Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller

Continuous-time self-tuning algorithms

This thesis proposes some new self-tuning algorithms. In contrast to the conventional discrete-time approach to self-tuning control, the continuous-time approach is used here, that is continuous-time design but digital implementation is used. The proposed underlying control methods are combined with a continuous-time version of the well-known discrete recursive least squares algorithms. The continuous-time estimation scheme is chosen to maintain the continuous-time nature of the algorithms. The first new algorithm proposed is emulator-based relay control (which has already been described in a paper by the author). The algorithm is based on the idea of constructing the switching surface by emulators; that is, unrealisable output derivatives are replaced by their emulated values. In particular, the relay is forced to operate in the sliding mode. In this case, it is shown that emulator-based control and its proposed relay version become equivalent in the sense that both give the same control law. The second new algorithm proposed is a continuous-time version of the discrete-time generalized predictive control (GPC) of Clarke et al (which has already been described in a paper by the author). The algorithm, continuous-time generalized predictive control (CGPC), is based on similar ideas to the GPC, however the formulation is very different. For example, the output prediction is accomplished by using the Taylor series expansion of the output and emulating the output derivatives involved. A detailed closed-loop analysis of this algorithm is also given. It is shown that the CGPC control law only changes the closed-loop pole locations leaving the open-loop zeros untouched (except one special case). It is also shown that LQ control can be considered in the CGPC framework. Further, the CGPC is extended to include some design polynomials so that the model-following and pole-placement control can be considered in the same framework. A third new algorithm, a relay version of the CGPC, is described. The method is based on the ideas of the emulator-based relay control and again it is shown that the CGPC and its relay version become equivalent when the relay operates in the sliding mode. Finally, the CGPC ideas are extended to the multivariable systems and the resulting closed-loop system is analysed in some detail. It is shown that some special choice of design parameters result in a decoupled closed-loop system for certain systems. In addition, it is shown that if the system is decouplable, it is possible to obtain model-following control. It is also shown that LQ control, as in the scalar case, can be considered in the same framework. An illustrative simulation study is also provided for all of the above methods throughout the thesis

L1 adaptive control for nonlinear and non-square multivariable systems

This research presents development of L1 adaptive output-feedback control theory for a class of uncertain, nonlinear, and non-square multivariable systems. The objective is to extend the L1 adaptive control framework to cover a wide class of underactuated systems with uniform performance and robustness guarantees. This dissertation starts by investigating some structural properties of multivariable systems that are used in the development of L1 adaptive output feedback controllers. In particular, a state-decomposition is introduced for adaptive laws that only depends on the output signals. The existence of the decomposition is ensured by defining a virtual system for underactuated plants. Based on the mathematical findings, we propose a set of output feedback solutions for uncertain underactuated systems. In adaptive control applications, a baseline control augmentation is often preferred, where the baseline controller defines the nominal system response. Adaptive controllers are incorporated into the control loop to improve the system response by recovering the nominal performance in the presence of uncertainties. This thesis provides a solution for L1 output feedback control augmentation. Stability and transient performance bounds are proven using Lyapunov analysis. To demonstrate the benefits of the L1 adaptive controllers we consider a missile system and an inverted pendulum, which are both underactuated systems. Finally, we propose a filter design framework in the frequency domain. A new sufficient condition is presented to ensure stability of the closed loop and the reference systems, which is subsequently used in the optimal filter design. Existing H-infinity optimization techniques are leveraged to address the performance and robustness trade-off issues

A Model-Based Approach for Gesture Interfaces

The description of a gesture requires temporal analysis of values generated by input sensors, and it does not fit well the observer pattern traditionally used by frameworks to handle the user’s input. The current solution is to embed particular gesture-based interactions into frameworks by notifying when a gesture is detected completely. This approach suffers from a lack of flexibility, unless the programmer performs explicit temporal analysis of raw sensors data. This thesis proposes a compositional, declarative meta-model for gestures definition based on Petri Nets. Basic traits are used as building blocks for defining gestures; each one notifies the change of a feature value. A complex gesture is defined by the composition of other sub-gestures using a set of operators. The user interface behaviour can be associated to the recognition of the whole gesture or to any other sub-component, addressing the problem of granularity for the notification of events. The meta-model can be instantiated for different gesture recognition supports and its definition has been validated through a proof of concept library. Sample applications have been developed for supporting multi-touch gestures in iOS and full body gestures with Microsoft Kinect. In addition to the solution for the event granularity problem, this thesis discusses how to separate the definition of the gesture from the user interface behaviour using the proposed compositional approach. The gesture description meta-model has been integrated into MARIA, a model-based user interface description language, extending it with the description of full-body gesture interfaces

Exploiting quaternions to support expressive interactive character motion

Thesis (Ph. D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2003.Includes bibliographical references (p. 261-266).A real-time motion engine for interactive synthetic characters, either virtual or physical, needs to allow expressivity and interactivity of motion in order to maintain the illusion of life. Canned animation examples from an animator or motion capture device are expressive, but not very interactive, often leading to repetition. Conversely, numerical procedural techniques such as Inverse Kinematics (IK) tend to be very interactive, but often appear "robotic" and require parameter tweaking by hand. We argue for the use of hybrid example-based learning techniques to incorporate expert knowledge of character motion in the form of animations into an interactive procedural engine. Example-based techniques require appropriate distance metrics, statistical analysis and synthesis primitives, along with the ability to blend examples; furthermore, many machine learning techniques are sensitive to the choice of representation. We show that a quaternion representation of the orientation of a joint affords us computational efficiency along with mathematical robustness, such as avoiding gimbal lock in the Euler angle representation. We show how to use quaternions and their exponential mappings to create distance metrics on character poses, perform simple statistical analysis of joint motion limits and blend multiple poses together. We demonstrate these joint primitives on three techniques which we consider useful for combining animation knowledge with procedural algorithms: 1) pose blending, 2) joint motion statistics and 3) expressive IK. We discuss several projects designed using these primitives and offer insights for programmers building real-time motion engines for expressive interactive characters.by Michael Patrick Johnson.Ph.D