Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.90001

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: ---

Authors: None

Abstract:

Keywords:

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.90002

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: ---

Authors: Demir, Ozan; Lunze, Jan

Abstract: This paper investigates the synchronization problem of multi-agent systems with event-based communication. A communication between the agents is invoked only after an event condition has been fulfilled, which can be checked in a decentralized way. Event-based synchronization reduces the communication effort in comparison to the continuous-time synchronization algorithms, while the convergence of the subsystems to a bounded region around the synchronous trajectory is guaranteed.

Keywords: Networked control systems; Event-triggered control

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00001

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 1-6

Authors: Lehmann, Daniel; Lunze, Jan; Johansson, Karl Henrik

Abstract: This paper investigates the stability as well as communication properties of sampled-data control and two event-triggered control schemes: deadband control and model-based event-triggered control. After proposing a uniform representation, these schemes are compared by deriving approximation error bounds with respect to the behavior of the continuous-time state-feedback loop and by specifying lower bounds on the minimum inter-sampling times. The results show that, under the conditions derived in this paper, the model-based approach guarantees the best stability and communication properties which is also demonstrated by a numerical example.

Keywords: Event-triggered control; Networked control systems; Model-based control

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00002

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 7-12

Authors: Kempker, Pia L.; Ran, André C.M.; van Schuppen, Jan H.

Abstract: This paper deals with infinite-horizon quadratic optimal control for coordinated linear systems, a particular class of hierarchical control systems with a top-to-bottom information structure. In contrast to the case of monolithic linear systems, the corresponding optimal control law is not a linear time-invariant state feedback. We derive an approximation to the optimal control law, combining a linear state feedback with event-based bottom-to-top communication. The performance of this control procedure is illustrated by simulations.

Keywords: Optimal control; Control over communication; Event-triggered control

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00003

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 13-18

Authors: Omran, Hassan; Hetel, Laurentiu; Richard, Jean-Pierre

Abstract: This note considers the problem of local stability of aperiodic sampled-data bilinear systems, controlled via linear state-feedback. The sampling intervals are time-varying and upper bounded. It is shown that by solving linear matrix inequalities (LMIs) the local asymptotic stability of the sampled system is guaranteed in an ellipsoidal region containing the origin of the state space. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of a numerical example.

Keywords: Networked control systems; Stability; LMIs

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00004

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 19-24

Authors: Margellos, Kostas; Lygeros, John

Abstract: In this paper, we revisit the problem of approximating viability sets for hybrid systems with nonlinear continuous dynamics and competing inputs. As usual in the literature, an iterative algorithm, based on the alternating application of a continuous and a discrete operator, is employed. Three different cases, based on whether the continuous evolution and the number of discrete transitions are finite or infinite, are considered. A complete characterization of the reach-avoid computation (involved in the continuous time calculation) is provided based entirely on optimal control. Moreover, we show convergence of the iterative process by using a constructive version of Tarski's fixed point theorem, to determine the maximal fixed point of a monotone operator on a complete lattice of closed sets. To illustrate its performance, the viability algorithm is applied to investigate voltage stability for a single machine-load system in case of a line fault.

Keywords: Hybrid automata; Verification; Reachability

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00005

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 25-32

Authors: Taringoo, Farzin; Caines, Peter E.

Abstract: This paper provides an algorithm for the optimization of autonomous and controlled hybrid systems on Lie groups. First, a geometrical derivation of the Hybrid Minimum Principle (HMP) for hybrid systems whose state manifolds constitute a Lie group (G,*) which is left invariant under the controlled dynamics of the system is presented. Second, a geometrical algorithm is developed by employing the notion of exponential curves on Lie groups. The convergence analysis for the proposed algorithm is based on Lasalle Theory. Simulation results are provided at the end of the paper.

Keywords: Switched systems; Optimal control

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00006

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 33-38

Authors: Wigström, Oskar; Sundström, Nina; Lennartson, Bengt

Abstract: In this paper we study a subset of hybrid systems and present a generalized method for their optimization. We outline Hybrid Cost Automata (HCA), an extension to Hybrid Automata, where discrete and continuous cost expressions are added. The class of hybrid systems with known spatial paths is dened in the context of HCA. This type of system is common in industry where for example AGVs transport goods from one location to another, or manipulators move between joint coordinates. The optimization is performed using Dynamic Programming as a preprocessing step, whereafter Mixed Integer Nonlinear Programming is used for scheduling. A case study of a four robot cell is presented with energy consumption used as a minimization criterion.

