With this, the considered system becomes a piecewise homogeneous Itô stochastic MJLS. Over 10 million scientific documents at your fingertipsThis book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for tw This paper investigates a linear quadratic mean eld leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. LINEAR QUADRATIC OPTIMAL CONTROL In this chapter, we study a different control design methodology, one which is based on optimization.
Part 2 Properties and application … Control design objectives are formulated in terms of a cost criterion. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.This service is more advanced with JavaScript available The optimal control law is the one which minimizes the cost criterion. SOCIAL OPTIMA IN LEADER-FOLLOWER MEAN FIELD LINEAR QUADRATIC CONTROL Jianhui Huang 1, Bing-Chang Wang2 and Tinghan Xie y; Abstract. This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. In this paper, the infinite time horizon linear quadratic optimal control problem is investigated for the continuous-time Itô stochastic Markovian jum… The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. It is assumed that the time-varying transition rates of the MJLSs possess piecewise homogeneous time-varying property, which implies that the transition rates are time-varying in the whole time domain but they are time-invariant in some small time intervals. The variations of the transition rates in these small time intervals are considered to be two cases: arbitrary variation and stochastic variation. Abstract:This paper studies a linear-quadratic optimal control problem derived by forward-backward stochastic differential equations, where the drift coefficient of the observation equation is linear with respect to the state $x$, and the observation noise is correlated with the state noise, in the sense that the cross-variation of the state and the observation is nonzero. Finally, a simulation example is provided to illustrate the effectiveness of the proposed linear quadratic optimal controllers.ScienceDirect ® is a registered trademark of Elsevier B.V. Linear quadratic (LQ) optimal control can be used to resolve some of these issues, by not specifying exactly where the closed loop eigenvalues should be directly, but instead by specifying some kind of performance objective function to be optimized. https://en.wikipedia.org/wiki/Linear–quadratic–Gaussian_control The main contribution of this paper is that two linear quadratic optimal controllers in infinite time horizon are proposed for the above modeled continuous-time piecewise homogeneous Itô stochastic MJLS in the sense of arbitrary variation and stochastic variation, respectively. In this paper, the infinite time horizon linear quadratic optimal control problem is investigated for the continuous-time Itô stochastic Markovian jump linear systems (MJLSs) with time-varying transition rates. Moreover, the sufficient and necessary conditions for the existence of the designed controllers are established based on the existence of the unique positive definite solution of two coupled algebraic Riccati matrix equations. The leader and the followers cooperate to optimize … Optimal Control: Linear Quadratic Methods @inproceedings{Anderson1979OptimalCL, title={Optimal Control: Linear Quadratic Methods}, author={Brian D. O. Anderson and John B. Moore}, year={1979} } Brian D. O. Anderson, John B. Moore; Published 1979; Mathematics; Part 1 Theory of the optimal regulator: the standard regulator problems I and II tracking systems.
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