http://ieeexplore.ieee.org TOC Alert for Publication# 9 2013 May 21 58 6 C1 C4 144 58 6 C2 C2 136 58 6 1361 1362 120 We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining process to a random allocation that lies in the core of the robust game under some mild conditions on the underlying communication graphs. The second part of the paper addresses the more general case where the robust game may have empty core. In this case, with the dynamic game we associate a dynamic average game by averaging over time the sequence of characteristic functions. Then, we consider an accordingly modified bargaining protocol. Assuming that the sequence of characteristic functions is ergodic and the core of the average game has a nonempty relative interior, we show that the modified bargaining protocol converges with probability 1 to a random allocation that lies in the core of the average game.]]> 58 6 1363 1376 3990 A multi-hop control network (MCN) consists of a plant where the communication between sensors, actuators, and computational units 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 control design problem on a MCN where the plant is a SISO LTI system and links are subject to permanent failures. We first characterize controllability and observability of a MCN: we provide necessary and sufficient conditions on the plant dynamics and on the communication scheduling, and we provide a design methodology to satisfy such conditions for any failure configuration. Then we address the problem of detecting the failure of links of the radio connectivity graph: we provide necessary and sufficient conditions on the plant dynamics and on the communication protocol, and we provide a design methodology to satisfy the above conditions.]]> 58 6 1377 1389 3495 The aim of this paper is to introduce and characterize observability and reconstructibility properties for Boolean networks and Boolean control networks, described according to the algebraic approach proposed by D. Cheng and co-authors in the series of papers , , and in the recent monography . A complete characterization of these properties, based both on the Boolean matrices involved in the network description and on the corresponding digraphs, is provided. Finally, the problem of state observer design for reconstructible BNs and BCNs is addressed, and two different solutions are proposed.]]> 58 6 1390 1401 3298 Cooperative control focuses on deriving desirable collective behavior in multiagent systems through the design of local control algorithms. Game theory is beginning to emerge as a valuable set of tools for achieving this objective. A central component of this game theoretic approach is the assignment of utility functions to the individual agents. Here, the goal is to assign utility functions within an “admissible” design space such that the resulting game possesses desirable properties. Our first set of results illustrates the complexity associated with such a task. In particular, we prove that if we restrict the class of utility functions to be local, scalable, and budget-balanced then 1) ensuring that the resulting game possesses a pure Nash equilibrium requires computing a Shapley value, which can be computationally prohibitive for large-scale systems, and 2) ensuring that the allocation which optimizes the system level objective is a pure Nash equilibrium is impossible. The last part of this paper demonstrates that both limitations can be overcome by introducing an underlying state space into the potential game structure.]]> 58 6 1402 1415 2996 We study the problem of maximizing the information in a wireless sensor network with unreliable links. We consider a sensor network with a tree topology, where the root corresponds to the sink, and the rest of the network detects an event and transmits data to the sink. We formulate a combinatorial optimization problem that maximizes the information that reaches the sink under deadline, energy, and interference constraints. This framework allows using a variety of error recovery schemes to tackle link unreliability. We show that this optimization problem is NP-hard in the strong sense when the input is the maximum node degree of the tree. We then propose a dynamic programming framework for solving the problem exactly, which involves solving a special case of the job interval selection problem (JISP) at each node. Our solution has a polynomial time complexity when the maximum node degree is $O(log N)$ in a tree with $N$ nodes. For trees with higher node degrees, we further develop a suboptimal solution, which has low complexity and allows distributed implementation. We investigate tree structures for which this solution is optimal to the original problem. The efficiency of the suboptimal solution is further demonstrated through numerical results on general trees.]]> 58 6 1416 1429 2711 In this paper, we present a general theory of motion planning for kinematic systems. In particular, the theory deals with $epsilon$-approximations of non-admissible paths by admissible ones in a certain optimal sense. The need for such an approximation arises for instance in the case of highly congested configuration spaces. This theory has been developed by one of the authors in a previous series of papers. It is based upon concepts from subriemannian geometry. Here, we summarize the results of the theory, and we improve on, by developing in details an intricate case: the ball with a trailer, which corresponds to a distribution with flag of type 2, 3, 5, 6.]]