Keywords: Optimal control; Manufacturing; Hybrid automata

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00007

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 39-45

Authors: Bourdais, Romain; Gueguen, Herve; Belmiloudi, Aziz

Abstract: In this paper, a distributed algorithm is proposed to solve a model predictive control problem for some continuous systems governed by discrete inputs. The first step is to rewrite the global problem, into a new optimization problem under constraints. Then the distributed structure can be obtained using Lagrangian relaxation. But, as the optimization variables are not continuous but discrete, the strong duality conditions are no longer ensured. The main contribution in this paper is to define a mechanism that overcomes this difficulty. The effectiveness of the proposed algorithm is illustrated with some academical simulations.

Keywords: Model predictive control; Switched systems

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00008

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 46-51

Authors: Mazo Jr, Manuel; Cao, Ming

Abstract: In this paper we propose an implementation of control systems in which measurements from the different sensors do not need to be synchronized in time and are aperiodically transmitted. Furthermore all the communication between sensors and controller, and between controller and sensors, require only the transmission of one bit of information (with the exception of an initialization round of measurements). The proposed implementation is based on the idea of measurements and transmissions being triggered by local events at the sensors. In this paper we extend our previous results proposing a fully event-triggered implementation for asymptotic stability of the closed loop system, and show how this new approach enables more efficient implementations in terms of communication requirements. From the more practical perspective, the proposed techniques can aid at greatly reducing power consumption of wireless sensors in a control system by not only reducing the amount of transmissions, but also the time the sensors spend listening for communications from other sensors or the controller.

Keywords: Event-triggered control; Networked control systems; Wireless sensor networks

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00009

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 52-57

Authors: Stoecker, Christian; Lunze, Jan; Vey, Daniel

Abstract: In event-based control the feedback link within a control loop is only closed when an event indicates the need for information exchange among the sensors, controller and actuators to maintain a required loop performance. The event-based control loop is a hybrid dynamical system, which is characterized by a sequence of continuous state flows and discontinuous state jumps at the event times. This paper analyzes the stability of interconnected decentralized event-based control loops where events are triggered asynchronously. A stability criterion is derived using the comparison principle. It is shown that conditions that are sufficient to prove the stability of the continuous control system imply ultimate boundedness of the event-based state-feedback loop. The conservatism of the proposed stability test is evaluated for a thermofluid process.

Keywords: Event-triggered control; Stability; Analysis

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00010

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 58-63

Authors: Molin, Adam; Hirche, Sandra

Abstract: This paper investigates the optimal design of event-triggered estimation for first-order linear stochastic systems. The problem is posed as a two-player team problem with a partially nested information pattern. The two players are given by an estimator and an event-trigger. The event-trigger has full state information and decides whether the estimator shall obtain the current state information by transmitting it through a resource constrained channel. The objective is to find an optimal trade-off between the mean squared estimation error and the expected transmission rate. The proposed iterative algorithm alternates between optimizing one player while fixing the other player. It is shown that the solution of the algorithm converges to a linear predictor and a symmetric threshold policy, if the densities of the initial state and the noise variables are even and radially decreasing functions. The effectiveness of the approach is illustrated via numerical simulations. In case of a multimodal distribution of the noise variables a significant performance improvement can be achieved compared to a separate design that assumes a linear prediction and a symmetric threshold policy.

