Euler's method applied to the control of switched systems

Hybrid systems are a powerful formalism for modeling and reasoning about cyber-physical systems. They mix the continuous and discrete natures of the evolution of computerized systems. Switched systems are a special kind of hybrid systems, with restricted discrete behaviours: those systems only have finitely many different modes of (continuous) evolution, with isolated switches between modes. Such systems provide a good balance between expressiveness and controllability, and are thus in widespread use in large branches of industry such as power electronics and automotive control. The control law for a switched system defines the way of selecting the modes during the run of the system. Controllability is the problem of (automatically) synthezing a control law in order to satisfy a desired property, such as safety (maintaining the variables within a given zone) or stabilisation (confinement of the variables in a close neighborhood around an objective point). In order to compute the control of a switched system, we need to compute the solutions of the differential equations governing the modes. Euler's method is the most basic technique for approximating such solutions. We present here an estimation of the Euler's method local error, using the notion of " one-sided Lispchitz constant " for modes. This yields a general control synthesis approach which can encompass several features such as bounded disturbance and compositionality

An improved algorithm for the control synthesis of nonlinear sampled switched systems

International audienc

Cooperative distributed pick and place algorithm for mobile manipulators with camera feedback

The main goal of this research is to perform a pick and place task done by several mobile robots equipped with a robotic arm by using a distributed algorithm and a formation control law for keeping the shape. Nowadays, the industry sometimes needs the cooperation of different robots to achieve what cannot be reached by a single robot. Sometimes, the fact of using only a single robot can be either really expensive or not powerful enough and it is worth to implement a system with several agents. The studied case will be with four agents and it will be tested experimentally with the mobile nexus robots which are in the DTPA lab. The fact of being a task performed by several agents means that formation control theory will be taken into account, specifically the formation control Law designed by Garcia de Marina, Jayawardhana, and Cao [1]. Several studies and tests related to formation control have been performed in the PhD Nexus Group. Furthermore, some research about pick and place task has also been studied but only for a single robot. Because of this reason, the aim of this research is to extrapolate the results of the pick and place task done for one robot to a formation of several agents by using the formation control law previously specified. Moreover once the algorithm is tested in a four agent formation is relatively easy to change the number of agents by simply modifying some parameters. Challenges such as recognition of objects (Markers), tracking them (PI control) and keeping the formation of the agents (formation control theory) will be achieved by using the suitable sensors. For instance, a camera mounted on the robotic arm will be used for the recognition of objects, while a RPLidar Laser Scanner will be used for measuring the distances between robots and ensure that they keep the formationOutgoin

Rewriting Modulo SMT and Open System Analysis

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.NSF Grant CNS 13-19109 and NASA Research Cooperative Agreement No. NNL09AA00AOpe

Fault-tolerant control policies for multi-robot systems

Throughout the past decade, we have witnessed an active interest in distributed motion coordination algorithms for networked mobile autonomous robots. Often, in multi-robot systems, each robot executing a coordination task is a little cost, a disposable autonomous agent that has ad-hoc sensing or communication capability, and limited mobility. Coordination tasks that a group of multiple mobile robots might perform include formation control, rendezvous, distributed estimation, deployment, flocking, etc. Also, there are challenging tasks that are more suitable for a group of mobile robots than an individual robot, such as surveillance, exploration, or hazardous environmental monitoring. The field has been collectively investigated by many researchers in robotics, control, artificial intelligence, and distributed computing. However, relatively little work has been done on developing algorithms to provide resilience to failures that can occur. The problem is extremely difficult to handle in that any partial failure of a robot is not readily detectable. Some failures in robot resources can have an adverse effect on not only the performance of the robot itself, but also other robots, and the collective task performance as well. This study presents the development of fault-tolerant distributed control policies for multi-robot systems. We consider two problems: rendezvous and coverage. For the former, the goal is to bring all robots to a common location, while for the latter the goal is to deploy robots to achieve optimal coverage of an environment. We consider the case in which each robot is an autonomous decision maker that is anonymous (i.e., robots are indistinguishable to one another), memoryless (i.e., each robot makes decisions based upon only its current information), and dimensionless (i.e., collision checking is not considered). Each robot has a limited sensing range and can directly estimate the state of only those robots within that sensing range, which induces a network topology for the multi-robot system. We assume that it is not possible for the fault-free robots to identify the faulty robots (e.g., due to the anonymous property of the robots). For each problem, we provide an efficient computational framework and analysis of algorithms, all of which converge in the face of faulty robots under a few assumptions on the network topology and sensing abilities. A suite of experiments and simulations confirm our theoretical analysis and demonstrate that our proposed algorithms are useful in fault-prone multi-robot systems

Control Theory: A Mathematical Perspective on Cyber-Physical Systems

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently the control field is facing new challenges motivated by application domains that involve networks of systems. Examples are interacting robots, networks of autonomous cars or the smart grid. In order to address the new challenges posed by these application disciplines, the special focus of this workshop has been on the currently very active field of Cyber-Physical Systems, which forms the underlying basis for many network control applications. A series of lectures in this workshop was devoted to give an overview on current theoretical developments in Cyber-Physical Systems, emphasizing in particular the mathematical aspects of the field. Special focus was on the dynamics and control of networks of systems, distributed optimization and formation control, fundamentals of nonlinear interconnected systems, as well as open problems in control