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The paradigm of Cyber-Physical Systems of Systems (CPSoS) is becoming rather popular in the control systems research community because of its expressive power able to properly handle many engineered complex systems of interest. Decentralized control techniques offer a promising approach in taming the inherent complexity of CPSoS, also connected with the design of needed communication infrastructures and computing units. In this paper, we propose decentralized control of networks of discrete-time nonlinear control systems, enforcing complex specifications expressed in terms of regular languages, within any desired accuracy. As discussed in the paper, regular languages, while being traditionally studied in the research community of discrete-event systems, also provide a useful mean to model a rather wide variety of complex specifications for control systems. The design of decentralized controllers is based on formal methods and in particular, on the use of discrete abstractions. Efficient synthesis of such controllers is derived by resorting to on-the-fly algorithmic techniques that also allow the use of parallel computing architectures. Advantages and disadvantages of the decentralized approach over a centralized one, also in terms of computational complexity, are discussed. An illustrative example is presented, which shows the applicability and effectiveness of the results proposed., Comment: 20 pages, 3 tables

Motivated by safety-critical applications in cyber-physical systems, in this paper we study the notion of critical observability and design of observers for networks of Finite State Machines (FSMs). Critical observability is a property of FSMs that corresponds to the possibility of detecting if the current state of an FSM belongs to a set of critical states modeling operations that may be unsafe or, in general, operations of specific interest in a particular application. A critical observer is an observer that detects on-line the occurrence of critical states. When a large-scale network of FSMs is considered, the construction of such an observer is prohibitive because of the large computational effort needed. In this paper we propose a decentralized architecture for critical observers of networks of FSMs, where on-line detection of critical states is performed by local critical observers, each associated with an FSM of the network. For the efficient design of decentralized critical observers we first extend on-the-fly algorithms traditionally used in the community of formal methods for the formal verification and control design of FSMs. We then extend to networks of FSMs, bisimulation theory traditionally given in the community of formal methods for single FSMs. The proposed techniques provide a remarkable computational complexity reduction, as discussed throughout the paper and also demonstrated by means of illustrative examples. Finally, we propose an example in the context of biological networks, which illustrates the applicability of our results and also the interest arising from concrete application domains., Comment: 18 pages, 10 figures, 3 algorithms, 1 table

The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear NCS with specifications expressed in terms of automata. We first derive symbolic models that are shown to approximate the given NCS in the sense of (alternating) approximate simulation. We then address symbolic control design with specifications expressed in terms of automata. We finally derive efficient algorithms for the synthesis of the proposed symbolic controllers that cope with the inherent computational complexity of the problem at hand., Comment: arXiv admin note: text overlap with arXiv:1203.1069

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed.

Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a discrete-time Piecewise Affine (PWA) system in the sense of approximate simulation and converges to the PWA system in the so-called simulation metric. Symbolic control design is then addressed with specifications expressed in terms of non-deterministic finite automata. A sequence of symbolic control strategies is derived which converges, in the sense of simulation metric, to the maximal controller solving the given specification on the PWA system., Comment: 11 pages, 2 figures, 1 table

Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the notion of non-flat systems. Non--flat systems are "finite state machines" where each "state" can be either a basic state or an aggregate of finite state machines. By expanding a non-flat system, a flat system is obtained which is an ordinary finite state machine. In this paper we introduce a novel class of non--flat systems called Arena of Finite State Machines (AFSM). AFSMs are collections of finite state machines that interact concurrently through a communication network. We propose a notion of compositional bisimulation that allows checking bisimulation equivalence of AFSMs by directly exploiting their communication networks and hence, without the need of expanding the AFSMs to finite state machines. Compositional bisimulation allows a computational complexity reduction when checking bisimulation equivalence of AFSMs, as formally quantified in the paper. An application of the proposed framework to the regulation of gene expression in the bacterium Escherichia coli is also presented.

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level., Comment: A short version of this paper (without proofs) will be presented at the 18th IFAC World Congress (IFAC 2011), Milan (Italy), August 28-September 2, 2011

A Multi-hop Control Network (MCN) consists of a plant where the communication between sensor, actuator and computational unit is supported by a wireless multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We address the problem of characterizing controllability and observability of a MCN, by means of necessary and sufficient conditions on the plant dynamics and on the communication scheduling and routing. We provide a methodology to design scheduling and routing, in order to satisfy controllability and observability of a MCN for any fault occurrence in a given set of configurations of failures., Comment: Accepted for publication; Proceedings of the 18th IFAC World Congress, Milan, Italy, 2011

Discrete abstractions of continuous and hybrid systems have recently been the topic of great interest from both the control systems and the computer science communities, because they provide a sound mathematical framework for analysing and controlling embedded systems. In this paper we give a further contribution to this research line, by addressing the problem of symbolic control design of nonlinear systems with infinite states specifications, modelled by differential equations. We first derive the symbolic controller solving the control design problem, given in terms of discrete abstractions of the plant and the specification systems. We then present an algorithm which integrates the construction of the discrete abstractions with the design of the symbolic controller. Space and time complexity analysis of the proposed algorithm is performed and a comparison with traditional approaches currently available in the literature for symbolic control design, is discussed. Some examples are included, which show the interest and applicability of our results., Comment: 22 pages, 2 figures, 4 tables

Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to economics. However, the inherent complexity of such systems poses serious difficulties to control design, when control objectives depart from the standard ones investigated in the current literature, e.g. stabilization, regulation, and etc. In this paper we propose one approach to control design, which is based on the construction of symbolic models, where each symbolic state and each symbolic label correspond to an aggregate of continuous states and to an aggregate of input signals in the original system. The use of symbolic models offers a systematic methodology for control design in which constraints coming from software and hardware, interacting with the physical world, can be integrated. The main contribution of this paper is in showing that incrementally input-to-state stable time-delay systems do admit symbolic models that are approximately bisimilar to the original system, with a precision that can be rendered as small as desired. An algorithm is also presented which computes the proposed symbolic models. When the state and input spaces of time-delay systems are bounded, which is the case in many realistic situations, the proposed algorithm is shown to terminate in a finite number of steps., Comment: 12 pages