Estimation and stability of nonlinear control systems under intermittent information with applications to multi-agent robotics

This dissertation investigates the role of intermittent information in estimation and control problems and applies the obtained results to multi-agent tasks in robotics. First, we develop a stochastic hybrid model of mobile networks able to capture a large variety of heterogeneous multi-agent problems and phenomena. This model is applied to a case study where a heterogeneous mobile sensor network cooperatively detects and tracks mobile targets based on intermittent observations. When these observations form a satisfactory target trajectory, a mobile sensor is switched to the pursuit mode and deployed to capture the target. The cost of operating the sensors is determined from the geometric properties of the network, environment and probability of target detection. The above case study is motivated by the Marco Polo game played by children in swimming pools. Second, we develop adaptive sampling of targets positions in order to minimize energy consumption, while satisfying performance guarantees such as increased probability of detection over time, and no-escape conditions. A parsimonious predictor-corrector tracking filter, that uses geometrical properties of targets\u27 tracks to estimate their positions using imperfect and intermittent measurements, is presented. It is shown that this filter requires substantially less information and processing power than the Unscented Kalman Filter and Sampling Importance Resampling Particle Filter, while providing comparable estimation performance in the presence of intermittent information. Third, we investigate stability of nonlinear control systems under intermittent information. We replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise environment, the developed algorithm yields stable, asymptotically stable, and Lp-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on Lp-stability are presented. Prediction of a triggering event is achieved by employing Lp-gains over a finite horizon in the small gain theorem. By resorting to convex programming, a method to compute Lp-gains over a finite horizon is devised. Next, we investigate optimal intermittent feedback for nonlinear control systems. Using the currently available measurements from a plant, we develop a methodology that outputs when to update the control law with new measurements such that a given cost function is minimized. Our cost function captures trade-offs between the performance and energy consumption of the control system. The optimization problem is formulated as a Dynamic Programming problem, and Approximate Dynamic Programming is employed to solve it. Instead of advocating a particular approximation architecture for Approximate Dynamic Programming, we formulate properties that successful approximation architectures satisfy. In addition, we consider problems with partially observable states, and propose Particle Filtering to deal with partially observable states and intermittent feedback. Finally, we investigate a decentralized output synchronization problem of heterogeneous linear systems. We develop a self-triggered output broadcasting policy for the interconnected systems. Broadcasting time instants adapt to the current communication topology. For a fixed topology, our broadcasting policy yields global exponential output synchronization, and Lp-stable output synchronization in the presence of disturbances. Employing a converse Lyapunov theorem for impulsive systems, we provide an average dwell time condition that yields disturbance-to-state stable output synchronization in case of switching topology. Our approach is applicable to directed and unbalanced communication topologies.\u2

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers

The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

Stitching Dynamic Movement Primitives and Image-based Visual Servo Control

Utilizing perception for feedback control in combination with Dynamic Movement Primitive (DMP)-based motion generation for a robot's end-effector control is a useful solution for many robotic manufacturing tasks. For instance, while performing an insertion task when the hole or the recipient part is not visible in the eye-in-hand camera, a learning-based movement primitive method can be used to generate the end-effector path. Once the recipient part is in the field of view (FOV), Image-based Visual Servo (IBVS) can be used to control the motion of the robot. Inspired by such applications, this paper presents a generalized control scheme that switches between motion generation using DMPs and IBVS control. To facilitate the design, a common state space representation for the DMP and the IBVS systems is first established. Stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically. The developed method is validated by two real world experiments using the eye-in-hand configuration on a Baxter research robot.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Measurement and mathematical model of a driver's intermittent compensatory steering control

The compensatory (feedback) component of a human driver's steering control is examined. In particular the effect of the cognitive process is studied. Model predictive control theory is used to implement models of intermittency in cognitive processing. Experiments using a fixed-base driving simulator with periodic occlusion of the visual display are used to reveal the nature of the driver's steering behaviour. An intermittent serial-ballistic control strategy is found to match the measured behaviour better than intermittent zero-order hold or continuous control. The findings may enable some insight to driver-vehicle interaction and vehicle handling qualities.This work was supported by the Engineering and Physical Sciences Research Council (EP/P505445/1); the Qualcomm European Research Studentship Fund in Technology; and the Lotus F1 Team (RG61664).This is the final version of the article. It first appeared from Taylor & Francis via http://dx.doi.org/10.1080/00423114.2015.110074