Model-Based and Machine Learning-Based Control of Biological Oscillators

Nonlinear oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. This dissertation investigates the dynamics of such oscillators arising in biology, and develops several control algorithms to modify their collective behavior. We demonstrate that these control algorithms have potential in devising treatments for Parkinson's disease, cardiac alternans, and jet lag. Phase reduction, a classical reduction technique, has been instrumental in understanding such biological oscillators. In this dissertation, we investigate a new reduction technique called augmented phase reduction, and calculate its associated analytical expressions for six dynamically different planar systems: This helps us to understand the dynamical regimes for which the use of augmented phase reduction is advantageous over the standard phase reduction. We further this study by developing a novel optimal control algorithm based on the augmented phase reduction to change the phase of a single oscillator using a minimum energy input. We show that our control algorithm is effective even when a large phase change is required or when the nontrivial Floquet multiplier of the oscillator is close to unity; in such cases, the previously proposed control algorithm based on the standard phase reduction fails.We then devise a novel framework to control a population of biological oscillators as a whole, and change their collective behavior. Our first two control algorithms are Lyapunov-based, and our third is an optimal control algorithm which minimizes the control energy consumption while achieving the desired collective behavior of an oscillator population. We show that the developed control algorithms can synchronize, desynchronize, cluster, and phase shift the population.We continue this investigation by developing two novel machine learning control algorithms, which have a simple and intelligent structure that makes them effective even with a sparse data set. We show that these algorithms are powerful enough to control a wide variety of dynamical systems and not just biological oscillators. We conclude this study by understanding how the developed machine learning algorithms work in terms of phase reduction.In this dissertation, we have developed all these algorithms with the goal of ease of experimental implementation, for which the model parameters/training data can be measured experimentally. We close the loop on this dissertation by carrying out robustness analysis for the developed algorithms; demonstrating their resilience to noise, and thus their suitability for controlling living biological tissue. They truly hold great potential in devising treatments for Parkinson's disease, cardiac alternans, and jet lag

Numerical and experimental studies of stick-slip oscillations in drill-strings.

The cyclic nature of the stick-slip phenomenon may cause catastrophic failures in drill-strings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stick-slip, in order to develop appropriate control methods for suppression. This paper studies the stick-slip oscillations encountered in drill-strings from both numerical and experimental points of view. The numerical part is carried out based on path-following methods for non-smooth dynamical systems, with a special focus on the multistability in drill-strings. Our analysis shows that, under a certain parameter window, the multistability can be used to steer the response of the drill-strings from a sticking equilibrium or stick-slip oscillation to an equilibrium with constant drill-bit rotation. In addition, a small-scale downhole drilling rig was implemented to conduct a parametric study of the stick-slip phenomenon. The parametric study involves the use of two flexible shafts with varying mechanical properties to observe the effects that would have on stick-slip during operation. Our experimental results demonstrate that varying some of the mechanical properties of the drill-string could in fact control the nature of stick-slip oscillations

Self-oscillations in an Alpha Stirling Engine: a bifurcation analysis

We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provide a dynamic relation between the forces and the angle, ultimately leading to a closed dynamical model. We are interested in the different behaviors that the engine displays as parameters are varied. The temperature of the hot piston and the mechanical phase between both pistons constitute our bifurcation parameters. Considering that energy conversion in the engine can only take place through cyclic motions, we are particularly interested in the appearance of limit cycles.Comment: To be submitte

Dynamics and Control of Nonholonomic Systems with Internal Degrees of Freedom

Nonholonomic systems model many robots as well as animals and other systems. Although such systems have been studied extensively over the last century, much work still remains to be done on their dynamics and control. Many techniques have been developed for controlling kinematic nonholonomic systems or simplified dynamic versions, however control of high dimensional, underactuated nonholonomic systems remains to be addressed. This dissertation helps fill this gap by developing a control algorithm that can be applied to systems with three or more configuration variables and just one input. We also analyze the dynamic effects of passive degrees of freedom and elastic potentials which are commonly observed in such systems showing that the addition of a passive degree of freedom can even be used to improve the locomotion characteristics of a system. Such elastic potentials can be present due to compliant mechanisms or origami, both of which can exhibit bistability and many other properties that can be useful in the design of robots

Control of limit cycling in frictional mechanical systems

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Torsional stick-slip vibrations and multistability in drill-strings

This is the final version. Available on open access from Elsevier via the DOI in this recordData accessibility: The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.The generalized lumped-parameter model of the drill-string system is studied in this paper to provide a fundamental understanding of the torsional stick-slip vibrations in downhole drilling. Our investigation focuses on analysing the cause of three coexisting states: bit sticking, stick-slip vibration, and constant rotation. A critical region of multistability is identified based on the lumped-parameter model, and the conditions for switching between these multiple stable states are discussed. Special attention is given to the bifurcation structure of the considered drill-string model, which is obtained via path-following methods for nonsmooth dynamical systems. The bifurcation scenario is compared to the case when a longer drill-string is considered, which amounts to drilling deeper. It is found that the main features of the bifurcation picture persist under variation of the drill-string length, with certain numerical differences regarding for instance the window of multistability.Engineering and Physical Sciences Research Council (EPSRC)National Natural Science Foundation of ChinaChina Scholarship Counci

On the nonlinear dynamics of automated vehicles - A nonholonomic approach

A simple mechanical model for the lateral and yaw motion of a vehicle is presented while taking into account rolling constraints. The governing equations are derived by utilizing the Appellian framework. Analytical and numerical bifurcation analysis is performed while utilizing a PD controller. The results provide insight into the local and global stability of forward and reverse motion of automated passenger vehicles and harvesters

Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle

This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio

Stick-slip suppression and speed tuning for a drill-string system via proportional-derivative control

This is the final version. Available from Elsevier via the DOI in this record. This paper studies the problems of stick-slip mitigation and speed tuning for a lumped-parameter drill-string system by using a proportional-derivative feedback controller via path-following analysis. In this study, we consider two main control parameters, the weight-on-bit and the desired drill-bit speed, which in general differs from the real angular speed. In particular, we determine the combinations of these two parameters for which the proposed control scheme is applicable, which is affected by the non-smooth nature of the system induced by bit-rock interaction. Our analysis using path-following techniques for non-smooth systems reveals the inherent coexistence of stick-slip vibration and constant rotation, and identifies a critical point where the drill-bit speed coincides with the desired angular speed. Furthermore, our analysis proposes a strategy that allows controlling the drill-bit speed to suppress stick-slip, by tuning the controller in a suitable manner.Engineering and Physical Sciences Research Council (EPSRC