nonlinear systems of a certain form, using only partial state information available. Lyapunov stability theory was used to prove the validity of this technique, given that certain conditions and assumptions are satisfied. A heuristic procedure was then developed to get a linearized model of the error transient behaviour that could form the upper bounds of the transient times of the observer. The technique above, characterized by a design algorithm, was then applied to three well-known nonlinear systems; namely the Lorenz attractor, the Rössler attractor, and the Van Der Pol oscillator. The results, illustrated through numerical simulation, clearly indicate that the technique developed is successful, provided all assumptions and conditions are satisfied.MT201

Modeling and Estimation of Biological Plants

Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants. After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model. The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios. Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure

A Hybrid Controller for Stability Robustness, Performance Robustness, and Disturbance Attenuation of a Maglev System

Devices using magnetic levitation (maglev) offer the potential for friction-free, high-speed, and high-precision operation. Applications include frictionless bearings, high-speed ground transportation systems, wafer distribution systems, high-precision positioning stages, and vibration isolation tables. Maglev systems rely on feedback controllers to maintain stable levitation. Designing such feedback controllers is challenging since mathematically the electromagnetic force is nonlinear and there is no local minimum point on the levitating force function. As a result, maglev systems are open-loop unstable. Additionally, maglev systems experience disturbances and system parameter variations (uncertainties) during operation. A successful controller design for maglev system guarantees stability during levitating despite system nonlinearity, and desirable system performance despite disturbances and system uncertainties. This research investigates five controllers that can achieve stable levitation: PD, PID, lead, model reference control, and LQR/LQG. It proposes an acceleration feedback controller (AFC) design that attenuates disturbance on a maglev system with a PD controller. This research proposes three robust controllers, QFT, Hinf , and QFT/Hinf , followed by a novel AFC-enhanced QFT/Hinf (AQH) controller. The AQH controller allows system robustness and disturbance attenuation to be achieved in one controller design. The controller designs are validated through simulations and experiments. In this research, the disturbances are represented by force disturbances on the levitated object, and the system uncertainties are represented by parameter variations. The experiments are conducted on a 1 DOF maglev testbed, with system performance including stability, disturbance rejection, and robustness being evaluated. Experiments show that the tested controllers can maintain stable levitation. Disturbance attenuation is achieved with the AFC. The robust controllers, QFT, Hinf , QFT/ Hinf, and AQH successfully guarantee system robustness. In addition, AQH controller provides the maglev system with a disturbance attenuation feature. The contributions of this research are the design and implementation of the acceleration feedback controller, the QFT/ Hinf , and the AQH controller. Disturbance attenuation and system robustness are achieved with these controllers. The controllers developed in this research are applicable to similar maglev systems

Vision in observers with enhanced S-cone syndrome: an excess of S-cones connected mainly to conventional S-cone pathways but also a faster pathway

Purpose: The effect of increased numbers of S-cone photoreceptors in enhanced S-cone syndrome (ESCS) was investigated psychophysically in six ESCS observers to understand more about the relative cone sensitivities and postreceptoral organization. Methods: Measures of temporal sensitivity or delay were made: S- and L-cone temporal acuity (critical flicker fusion or cff), S-cone temporal contrast sensitivity, and S-cone delay. Results: ESCS observers showed uniform enhancements of S-cone cff of between 0.85 and 6.25 Hz, but reductions in L-cone cff. They also showed higher S-cone temporal-contrast-sensitivities at medium and high S-cone adaptation levels with sensitivity functions that peaked near 7.5 Hz but fell off at lower and higher frequencies; in contrast, the mean normal function was flat at low frequencies and fell-off only at high frequencies. The S-cone signal, as in the normal, is subject to large phase delays. Conclusions: We interpret the enhancements in cff as increases in S-cone number in ESCS of between 1.39 and 11.32 times normal density (with a mean of 3.48). The peaked ESCS contrast-sensitivity functions are consistent with S-cone signal interactions that increase sensitivity at intermediate frequencies through constructive interference but decrease it at lower and higher frequencies through destructive interference. Measures of S-cone delays relative to L- and M-cone signals show that the predominant S-cone signals in ESCS are negative and delayed as in normal observers, but reveal another faster, positive S-cone signal. This signal is also likely to be the cause of constructive and destructive interference in the contrast-sensitivity data of ESCS observers

Visual Psychophysics and Physiological Optics Vision in Observers With Enhanced S-Cone Syndrome: An Excess of S-Cones but Connected Mainly to Conventional S-Cone Pathways

Citation: Ripamonti C, Aboshiha J, Henning GB, et al. Vision in observers with enhanced S-cone syndrome: an excess of S-cones but connected mainly to conventional S-cone pathways. Invest Ophthalmol Vis Sci. 2014;55:963-976. DOI:10.1167/iovs. 13-12897 PURPOSE. The effect of increased numbers of S-cone photoreceptors in enhanced S-cone syndrome (ESCS) was investigated psychophysically in six ESCS observers to understand more about relative cone sensitivities and postreceptoral organization. METHODS. Measures of temporal sensitivity or delay were made: S-and L-cone temporal acuity (critical flicker fusion, or CFF), S-cone temporal contrast sensitivity, and S-cone delay. RESULTS. ESCS observers showed uniform enhancements of S-cone CFF of between 0.85 and 6.25 Hz, but reductions in L-cone CFF. They also showed higher S-cone temporal contrast sensitivities at medium and high S-cone adaptation levels, with sensitivity functions that peaked near 7.5 Hz but fell off at lower and higher frequencies. In contrast, the mean normal function was flat at low frequencies and fell off only at high frequencies. The S-cone signal, as in the normal, is subject to large phase delays. CONCLUSIONS. We interpret the enhancements in CFF as increases in S-cone number in ESCS of between 1.39 and 11.32 times normal density (with a mean of 3.48). The peaked ESCS contrast-sensitivity functions are consistent with S-cone signal interactions that increase sensitivity at intermediate frequencies through constructive interference but decrease it at lower and higher frequencies through destructive interference. Measurements of S-cone delays relative to L-and M-cone signals show that the predominant S-cone signals in ESCS are negative and delayed as in normal observers, but reveal another faster, positive S-cone signal. This signal is also likely to be the cause of constructive and destructive interference in the contrast-sensitivity data of ESCS observers Keywords: enhanced S-cone syndrome, flicker sensitivity, critical flicker fusion, temporal processing, NR2E3, temporal acuity, short-wavelength-sensitive cones. E nhanced S-cone syndrome (ESCS) is a rare inherited degenerative retinal disease named after the associated unusual gain in function-an increase in short-wavelengthsensitive (S) cone sensitivity. 1 The syndrome is also characterized by severely reduced rod sensitivity (night blindness), foveal schisis and macular cysts, varying degree of visual acuity loss, and atypical ERGs that show little or no responses to dim rod (scotopic) stimuli, but have large, slow responses to brighter cone (photopic) stimuli. 1-4 The photopic ERG was originally thought to be of rod origin, 5-7 but spectral measurements have shown that it is dominated by S-cones with reduced contributions from long-and middle-wavelength-sensitive (L and M) cones. 9,10,12 Hood et al. 10 More direct evidence for a relative increase in the number of Scones was provided by histological examination of a disordered ESCS retina of a 77-year-old woman, 12 in which twice the normal number of cones was found, 92% of which were Scones. A more recent study used adaptive optics imaging to attempt to visualize individual cones directly in vivo in three young adults with ESCS. The excess of S-cones can be related to a molecular defect. The gene NR2E3 codes for a photoreceptor-specific nuclear receptor NR2E