Invariance Principles and Observability in Switched Systems with an Application in Consensus

Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak observability (WO) associated with this output. WO is what the output informs about the limiting behavior of state trajectories (hidden in the zero locus of the output). In the context of switched NLTV systems, WO can be explored using the recently established framework of limiting zeroing-output solutions. Adding to this, an extension of the integral invariance principle for switched NLTV systems with a new method to guarantee uniform global attractivity of a closed set (without assuming uniform Lyapunov stability or dwell-time conditions) is proposed. By way of illustrating the proposed method, a leaderless consensus problem for nonholonomic mobile robots with a switching communication topology is addressed, yielding a new control strategy and a new convergence result

Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies

In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here that if the network of oscillators synchronizes for the static time-average of the topology, then the network will synchronize with the time-varying topology if the time-average is achieved sufficiently fast. Fast switching, fast on the time-scale of the coupled oscillators, overcomes the descychnronizing decoherence suggested by disconnected instantaneous networks. This result agrees in spirit with that of where empirical evidence suggested that a moving averaged graph Laplacian could be used in the master-stability function analysis. A new fast switching stability criterion here-in gives sufficiency of a fast-switching network leading to synchronization. Although this sufficient condition appears to be very conservative, it provides new insights about the requirements for synchronization when the network topology is time-varying. In particular, it can be shown that networks of oscillators can synchronize even if at every point in time the frozen-time network topology is insufficiently connected to achieve synchronization.Comment: Submitted to SIAD

An Unsupervised Neural Network for Real-Time Low-Level Control of a Mobile Robot: Noise Resistance, Stability, and Hardware Implementation

We have recently introduced a neural network mobile robot controller (NETMORC). The controller is based on earlier neural network models of biological sensory-motor control. We have shown that NETMORC is able to guide a differential drive mobile robot to an arbitrary stationary or moving target while compensating for noise and other forms of disturbance, such as wheel slippage or changes in the robot's plant. Furthermore, NETMORC is able to adapt in response to long-term changes in the robot's plant, such as a change in the radius of the wheels. In this article we first review the NETMORC architecture, and then we prove that NETMORC is asymptotically stable. After presenting a series of simulations results showing robustness to disturbances, we compare NETMORC performance on a trajectory-following task with the performance of an alternative controller. Finally, we describe preliminary results on the hardware implementation of NETMORC with the mobile robot ROBUTER.Sloan Fellowship (BR-3122), Air Force Office of Scientific Research (F49620-92-J-0499

Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

Remote control and motion coordination of mobile robots

As robots destined for personal and professional applications advance towards becoming part of our daily lives, the importance and complexity of the control algorithms which regulate them should not be underestimated. This thesis is related to two fields within robotics which are of major importance in this paradigm shift; namely, telerobotics and cooperative robotics. On the one hand, telerobotic systems support remote or dangerous tasks, whereas, on the other hand, the use of cooperative robotic systems supports distributed tasks and has several advantages with respect to the use of single-robot systems. The use of robotic systems in remote tasks implies in many cases the physical separation of the controller and the robot. This separation is advantageous when carrying out a variety of remote or hazardous tasks, but at the same time constitutes one of the main drawbacks of this type of robotic systems. Namely, as information is being relayed from the controller to the robot and back over the communication network, a time-delay unavoidably appears in the overall control loop. Hence, controller designs which guarantee the stability and performance of the robot even in the presence of the aforementioned time-delay become necessary in order to ensure a safe and reliable completion of the assigned tasks. On the other hand, using a group of robots to carry out a certain assignment, as compared to a single robot, provides several advantages such as an increased flexibility and the ability to complete distributed or more complex tasks. In order to successfully complete their collective task, the robots in the group generally need to coordinate their behavior by mutually exchanging information. When this information exchange takes place over a delay-inducing communication network, the consequences of the resulting time-delay must be taken into account. As a result, it is of great importance to design controllers which allow the group of robots to work together and complete their task in spite of the time-delay affecting their information exchange. The two control problems explained previously are addressed in this thesis. Firstly, the control of wheeled mobile robots over a delay-inducing communication network is considered by studying the remote tracking control problem for a unicycle-type mobile robot with communication delays. The most important issue to consider is that the communication delay in the control loop most probably compromises the performance and stability of the robot. In order to tackle this problem, a state estimator with a predictor-like structure is proposed. The state estimator is based on the notion of anticipating synchronization and, when acting in conjunction with a tracking control law, the resulting control strategy stabilizes the system and mitigates the negative effects of the time-delay. By exploiting existing results on nonlinear cascaded systems with time-delay, the local uniform asymptotic stability of the closed-loop tracking error dynamics is guaranteed up to a maximum admissible time-delay. Ultimately, explicit expressions which illustrate the relationship between the allowable time-delay and the control parameters of the robot are provided. Secondly, the coordination of a group of wheeled mobile robots over a delayinducing communication network is considered by studying the remote motion coordination problem for a group of unicycle-type mobile robots with a delayed information exchange between the robots. Specifically, master-slave and mutual motion coordination are considered. A controller design which allows the robots to maintain motion coordination even in the presence of a time-delay is proposed and the ensuing global stability analysis provides expressions which relate the control parameters of the robot and the allowable time-delay. The thesis places equal emphasis on theoretical developments and experimental results. In order to do so, the proposed control strategies are experimentally validated using the Internet as the communication network and multi-robot platforms located in Eindhoven, The Netherlands and Tokyo, Japan. To summarize, this thesis addresses two related control problems. On the one hand, we consider the tracking control of a wheeled mobile robot over a communication network which induces a time-delay. On the other hand, we focus on the motion coordination of a group of these robots under the consideration that the information exchange between the robots takes place over a delay-inducing communication network

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