Keywords: Event-triggered control; Networked control systems; Optimal control

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00011

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 64-69

Authors: Li, Lichun; Wang, Xiaofeng; Lemmon, Michael

Abstract: Event triggering is a sampling method where sampling occurs only if data 'novelty' exceeds a threshold. Prior work has demonstrated that event triggered systems have longer average sampling periods than periodic sampled systems with comparable system performance. Based on this fact, it is claimed that event triggered systems make more efficient use of communication resources than periodic sampled systems. If, however, we account for the number of bits in each sample and the maximum acceptable delay of this sample, it is possible that the bit-rates generated by event triggered systems are greater than that of periodic sampled systems. Our prior work in Li et al. [2012] has established, in noise-free cases, the condition under which the stabilizing bit-rates for quantized event-triggered systems converge asymptotically to a finite rate as the system approaches its equilibrium point. In some cases, it was shown that this limiting bit rate may actually be zero. This paper extends that earlier work to quantized event-triggered systems with essentially bounded disturbances. Conditions on triggering event, quantization error and maximum delay are established to assure the input-to-state stability (ISS). The stabilizing bit-rate is, then, shown to be always bounded by a continuous, positive definite, increasing function with respect to the norm of the state. Since the system is ISS, the stabilizing bit-rate can be bounded from above by a function of time. This result provides a guide on how to assign communication resource to the control system. If we set external disturbance to be $0$, the results in Li et al. [2012] are recovered.

Keywords: Event-triggered control; Self-triggered control; Communication networks

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00012

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 70-75

Authors: Tiberi, Ubaldo; Johansson, Karl Henrik

Abstract: Self-triggered control is a promising aperiodic control paradigm that allows the design of resource-efficient control schemes. Several results were recently developed for self-triggered control of linear systems, but self-triggered control for nonlinear systems is still not well understood. Existing techniques are mainly limited to homogeneous or polynomial closed-loop systems that are input-to- state stable with respect to measurement errors. These assumptions obviously limit the class of applicable cases. In this paper, a new simple self-triggered controller, based on the assumption of local asymptotic stability of the closed-loop system, is presented. The controller ensures local ultimate uniform boundedness of the state trajectories in the sense that the self-triggered controller guarantees the trajectories to be confined into an arbitrary small region. In the case with measurement time delays, it is shown how the size of the region depends on the maximum delay. The effectiveness of the proposed method is illustrated by simulations.

Keywords: Self-triggered control; Event-triggered control; Networked control systems

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00013

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 76-81

Authors: Girard, Antoine

Abstract: In this paper, we consider the problem of synthesizing low-complexity safety 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 quantized switching controllers for safety specifications; these can be computed offline and therefore the online execution time is greatly 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 inherent to safety controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.

Keywords: Control; Switched systems; Complexity

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00014

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 82-87

Authors: Ding, Xu Chu; Lazar, Mircea; Belta, Calin

Abstract: In this paper we present an abstraction algorithm that produces a finite bisimulation quotient for an autonomous discrete-time linear system. We assume that the bisimulation quotient is required to preserve the observations over an arbitrary, finite number of polytopic subsets of the system state space. We generate the bisimulation quotient with the aid of a sequence of contractive polytopic sublevel sets obtained via a polyhedral Lyapunov function. The proposed algorithm guarantees that at iteration i, the bisimulation of the system within the i-th sublevel set of the Lyapunov function is completed. We then show how to use the obtained bisimulation quotient to verify the system with respect to arbitrary Linear Temporal Logic formulas over the observed regions.

Keywords: Analysis; Specification; Verification

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00015

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 88-93

Authors: Frehse, Goran; Ray, Rajarshi

Abstract: Recently, efficient reachability algorithms for hybrid systems with piecewise affine dynamics have been developed. They achieve good scalability and precision by using support functions to represent continuous sets. In this paper, we propose an improvement of these algorithms that reduces the overapproximation error of the image computation of discrete transitions (jumps). The critical operation of this image computation is the intersection of the flowpipe with the guard sets of the transitions, since intersection is in general a difficult operation when using support functions. We propose an approach for computing the intersection of the flowpipe with polyhedral guards up to arbitrary accuracy. We reduce computing the support function of the intersection of a single convex set with a guard to a convex minimization problem. To solve it, we present a custom-tailored sandwich algorithm. The intersection of a flowpipe (a sequence of convex sets) with a guard reduces to a set of such minimization problems. Where possible, we use branch-and-bound techniques and solve these minimization problems simultaneously to avoid redundant computations. Experimental results illustrate the gain in accuracy and the performance of the algorithms.

Keywords: Reachability; Hybrid automata; Piecewise affine systems

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00016

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 94-101

Authors: Aydin Gol, Ebru; Belta, Calin

Abstract: We consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution.

