The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Wei Ren - One of the best experts on this subject based on the ideXlab platform.
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distributed continuous time algorithms for optimal resource allocation with time varying Quadratic Cost functions
IEEE Transactions on Control of Network Systems, 2020Co-Authors: Bo Wang, Shan Sun, Wei RenAbstract:In this article, we propose distributed continuous-time algorithms to solve the optimal resource allocation problem with certain time-varying Quadratic Cost functions for multiagent systems. The objective is to allocate a quantity of resources while optimizing the sum of all the local time-varying Cost functions. Here, the optimal solutions are trajectories rather than some fixed points. We consider a large number of agents that are connected through a network, and our algorithms can be implemented using only local information. By making use of the prediction–correction method and the nonsmooth consensus idea, we first design two distributed algorithms to deal with the case when the time-varying Cost functions have identical Hessians. We further propose an estimator-based algorithm which uses distributed average tracking theory to estimate certain global information. With the help of the estimated global information, the case of nonidentical constant Hessians is addressed. In each case, it is proved that the solutions of the proposed dynamical systems with certain initial conditions asymptotically converge to the optimal trajectories. We illustrate the effectiveness of the proposed distributed continuous-time optimal resource allocation algorithms through simulations.
Yunjian Xu - One of the best experts on this subject based on the ideXlab platform.
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Segregated Linear Decision Rules for Distributionally Robust Control with Linear Dynamics and Quadratic Cost
2018 Annual American Control Conference (ACC), 2018Co-Authors: Yunjian XuAbstract:We investigate the multi-stage stochastic constrained control problem with linear dynamics and Quadratic Costs when only partial information of the disturbance distribution (i.e., the first two moments) is known. By constructing a distribution family or ambiguity set based on the known information, we adopt a distributionally robust chance constraint (DRCC) based approach, where the DRCC holds (with high probability) as long as the true distribution of the uncertainty belongs to the ambiguity set. We approximate the DRCC with the worst-case conditional value-at-risk (CVaR) constraint, which bounds the expected constraint violation with respect to all distributions in the ambiguity set. Although the worst-case CVaR problem is not guaranteed to be tractable in general, it is computationally tractable under linear decision rules (LDRs). To improve the performance of LDRs, we propose to apply the segregated linear decision rules (SLDRs) on dynamical control systems with the worst-case CVaR approximation. Without loss of optimality, we construct a special group of segregation leading to problems that are shown to be equivalent to tractable semidefinite programs (SDPs).
Tamer Basar - One of the best experts on this subject based on the ideXlab platform.
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bayesian persuasion with state dependent Quadratic Cost measures
IEEE Transactions on Automatic Control, 2021Co-Authors: Muhammed O Sayin, Tamer BasarAbstract:We address Bayesian persuasion between a sender and a receiver with state-dependent Quadratic Cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receiver's estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multi-agent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely-positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the sender's Cost for large state spaces.
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optimal hierarchical signaling for Quadratic Cost measures and general distributions a copositive program characterization
arXiv: Computer Science and Game Theory, 2019Co-Authors: Muhammed O Sayin, Tamer BasarAbstract:In this paper, we address the problem of optimal hierarchical signaling between a sender and a receiver for a general class of square integrable multivariate distributions. The receiver seeks to learn a certain information of interest that is known to the sender while the sender seeks to induce the receiver to perceive that information as a certain private information. For the setting where the players have Quadratic Cost measures, we analyze the Stackelberg equilibrium, where the sender leads the game by committing his/her strategies beforehand. We show that when the underlying state space is "finite", the optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. The equivalence established enables us to use the existing computational tools to solve this class of cone programs approximately with any error rate. For continuous distributions, we also analyze the error of approximation, if the optimal signaling strategy is computed for a discretized version obtained through a quantization scheme, and we provide an upper bound in terms of the quantization error.
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optimal coding and control for linear gaussian systems over gaussian channels under Quadratic Cost
2013Co-Authors: Serdar Yuksel, Tamer BasarAbstract:This chapter obtains optimal solutions for encoders and controllers under Quadratic Cost functions for linear Gaussian systems controlled over Gaussian channels, proving also the existence of optimal solutions. Furthermore, the chapter identifies conditions under which optimal coding and control policies are linear. A large class of network settings where optimal policies are non-linear is identified.
