This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm ...This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ＇smallest＇ possible asymptotic variance.展开更多
In this paper,a distributed stochastic approximation algorithm is proposed to track the dynamic root of a sum of time-varying regression functions over a network.Each agent updates its estimate by using the local obse...In this paper,a distributed stochastic approximation algorithm is proposed to track the dynamic root of a sum of time-varying regression functions over a network.Each agent updates its estimate by using the local observation,the dynamic information of the global root,and information received from its neighbors.Compared with similar works in optimization area,we allow the observation to be noise-corrupted,and the noise condition is much weaker.Furthermore,instead of the upper bound of the estimate error,we present the asymptotic convergence result of the algorithm.The consensus and convergence of the estimates are established.Finally,the algorithm is applied to a distributed target tracking problem and the numerical example is presented to demonstrate the performance of the algorithm.展开更多
This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are...This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are not zero at the sought-for x^0, 2. lim supnot zero, here {ξ_i} are the measurement errors and {a_n} are the weighting coefficients in thealgorithm. Allowing these deviations from zero to occur simultaneously but to remain small, thispaper shows that the estimation error is still small even for a class fo measurement errors moregeneral than that considered in [2].展开更多
In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange mu...In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange multiplier algorithm of Bertsekas type. Thus this methodhas the advantages of both the two.展开更多
The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions wi...The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the systems,adaptive regulators are directly designed based on the event-triggered observations on the regulation errors.The adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions,the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically minimized.The authors also testify the theoretical results through simulation studies.展开更多
基金supported by the U.S. Army Research Office (No. W911NF-12-1-0223)
文摘This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ＇smallest＇ possible asymptotic variance.
基金This work was supported by the National Key Research and Development Program of China under Grant 2018YFA0703800the National Natural Science Foundation of China under Grant 61822312This work was also supported(in part)by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA27000000.
文摘In this paper,a distributed stochastic approximation algorithm is proposed to track the dynamic root of a sum of time-varying regression functions over a network.Each agent updates its estimate by using the local observation,the dynamic information of the global root,and information received from its neighbors.Compared with similar works in optimization area,we allow the observation to be noise-corrupted,and the noise condition is much weaker.Furthermore,instead of the upper bound of the estimate error,we present the asymptotic convergence result of the algorithm.The consensus and convergence of the estimates are established.Finally,the algorithm is applied to a distributed target tracking problem and the numerical example is presented to demonstrate the performance of the algorithm.
基金This project is supported by the National Natural Science Foundation of China
文摘This paper is a continuation of the research carried out in [1]-[2], where the robustnessanalysis for stochastic approximation algorithms is given for two cases: 1. The regression functionand the Liapunov function are not zero at the sought-for x^0, 2. lim supnot zero, here {ξ_i} are the measurement errors and {a_n} are the weighting coefficients in thealgorithm. Allowing these deviations from zero to occur simultaneously but to remain small, thispaper shows that the estimation error is still small even for a class fo measurement errors moregeneral than that considered in [2].
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper we design an approximation method for solving stochastic programs with com-plete recourse and nonlinear deterministic constraints. This method is obtained by combiningapproximation method and Lagrange multiplier algorithm of Bertsekas type. Thus this methodhas the advantages of both the two.
基金supported by the National Key Research and Development Program of China under Grant No.2018YFA0703800the Chinese Academy of Sciences(CAS)Project for Young Scientists in Basic Research under Grant No.YSBR-008the Strategic Priority Research Program of CAS under Grant No.XDA27000000。
文摘The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the systems,adaptive regulators are directly designed based on the event-triggered observations on the regulation errors.The adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions,the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically minimized.The authors also testify the theoretical results through simulation studies.