> 58 6 1430 1442 3355 We study limited-coordination scheduling in a wireless downlink network with multiple base stations, each serving a collection of users over shared channel resources. When neighboring base stations simultaneously schedule users on the same channel resource, collisions occur due to interference, leading to loss of throughput. Full coordination to avoid this problem requires each base station to have complete “instantaneous” channel-state information for all its own users, as well as the ability to communicate on the same timescale as channel fluctuations with neighboring base stations. As such a scheme is impractical, if not impossible, to implement, we consider the setting where each base station has only limited instantaneous channel-state information for its own users, and can communicate with other base stations with a significant lag from the channel state variations to coordinate scheduling decisions.]]> 58 6 1443 1456 2500 This paper analyzes causal closed-loop continuous-time systems in the presence of limited information. Assuming that the exogenous signals can be modeled as a stochastic process, a mutual information rate inequality is obtained that can be viewed as an extended Bode-type formula for stationary processes. The tightness of the resulting Bode's integral inequality is then analyzed for the linear time invariant closed loops. Within the developed framework we consider the control-communication interplay and analyze the underlying fundamental limitations.]]> 58 6 1457 1469 3261 In this paper, we formulate tracking and state-estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set. Due to the discontinuous trajectories arising from the impacts, we use hybrid systems stability analysis tools to establish the results. Using a novel concept of mirrored images of the target mass we prove that 1) a tracking control algorithm, and 2) an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards, including rectangles. Moreover, we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking. The results are illustrated via simulations.]]> 58 6 1470 1485 6571 In the robust stability analysis of linear time invariant systems, the frequency domain and uncertainty domain of interest play algebraically symmetric roles. This paper presents a new formulation of the S-procedure and the KYP lemma which emphasizes this symmetry. The new formulation provides a novel and unified approach for understanding when the KYP lemma provides an exact LMI test for robust stability. The notions of weak and strong mutual losslessness are introduced to characterize lossless S-procedure and KYP lemma. The new formulation has sufficient flexibility to accommodate some recent extensions of the KYP lemma, including the Generalized KYP lemma, the KYP lemma for nD systems, and the diagonal bounded real lemma for internally positive systems. Using the proposed framework, we also provide a lossless scaled small gain test for internally positive systems which gives an alternative proof that the structured singular value for such systems with arbitrary number of scalar uncertainties can be efficiently computed.]]> 58 6 1486 1496 2731 58 6 1497 1510 3321 This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics, we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics. The perturbations are assumed to be stable and bounded in ${cal H}_{infty}$-norm by some a priori given desired tolerance. We derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance. It is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given, single linear system. Our protocols are expressed in terms of real symmetric solutions of certain algebraic Riccati equations and inequalities, and also involve weighting factors that depend on the eigenvalues of the graph Laplacian. For undirected network graphs we show that within the class of such dynamic protocols, a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the Laplacian. We also extend our results to additive nonlinear perturbations with ${cal L}_{2}$-gain bounded by a given tolerance.]]> 58 6 1511 1523 3410 58 6 1524 1529 659 58 6 1529 1534 1270 58 6 1534 1539 1409 58 6 1540 1545 1566 58 6 1546 1551 1081 58 6 1551 1556 1331 58 6 1557 1561 1003 58 6 1561 1566 1147 $H_{infty} $ control problem for a class of discrete-time Markov jump systems (MJSs) with uncertain transition probabilities (TPs) is investigated. The uncertain information of transition probabilities is quantized by Gaussian transition probability density function (pdf). In light of the proposed descriptions, the MJSs with Gaussian PDF of TPs cover the systems with precisely known and partially known TPs as two special cases. Sufficient conditions for the existence of $H_{infty} $ controller of the underlying systems are derived in term of linear matrix inequalities. A numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.]]> 58 6 1566 1572 1147 58 6 1573 1579 1491 $s^{-nu}$ (or $s^{nu}$ ) is stable and minimum-phase for any value $0<nu<1$ of the fractional order $nu$. It is also shown that zeros and poles of the approximation are interlaced and lie in the unit circle of the complex $z$ -plane, keeping a special symmetry on the real axis. The quality of the approximation is analyzed both in the frequency and time domain. Truncation error bounds of the approximants are given.]]> 58 6 1579 1585 1498 58 6 1585 1590 1373 58 6 1591 1596 1467 58 6 1597 1602 1056 58 6 1602 1608 1522 ${cal K}_{infty}$-continuous, the result applies to unbounded sets as well.]]> 58 6 1609 1613 1231 58 6 1613 1619 925 58 6 1620 1625 796 58 6 1626 1626 1156 58 6 1627 1627 1792 58 6 1628 1628 1637 58 6 C3 C3 160