Switching control of quantum dynamics

This work introduces a solution based on switching techniques for controlling open quantum systems. Assuming the existence of a shared steady state for a set of marginally stable generators of quantum Markov semigroups, we propose algorithms for asymptotically stabilizing such state by suitably switching between the dynamical generators

Stability analysis and controller synthesis for a class of piecewise smooth systems

This thesis deals with the analysis and synthesis of piecewise smooth (PWS) systems. In general, PWS systems are nonsmooth systems, which means their vector fields are discontinuous functions of the state vector. Dynamic behavior of nonsmooth systems is richer than smooth systems. For example, there are phenomena such as sliding modes that occur only in nonsmooth systems. In this thesis, a Lyapunov stability theorem is proved to provide the theoretical framework for the stability analysis of PWS systems. Piecewise affine (PWA) and piecewise polynomial (PWP) systems are then introduced as important subclasses of PWS systems. The objective of this thesis is to propose efficient computational controller synthesis methods for PWA and PWP systems. Three synthesis methods are presented in this thesis. The first method extends linear controllers for uncertain nonlinear systems to PWA controllers. The result is a PWA controller that maintains the performance of the linear controller while extending its region of convergence. However, the synthesis problem for the first method is formulated as a set of bilinear matrix inequalities (BMIs), which are not easy to solve. Two controller synthesis methods are then presented to formulate PWA and PWP controller synthesis as convex problems, which are numerically tractable. Finally, to address practical implementation issues, a time-delay approach to stability analysis of sampled-data PWA systems is presented. The proposed method calculates the maximum sampling time for a sampled-data PWA system consisting of a continuous-time plant and a discrete-time emulation of a continuous-time PWA state feedback controller

On the synthesis of switched output feedback controllers for linear, time-invariant systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 189-193).The theory of switching systems has seen many advances in the past decade. Its beginnings were founded primarily due to the physical limitations in devices to implement control such as relays, but today there exists a strong interest in the development of switching systems where switching is introduced as a means of increasing performance. With the newer set of problems that arise from this viewpoint comes the need for many new tools for analysis and design. Analysis tools which include, for instance, the celebrated work on multiple Lyapunov functions are extensive. Tools for the design of switched systems also exist, but, in many cases, the method of designing stabilizing switching laws is often a separate process from the method which is used to determine the set of vector fields between which switching takes place. For instance, one typical method of designing switching controllers for linear, time-invariant (LTI) systems is to first design a set of stabilizing LTI controllers using standard LTI methods, and then design a switching law to increase performance. While such design algorithms can lead to increases in performance, they often impose restrictions that do not allow the designer to take full advantage of the switching architecture being considered.(cont.) For instance, if one switches between controllers that are individually stabilizing (without any switching), then, effectively, one is forced to switch only between stable systems and, hence, cannot take advantage of the potential benefits of switching between unstable systems in a stable way. It is, therefore, natural to wonder whether design algorithms can be developed which simultaneously design both the set of controllers to be switched and a stabilizing switching law. The work investigated here attempts to take a small step in the above direction. We consider a simple switching architecture that implements switched proportional gain control for second order LTI systems. Examination of this particular structure is motivated by its mathematical simplicity for ease of analysis (and, hence, as a means of gaining insight into the problem-at-large), but, as we will see, the design techniques investigated here can be extended to a larger class of (higher order, potentially non-linear and/or time-varying) systems using standard tools from robust control. The overall problem we investigate is the ability to create algorithms to simultaneously determine a set of switching gains and an associated switching law for a particular plant and performance objective.(cont.) After determining a set of necessary and sufficient conditions for a given second order plant to be stabilizable via the given switching architecture, we synthesize an algorithm for constructing controllers for which the corresponding closed-loop system dynamics are finite L, gain stable. Also, in an effort to demonstrate that the the given structure can, in fact. he used to increase performance. we consider a step-tracking design problem for a class of plants, where we use overshoot and settling time of the output step response to measure performance. We compare the results obtained using our switching architecture to the performance that can be obtained via two other LTI controller architectures to illustrate some of the performance benefits.by Keith Robert Santarelli.Ph.D

FEEDBACK CONTROL OF QUANTUM SYSTEMS AND ENTANGLEMENT

Ph.DDOCTOR OF PHILOSOPH

Robust adaptive control of switched systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 141-149).In this thesis, robust adaptive controllers are developed for classes of switched nonlinear systems. Switched systems are those governed by differential equations, which undergo vector field switching due to sudden changes in model characteristics. Such systems arise in many applications such as mechanical systems with contacts, electrical systems with switches, and thermal-fluidic systems with valves and phase changes. The presented controllers guarantee system stability, under typical adaptive control assumptions, for systems with piecewise differentiable bounded parameters and piecewise continuous disturbances without requiring a priori knowledge on such parameters or disturbances. The effect of plant variation and switching is reduced to piecewise continuous and impulsive inputs acting on a Bounded Input Bounded State (BIBS) stable closed loop system. This, in turn, provides a separation between the robust stability and robust performance control problems. The developed methodology provides clear guidelines for steady-state and transient performance optimization and allows for parameter scheduling and multiple model controller adjustment techniques to be utilized with no stability concerns. The results are illustrated for various systems including contact-based robotic manipulation and Atomic Force Microscope (AFM) based nano-manipulation.by Khalid El Rifai.Ph.D