Low-Complexity Quantized Switching Controllers using Approximate Bisimulation

In this paper, we consider the problem of synthesizing low-complexity controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design naturally quantized switching controllers for safety or reachability specifications; these can be pre-computed offline and therefore the online execution time is reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism of the synthesized controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building

Continuous-time consensus under persistent connectivity and slow divergence of reciprocal interaction weights

In this paper, we present new results on consensus for continuous-time multi- agent systems. We introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights. Persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete- time consensus protocols. Slow divergence of reciprocal interaction weights generalizes the assumption of cut-balanced interactions. We show that under these two assumptions, the continuous-time consensus protocol succeeds: the states of all the agents converge asymptotically to a common value. Moreover, our proof allows us to give an estimate of the rate of convergence towards the consensus. We also provide two examples that make us think that both of our assumptions are tight

Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices

In this paper, we propose an approach to controller synthesis for a class of constrained nonlinear systems. It is based on the use of a hybridization, that is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined on a triangulation of the state-space where on each simplex of the triangulation, the nonlinear dynamics is conservatively approximated by an affine system subject to disturbances. Except for the disturbances, this hybridization can be seen as a piecewise affine hybrid system on simplices for which appealing control synthesis techniques have been developed in the past decade. We extend these techniques to handle systems subject to disturbances by synthesizing and coordinating local robust affine controllers defined on the simplices of the triangulation. We show that the resulting hybrid controller can be used to control successfully the original constrained nonlinear system. Our approach, though conservative, can be fully automated and is computationally tractable. To show its effectiveness in practical applications, we apply our method to control a pendulum mounted on a cart

Approximately bisimilar symbolic models for nonlinear control systems

Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they are less suitable to describe software and hardware interfacing the physical world. For this reason there is a growing interest in describing control systems through symbolic models that are abstract descriptions of the continuous dynamics, where each "symbol" corresponds to an "aggregate" of states in the continuous model. Since these symbolic models are of the same nature of the models used in computer science to describe software and hardware, they provide a unified language to study problems of control in which software and hardware interact with the physical world. Furthermore the use of symbolic models enables one to leverage techniques from supervisory control and algorithms from game theory for controller synthesis purposes. In this paper we show that every incrementally globally asymptotically stable nonlinear control system is approximately equivalent (bisimilar) to a symbolic model. The approximation error is a design parameter in the construction of the symbolic model and can be rendered as small as desired. Furthermore if the state space of the control system is bounded the obtained symbolic model is finite. For digital control systems, and under the stronger assumption of incremental input-to-state stability, symbolic models can be constructed through a suitable quantization of the inputs.Comment: Corrected typo

Femtosecond spectral electric field reconstruction using coherent transients

We have implemented a new approach for measuring the time-dependent intensity and phase of ultrashort optical pulses. It is based on the interaction between shaped pulses and atoms, leading to coherent transients.Comment: 4 pages Accepted in Optics Letter

Symbolic Models for Stochastic Switched Systems: A Discretization and a Discretization-Free Approach

Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different techniques have been developed to assist in the stability analysis of stochastic switched systems. However, more complex and challenging objectives related to the verification of and the controller synthesis for logic specifications have not been formally investigated for this class of systems as of yet. With logic specifications we mean properties expressed as formulae in linear temporal logic or as automata on infinite strings. This paper addresses these complex objectives by constructively deriving approximately equivalent (bisimilar) symbolic models of stochastic switched systems. More precisely, this paper provides two different symbolic abstraction techniques: one requires state space discretization, but the other one does not require any space discretization which can be potentially more efficient than the first one when dealing with higher dimensional stochastic switched systems. Both techniques provide finite symbolic models that are approximately bisimilar to stochastic switched systems under some stability assumptions on the concrete model. This allows formally synthesizing controllers (switching signals) that are valid for the concrete system over the finite symbolic model, by means of mature automata-theoretic techniques in the literature. The effectiveness of the results are illustrated by synthesizing switching signals enforcing logic specifications for two case studies including temperature control of a six-room building.Comment: 25 pages, 4 figures. arXiv admin note: text overlap with arXiv:1302.386

Approximately bisimilar symbolic models for incrementally stable switched systems

Switched systems constitute an important modeling paradigm faithfully describing many engineering systems in which software interacts with the physical world. Despite considerable progress on stability and stabilization of switched systems, the constant evolution of technology demands that we make similar progress with respect to different, and perhaps more complex, objectives. This paper describes one particular approach to address these different objectives based on the construction of approximately equivalent (bisimilar) symbolic models for switched systems. The main contribution of this paper consists in showing that under standard assumptions ensuring incremental stability of a switched system (i.e. existence of a common Lyapunov function, or multiple Lyapunov functions with dwell time), it is possible to construct a finite symbolic model that is approximately bisimilar to the original switched system with a precision that can be chosen a priori. To support the computational merits of the proposed approach, we use symbolic models to synthesize controllers for two examples of switched systems, including the boost DC-DC converter.Comment: 17 page

Compositional abstraction and safety synthesis using overlapping symbolic models

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems

Triggering mechanism using freely selected sensors for linear time-invariant systems

International audienceExisting event-triggering sampling techniques for state feedback controllers generally use full state information. This may be a source of important computational and communication costs, particularly if sensors are numerous and/or distributed, as the triggering condition needs to be continuously evaluated. We propose an approach to redesign triggering mechanisms for linear time-invariant systems based on limited sensors information, which we freely select, and an internal scalar dynamic variable. We prove that the resulting closed loop system ensures a uniform global exponential stability property and that a uniform minimal inter-execution time is guaranteed. Besides stabilizability, no additional assumption on the system is needed. Guidelines are provided to derive the redesigned triggering conditions using linear matrix inequalities. We show on an academic example that, using a suitable choice of sensors and parameters, inter-execution times using our approach are comparable to those using triggering mechanisms that monitor the full state of the syste