NDLI: Mean-field formulation for the infinite-horizon mean–variance control of discrete-time linear systems with multiplicative noises

Content Provider	IET Digital Library
Author	Barbieri, Fabio Costa, Oswaldo L. V.
Abstract	This study considers the infinite-horizon stochastic optimal control of a discounted and long-run average costs under a mean–variance trade-off performance criterion for discrete-time linear systems subject to multiplicative noises. The authors adopt a mean-field approach to tackle the problem and get an optimal control solution in terms of a set of two generalised coupled algebraic Riccati equations (GCAREs). Then, they establish sufficient conditions for the existence of the maximal solution and necessary and sufficient conditions for the existence of the mean-square stabilising solution to the GCARE. From this solution, they derive optimal control policies to the related discounted and long-run average cost problems. A numerical example illustrates the obtained results for the multi-period portfolio selection problem in which it is desired to minimise the sum of the mean–variance trade-off costs of a portfolio against a benchmark along the time.
Starting Page	2600
Ending Page	2612
Page Count	13
ISSN	17518644
Volume Number	14
e-ISSN	17518652
Issue Number	Issue 17, Nov (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/14/17
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2020.0442
Journal	IET Control Theory & Applications
Publisher Date	2020-09-07
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Average Cost Average Cost Problem Closed Loop System Discrete Control System Discrete Time System Discrete-time Linear System Field Formulation GCARE Generalised Coupled Algebraic Riccati Equation Infinite-horizon Mean–variance Control Infinite-horizon Stochastic Optimal Control Interpolation And Function Approximation Investment Linear System Matrix Algebra Maximal Solution Mean-field Approach Mean-square Stabilising Solution Mean–variance Trade-off Costs Mean–variance Trade-off Performance Criterion Multiperiod Portfolio Selection Problem Multiplicative Noises Numerical Analysis Optimal Control Optimal Control Policy Optimal Control Solution Optimisation Optimisation Technique Riccati Equation Stability Stability in Control Theory Statistics Stochastic Linearised SCUC Stochastic System Sufficient Condition
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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