797 research outputs found
Large networks of dynamic agents: Consensus under adversarial disturbances
No full textThis paper studies interactions among homogeneous social groups within the framework of large population games. Each group is represented by a network and the behavior described by a two-player repeated game. The contribution is three-fold. Beyond the idea of providing a novel two-level model with repeated games at a lower level and population games at a higher level, we also establish a mean field equilibrium and study state feedback best-response strategies as well as worst-case adversarial disturbances in that context. © 2012 IEEE
Optimal monotone forwarding policies in delay tolerant mobile ad-hoc networks
No full textWe study fluid approximations for a class of monotone relay policies in delay tolerant ad-hoc networks. This class includes the epidemic routing and the two-hops routing protocols. We enhance relay policies with probabilistic forwarding, i.e., a message is forwarded to a relay with some probability . We formulate an optimal control problem where a tradeoff between delay and energy consumption is captured and optimized. We compute both the optimal static value of as well as the optimal time dependent value of . We show that the time-dependent problem is optimized by threshold type policies, and we compute explicitly the value of the optimal threshold for some special classes of relay policies
Optimal Control in Two-Hop Relay Routing
No full textWe study the optimal control of propagation of packets in delay tolerant mobile ad-hoc networks. We consider a two-hop forwarding policy under which the expected number of nodes carrying copies of the packets obeys a linear dynamics. We exploit this property to formulate the problem in the framework of linear quadratic optimal control which allows us to obtain closed-form expressions for the optimal control and to study numerically the tradeoffs by varying various parameters that define the cost
Optimal control in two-hop relay routing
No full textWe study the optimal control of propagation of packets in delay tolerant mobile ad-hoc networks. We consider a two-hop forwarding policy under which the expected number of nodes carrying copies of the packets obeys a linear dynamics. We exploit this property to formulate the problem in the framework of linear quadratic optimal control which allows us to obtain closed-form expressions for the optimal control and to study numerically the tradeoffs by varying various parameters that define the cost
The Stackelberg Equilibria of the Kelly Mechanism
No full textThe Kelly mechanism dictates that players share a resource proportionally to their bids. The corresponding game is known to have a unique Nash equilibrium. A related question arises, which is the nature of the behavior of the players for different prices imposed by the resource owner, who may be viewed as the leader in a Stackelberg game where the other players are followers. In this work, we describe the dynamics of the Nash equilibrium as a function of the price. Toward that goal, we characterize analytical properties of the Nash equilibrium by means of the implicit function theorem. With regard to the revenue generated by the resource owner, we provide a counterexample which shows that the Stackelberg equilibrium of the Kelly mechanism may not be unique. We obtain sufficient conditions which guarantee the set of Stackelberg equilibria to be finite and unique in the symmetric case. Finally, we describe the dependency between the resource’s signal and the maximum revenue that the resource owner can generate
Topics in decentralized detection
No full textIn this thesis we obtain several new results in the areas of decentralized sequential detection and robust decentralized detection.In the area of decentralized sequential detection, we first consider the case in which each sensor performs a sequential test on its observations and arrives at a local decision about the true hypothesis; subsequently, the local decisions of all of the sensors are used for a common purpose. Here we assume that decision errors at the sensors are penalized through a common cost function and that each time step taken by the detectors as a team is assigned a positive cost. We show that optimal sensor decision functions can be found in the class of generalized sequential probability ratio tests with monotonically convergent thresholds. We present a technique for obtaining optimal thresholds.We also consider the case in which each sensor sends a sequence of summary messages to a fusion center in which a sequential test is carried out to determine the true hypothesis. Here we assume that decision errors at the fusion center are penalized through a cost function and that each time step taken to arrive at the final decision costs a positive amount. We show that the problem is tractable when the information structure in the system is quasiclassical. In particular, we show that an optimal fusion center policy has a simple structure resembling a sequential probability ratio test and that a stationary set of monotone likelihood ratio tests is optimal at the sensors. Finally, we compute the optimal decision functions for some representative examples.In the area of robust decentralized detection, we consider the case in which the sensor distributions are assumed to belong to known uncertainty classes. We show for a broad class of such decentralized detection problems that a set of least favorable distributions exists for minimax robust testing between the hypotheses. We thus establish that minimax robust tests are obtained as solutions to simple decentralized detection problems in which the sensor distributions are specified to be the least favorable distributions.Made available in DSpace on 2011-05-07T12:48:37Z (GMT). No. of bitstreams: 2
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Model simplification and robust control in deterministic and stochastic systems using singular perturbation methods
No full text"The class of uncertainties that may be present in dynamical systems includes, but is not limited to, unknown disturbance inputs, unpredictable abrupt structural changes, unknown parameters, and unmodeled fast dynamics. A number of different stochastic and deterministic models that incorporate these uncertainties have been proposed in the literature, and these have led to different robust control and filtering problem formulations, methodologies, and resulting robust designs. This thesis presents novel formulations of three different classes of problems featuring the types of uncertainties described above, studies them from the points of view of model reduction and robust controller design, and develops new theory and methodology for their solutions. The common thread that runs through these three classes of problems (which involve both deterministic and stochastic systems) is the use of ""singular perturbations,"" either as a modeling tool or as a computational tool. The reason for adopting the singular perturbations framework is threefold. First, we must study robustness with respect to fast unmodeled dynamics of different control or filtering designs. The second reason is to incorporate appropriate knowledge on fast dynamics into the design, without using the full-order system, so as to improve performance and to alleviate the numerical ill-conditioning associated with the computation of the full-order