Stability and Stabilization of Systems with Time Delay: Limitations and Opportunities

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Bounded Control of the Kuramoto-Sivashinsky equation

Feedback control is used in almost every aspect of modern life and is essential in almost all engineering systems. Since no mathematical model is perfect and disturbances occur frequently, feedback is required. The design of a feedback control has been widely investigated in finite-dimensional space. However, many systems of interest, such as fluid flow and large structural vibrations are described by nonlinear partial differential equations and their state evolves on an infinite-dimensional Hilbert space. Developing controller design methods for nonlinear infinite-dimensional systems is not trivial. The objectives of this thesis are divided into multiple tasks. First, the well-posedness of some classes of nonlinear partial differential equations defined on a Hilbert space are investigated. The following nonlinear affine system defined on the Hilbert space H is considered z ̇(t)=F(z(t))+Bu(t), t≥0 z (0) = z0, where z(t) ∈ H is the state vector and z0 is the initial condition. The vector u(t) ∈ U, where U is a Hilbert space, is a state-feedback control. The nonlinear operator F : D ⊂ H → H is densely defined in H and the linear operator B : U → H is a linear bounded operator. Conditions for the closed-loop system to have a unique solution in the Hilbert space H are given. Next, finding a single bounded state-feedback control for nonlinear partial differential equations is discussed. In particular, Lyapunov-indirect method is considered to control nonlinear infinite-dimensional systems and conditions on when this method achieves the goal of local asymptotic stabilization of the nonlinear infinite-dimensional system are given. The Kuramoto-Sivashinsky (KS) equation defined in the Hilbert space L2(−π,π) with periodic boundary conditions is considered. ∂z/∂t =−ν∂4z/∂x4 −∂2z/∂x2 −z∂z/∂x, t≥0 z (0) = z0 (x) , where the instability parameter ν > 0. The KS equation is a nonlinear partial differential equation that is first-order in time and fourth-order in space. It models reaction-diffusion systems and is related to various pattern formation phenomena where turbulence or chaos appear. For instance, it models long wave motions of a liquid film over a vertical plane. When the instability parameter ν < 1, this equation becomes unstable. This is shown by analyzing the stability of the linearized system and showing that the nonlinear C0- semigroup corresponding to the nonlinear KS equation is Fr ́echet differentiable. There are a number of papers establishing the stabilization of this equation via boundary control. In this thesis, we consider distributed control with a single bounded feedback control for the KS equation with periodic boundary conditions. First, it is shown that sta- bilizing the linearized KS equation implies local asymptotical stability of the nonlinear KS equation. This is done by establishing Fr ́echet differentiability of the associated nonlinear C0-semigroup and showing that it is equal to the linear C0-semigroup generated by the linearization of the equation. Next, a single state-feedback control that locally asymptot- ically stabilizes the KS equation is constructed. The same approach to stabilize the KS equation from one equilibrium point to another is used. Finally, the solution of the uncontrolled/state-feedback controlled KS equation is ap- proximated numerically. This is done using the Galerkin projection method to approximate infinite-dimensional systems. The numerical simulations indicate that the proposed Lyapunov-indirect method works in stabilizing the KS equation to a desired state. Moreover, the same approach can be used to stabilize the KS equation from one constant equilibrium state to another

ヒ ホロノミック イドウ ロボット シャ ノ ギジ レンゾク シスウ アンテイカ セイギョ 二 カンスル ケンキュウ

博士(工学)佐賀大

Experimental setup for fast BEC generation and number-stabilized atomic ensembles

Ultracold atomic ensembles represent a cornerstone of today’s modern quantum experiments. In particular, the generation of Bose-Einstein condensates (BECs) has paved the way for a myriad of fundamental research topics as well as novel experimental concepts and related applications. As coherent matter waves, BECs promise to be a valuable resource for atom interferometry that allows for high-precision sensing of gravitational fields or inertial moments as accelerations and rotations. In general, the sensitivity of state-of-the-art atom interferometers is fundamentally restricted by the Standard Quantum Limit (SQL). Multi-particle entangled states (e.g. spin-squeezed states, Twin-Fock states, Schrödinger cat states) generated in BECs can be employed to surpass the SQL and shift the sensitivity limit further towards the more fundamental Heisenberg Limit (HL). However, in current real-world atom interferometric applications, ultracold but uncondensed atomic clouds are employed, due to their speed advantage in the sample preparation. The creation of a BEC can take up several tens of seconds, while standard high-precision atom interferometers operate with a cycle rate of several Hz. In addition, the pursued entangled states can be only beneficial if technical noise sources, such as magnetic field or detection noise are not dominating the measurement resolution. These challenges need to be overcome in order to fully exploit the potential sensitivity gain offered by a quantum-enhanced atom interferometer. This thesis describes the design and implementation of a new experimental setup for Heisenberg-limited atom interferometry, which incorporates a high-flux BEC source and the manipulation and detection of atoms at the single-particle level. The presented fast BEC preparation includes a high-flux atom source in a double magneto-optical trap (MOT) configuration that allows to collect 87Rb atoms in a 3D-MOT, which is supplied by a 2D+-MOT with 2×10^10 atoms/s. Forced evaporative cooling of the atoms is divided into two stages, which is sequentially carried out in a magnetic quadrupole trap (QPT) and a crossed-beam optical dipole trap (cODT). The high-flux atom source together with the hybrid evaporation scheme allows to consistently produce BECs with an average of 2×10^5 atoms within 3.5 s. The capabilities of the single-particle resolving detection are demonstrated by realizing a feedback control loop to stabilize the captured number of atoms in a small MOT. A proof-of-principle measurement is demonstrated for the successful stabilization of a target number of 7 atoms with sub-Poissonian fluctuations. The number noise is suppressed by 18 dB below shot noise, which corresponds to a preparation fidelity of 92%. Based on this success, the thesis presents an even improved single-particle resolution. The system comprises a six-channel fiber-based optical setup, which provides independent intensity stabilization and frequency detuning, improved pointing stability as well as a better spatial overlap of the MOT beams. The presented high-speed BEC production combined with accurate atom number preparation and detection, as the two main features of the experimental apparatus, pave the way for a future entanglement-enhanced performance of atom interferometers

Advances in Spacecraft Systems and Orbit Determination

"Advances in Spacecraft Systems and Orbit Determinations", discusses the development of new technologies and the limitations of the present technology, used for interplanetary missions. Various experts have contributed to develop the bridge between present limitations and technology growth to overcome the limitations. Key features of this book inform us about the orbit determination techniques based on a smooth research based on astrophysics. The book also provides a detailed overview on Spacecraft Systems including reliability of low-cost AOCS, sliding mode controlling and a new view on attitude controller design based on sliding mode, with thrusters. It also provides a technological roadmap for HVAC optimization. The book also gives an excellent overview of resolving the difficulties for interplanetary missions with the comparison of present technologies and new advancements. Overall, this will be very much interesting book to explore the roadmap of technological growth in spacecraft systems