Keywords: Optimal control; Specification

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00017

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 102-107

Authors: Mitchell, Ian M.; Chen, Mo; Oishi, Meeko

Abstract: In sampled data systems the controller receives periodically sampled state feedback about the evolution of a continuous time plant, and must choose a constant control signal to apply between these updates; however, unlike purely discrete time models the evolution of the plant between updates is important. In contrast, for systems with nonlinear dynamics existing reachability algorithms - based on Hamilton-Jacobi equations or viability theory - assume continuous time state feedback and the ability to instantaneously adjust the input signal. In this paper we describe an algorithm for determining an implicit surface representation of minimal backwards reach tubes for nonlinear sampled data systems, and then construct switched, set-valued feedback controllers which are permissive but ensure safety for such systems. The reachability algorithm is adapted from the Hamilton-Jacobi formulation proposed in Ding and Tomlin [2010]. We show that this formulation is conservative for sampled data systems. We implement the algorithm using approximation schemes from level set methods, and demonstrate it on a modified double integrator.

Keywords: Reachability; Verification; Numerical tools

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00018

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 108-114

Authors: Núñez, Felipe; Wang, Yongqiang; Teel, Andrew R.; Doyle III, Francis Joseph

Abstract: Pulse-coupled oscillators (PCOs) comprise a class of limit cycle oscillators coupled in an impulsive rather than smooth manner. Their importance in biology and engineering motivated the analysis of the basic properties and design principles of PCO networks. In this work we address synchronization of non-identical PCO networks with a global cue by using a hybrid systems approach. Using phase response curves as a design element, we characterize solutions and give conditions under which frequency synchronization is achieved. Numerical experiments are provided, which confirm the theoretical findings.

Keywords: Networks; Stability; Wireless sensor networks

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00019

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 115-120

Authors: Camlibel, Kanat; Zhang, Shuo

Abstract: In this paper, we study partial consensus problem for diffusively coupled multi-agent systems with position/velocity (double integrator) dynamics. We allow different communication topologies for positions and velocities and investigate partial consensus for such systems. First, we provide algebraic necessary and sufficient conditions for partial consensus. Then, we study almost equitable graph partitions and present necessary graph topological conditions for partial consensus.

Keywords: Networks; Networked control systems; Analysis

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00020

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 121-126

Authors: Al-Areqi, Sanad; Görges, Daniel; Liu, Steven

Abstract: Networked embedded control systems (NECSs) with uncertain but interval-bounded time-varying computation and transmission delays are addressed in this paper. They are modeled as discrete-time switched linear systems with norm-bounded uncertainty. Considering an infinite-horizon quadratic cost function as a performance measure, a novel control and scheduling codesign strategy is proposed and evaluated through a practical example. The proposed strategy can be formulated as an LMI optimization problem for which many efficient solvers are available. Notably, the proposed codesign strategy is generally applicable to discrete-time switched linear systems with norm-bounded uncertainty.

Keywords: Control over communication; Switched systems; Networked control systems

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00021

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 127-132

Authors: Demirel, Burak; Briat, Corentin; Johansson, Mikael

Abstract: This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov-Krasovskii functional. We develop analysis conditions that can be verified by semi-definite programming, and show that associated state feedback synthesis problem also can be solved using convex optimization. Small and large scale networked control systems are used to illustrate the effectiveness of our approach.

Keywords: Switched systems; Networked control systems; LMIs

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00022

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 133-140

Authors: Riedinger, Pierre; Morarescu, Irinel Constantin

Abstract: In this paper, we address the problem of numerical implementation of optimal control for switched affine systems with state constraints. In order to properly solve the problem, a relaxed system is introduced and the connection between the solution of this system and the solution of the initial one is established. One of the main difficulties is then related to the fact that the optimal solution is generally singular. We show that, using slack variables, a set of complementarity constraints can be used to take into account the singular nature of the solution. The optimal control problem is then reformulated as a constraint optimization problem over the Hamiltonian systems and solved via a direct method. This formulation does not require a priori knowledge on the structure (regular/singular) of the solution. In addition, state path constraints are included. Numerical simulations for power converters, both in continuous and discontinuous conduction mode, illustrate the effectiveness of the proposed methodology.

Keywords: Control; Analysis; Modeling

Digital Object Identifier (DOI): 10.3182/20120606-3-NL-3011.00023

Conference: 4th IFAC Conference on Analysis and Design of Hybrid Systems

Location: TU Eindhoven, Netherlands

Start Date: Wed Jun 06 2012 - End Date: Fri Jun 08 2012

Page Numbers: 141-146