In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are...In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are restricted to be linear.The authors show that the multiple decentralized control models,the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption.The main contribution of the paper is the solution technique.Traditionally,optimal controllers for decentralized LQ systems are identified using dynamic programming,maximum principle,or spectral decomposition.The authors present an alternative approach which is based by combining elementary building blocks from linear systems,namely,completion of squares,state splitting,static reduction,orthogonal projection,(conditional)independence of state processes,and decentralized estimation.展开更多
基金supported in part by the Natural Sciences and Engineering Research Council of Canada(NSERC)Discovery Grant under Grant No.RGPIN-2021-0351.
文摘In this paper,the authors revisit decentralized control of linear quadratic(LQ)systems.Instead of imposing an assumption that the process and observation noises are Gaussian,the authors assume that the controllers are restricted to be linear.The authors show that the multiple decentralized control models,the form of the best linear controllers is identical to the optimal controllers obtained under the Gaussian noise assumption.The main contribution of the paper is the solution technique.Traditionally,optimal controllers for decentralized LQ systems are identified using dynamic programming,maximum principle,or spectral decomposition.The authors present an alternative approach which is based by combining elementary building blocks from linear systems,namely,completion of squares,state splitting,static reduction,orthogonal projection,(conditional)independence of state processes,and decentralized estimation.