solution. Third, we must obtain ""reliable"" reduced-order models for large-scale systems that exhibit two or multi time-scale behavior, such that the solution to the reduced-order model can achieve a desired performance for the full-order system."The thesis can naturally be divided into three parts. In the first part, the problem of optimal control and model reduction for singularly perturbed linear Gaussian systems under an exponential-of-quadratic performance index is addressed, for which a complete solution is obtained that achieves all three objectives stated above. In the second part, which comprises two chapters, solutions to the problem of model reduction for large-scale jump linear systems are presented. The original system is again assumed to exhibit a two-time-scale behavior, and two types of time-scale separations are studied in detail in two separate chapters. Finally, in the last part of the thesis, which also comprises two chapters, solutions to problems of robust parameter identification and robust adaptive control are presented. For these classes of problems, the original system may not exhibit a two-time-scale behavior at the outset, but time-scale decomposition arises naturally due to singularity in the measurement scheme. A singular perturbation analysis is then employed to construct reduced-order identifiers and controllers and to prove their optimality. Again, the three objectives are achieved for the closed-loop system. The thesis ends with some concluding remarks, delineation of its main contributions, and some discussions on future extensions of these results.Made available in DSpace on 2011-05-07T12:51:23Z (GMT). No. of bitstreams: 2
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Previous issue date: 1996Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding ([email protected]) on 2011-05-07T14:46:47Z
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Design of minimax controllers for nonlinear systems using cost-to-come methods
No full textThis thesis develops and utilizes the cost-to-come methodology for the construction of minimax controllers for nonlinear systems with partial-state information (PSI), which are subjected to deterministic uncertainty. It introduces the notion of a cost-to-come function and shows how it leads to necessary and sufficient conditions for the existence of a minimax controller. These conditions are the existence of the cost-to-come function and the existence of a solution to an auxiliary full-information (FI) minimax problem. It is also proven that a solution of the FI problem leads directly to a solution of the original PSI problem. The significance of this result is that the auxiliary FI problem can be solved using better-known dynamic programming (DP) techniques."Generally, the auxiliary problem has an infinite-dimensional state, which may make the cost-to-come methodology impractical. Toward resolving this impediment, the thesis first identifies two classes of problems for which cost-to-come methods offer significant insights: one, problems that satisfy a certainty-equivalence principle (which is attributed to the case when a minimax controller can be chosen to be a full-state information (FSI) minimax controller with the state replaced by a ""worst-case"" value of the state), and two, problems for which the cost-to-come function can be characterized by a finite number of parameters (which is attributed to the case where the auxiliary FI problem has a finite-dimensional state). Outside these two classes, bounding techniques can be used to reduce the problem complexity, at the expense of some possible performance degradation. By bounding the FSI cost-to-go function from above, the certainty-equivalence principle can be generalized to gain some insight into the structure of cost-bounding controllers, which may lead to alternative parameter design methods. Bounding the cost-to-come function by finite-dimensional structured cost-to-come functions allows the construction of an auxiliary FI problem, which leads to a cost-bounding controller policy."As an application of the cost-to-come methodology, a class of affine-quadratic (AQ) disturbance attenuation problems is considered in some detail. This class contains H\sp\infty-optimal control and filtering problems, problems of parameter identification and nonlinear adaptive control, and memoryless control problems. For the former subclass, cost-to-come methods provide an alternative derivation of the well-known necessary and sufficient conditions and of a minimax policy. For the latter three subclasses, new algorithms are developed that lead either directly or recursively to optimal solutions. Some numerical examples and simulation studies are provided to illustrate the theoretical results.Made available in DSpace on 2011-05-07T14:21:39Z (GMT). No. of bitstreams: 2
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Dynamic multi-person optimization with weakly coupled agents
No full textIn this thesis, we study multiple decision maker problems where the decision makers are coupled through a small parameter . The class of systems considered exhibit the common feature that when the weak coupling is completely absent (i.e., when the coupling parameter = 0), the problem decomposes into a number of independent tractable problems or into a single tractable problem, but when the coupling is strong the problem may be difficult to solve. We are interested in the intermediate case when the coupling is neither absent nor strong. The central idea behind the construction of approximate solutions is to start with the zeroth order solution (obtained by setting = 0) and iteratively obtain successively better approximations to the optimal or equilibrium solution. Specifically, we have studied LQG teams featuring a nonclassical information pattern, nonlinear deterministic differential games, LQG nonzero-sum games and Markov decision problems. In the case of LQG teams, we showed the existence of finite-dimensional linear controllers (FDLCs) which approximate the optimal cost to O(). Then, by restricting ourselves to the class of FDLCs, we obtained higher order approximations to the optimal cost by solving a sequence of single decision maker LQG stochastic control problems. In LQG nonzero-sum games, we established the existence of a finite-dimensional Nash equilibrium for small values of the coupling parameter; further, we also showed that this equilibrium solution is well-posed and admissible as tends to zero. For the class of nonlinear, nonzero-sum differential games, we considered two types of information structures. In the case of the open-loop information structure, we have shown that approximate Nash equilibria can be obtained by solving the zeroth order problems and a sequence of LQ optimal control problems. When the information structure is dynamic, the decomposition involves the solution of the zeroth order problems and a sequence of cost evaluations (no control involved) followed by static optimization problems. We have also shown the existence of solutions to Markov decision problems featuring nonclassical information under the assumption of a finite-control set. Through the weak-coupling approach, we have thus been able to identify a class of tractable problems which were long thought to be intractable.Made available in DSpace on 2011-05-07T13:47:05Z (GMT). No. of bitstreams: 2
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