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model simplification and optimal control of stochastic singularly perturbed systems under exponentiated Quadratic Cost
Siam Journal on Control and Optimization, 1996Co-Authors: Zigang Pan, Tamer BasarAbstract:We study the optimal control of a general class of stochastic singularly perturbed linear systems with perfect and noisy state measurements under positively and negatively exponentiated Quadratic Cost. The (expected) Cost function to be minimized is actually taken as the long-term time average of the logarithm of the expected value of an exponentiated Quadratic loss. We identify appropriate ``slow'' and ``fast'' subproblems, obtain their optimum solutions (compatible with the corresponding measurement structure), and subsequently study the performances they achieve on the full-order system as the singular perturbation parameter $\epsilon $ becomes sufficiently small, with the expressions given in all cases being exact to within $O(\sqrt{\epsilon})$. It is shown that the composite controller (obtained by appropriately combining the optimum slow and fast controllers) achieves a performance level close to the optimal one whenever the full-order problem has a solution. The slow controller, on the other hand, achieves (asymptotically, as $\epsilon \to 0$) only a finite performance level (but not necessarily optimal), provided that the fast subsystem is open-loop stable. If the intensity of the noise in the system dynamics decreases to zero, however, the slow controller also achieves a performance level close to the optimal one. The paper also presents a more direct derivation (than heretofore available) of the solution to the linear exponential Quadratic Gaussian (LEQG) problem under noisy state measurements, which allows for a general Quadratic Cost (with cross terms) in the exponent and correlation between system and measurement noises, and obtains both necessary and sufficient conditions for existence of an optimal solution. Such a general LEQG problem is encountered in the slow-fast decomposition of the full-order problem, even if the original problem does not feature correlated noises. In this general context, the paper also establishes a complete equivalence between the LEQG problem and the \hi optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation.
T. Basar - One of the best experts on this subject based on the ideXlab platform.
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Model simplification and optimal control of stochastic singularly perturbed systems under exponentiated Quadratic Cost
Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994Co-Authors: T. BasarAbstract:Studies the optimal control of a class of stochastic singularly perturbed linear systems with noisy state measurements under positively and negatively exponentiated Quadratic Cost the so-called LEQG problem. The authors identify appropriate "slow" and "fast" subproblems, obtain their optimum solutions (compatible with the corresponding measurement structures), and subsequently study the performances they achieve on the full-order system as the singular perturbation parameter /spl epsiv/ becomes sufficiently small. A by-product of this analysis is a more direct derivation (than heretofore available) of the solution to the LEQG problem under noisy state measurements, which allows for a general Quadratic Cost (with cross terms) in the exponent and correlation between system and measurement noises. Such a general LEQG problem is encountered in the slow-fast decomposition of the full-order problem, even if the original problem does not feature correlated noises. In this general context, the paper also establishes a complete equivalence between the LEQG problem and the H/sup /spl infin//-optimal control problem with measurement feedback, though this equivalence does not extend to the slow and fast subproblems arrived at after time-scale separation.
Jiangliang Jin - One of the best experts on this subject based on the ideXlab platform.
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segregated linear decision rules for distributionally robust control with linear dynamics and Quadratic Cost
IEEE Systems Journal, 2021Co-Authors: Jiangliang JinAbstract:In this article, we investigate the multistage stochastic constrained control problem with linear dynamics and Quadratic Costs when only partial information of the disturbance distribution (i.e., the first two moments) is known. We adopt a distributionally robust chance constraint (DRCC)-based approach, where the DRCC holds (with high probability) as long as the true distribution of uncertainty belongs to a distribution family or the ambiguity set (constructed based on the known information). We approximate the DRCC with the worst-case conditional value-at-risk (CVaR) constraint, which bounds the expected constraint violation with respect to all distributions in the ambiguity set. The worst-case CVaR problem is known to be computationally tractable under linear decision rules (LDRs). To improve the performance of LDRs, we propose to apply the segregated linear decision rules (SLDRs) on dynamical control systems with the worst-case CVaR approximation. To deal with the tractability issue of the worst-case CVaR constraint, we construct a special group of segregation (of the random disturbance) that is shown to be without loss of optimality. The proposed segregation method enables us to establish the equivalence between the stochastic control problem (with worst-case CVaR constraints and under SLDRs) and a tractable semidefinite program.
