Convexity and convex approximations of discrete-time stochastic control problems with constraints

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost subject to probabilistic constraints. We study the convexity of a finite-horizon optimization problem in the case where the contro...

Full description

Saved in:
Bibliographic Details
Published in:Automatica (Oxford) 2011-09, Vol.47 (9), p.2082-2087
Main Authors: Cinquemani, Eugenio, Agarwal, Mayank, Chatterjee, Debasish, Lygeros, John
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Automatic
Bioinformatics
Calculus of variations and optimal control
Computer Science
Computer science
control theory
systems
Control system analysis
Control theory. Systems
Convex optimization
Convexity
Dynamical Systems
Engineering Sciences
Exact sciences and technology
Linear matrix inequalities
Mathematical analysis
Mathematical models
Mathematics
Optimal control
Optimization
Optimization and Control
Probabilistic constraints
Probabilistic methods
Probability theory
Sciences and techniques of general use
Signal and Image Processing
Stochastic processes
Stochasticity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost subject to probabilistic constraints. We study the convexity of a finite-horizon optimization problem in the case where the control policies are affine functions of the disturbance input. We propose an expectation-based method for the convex approximation of probabilistic constraints with polytopic constraint function, and a Linear Matrix Inequality (LMI) method for the convex approximation of probabilistic constraints with ellipsoidal constraint function. Finally, we introduce a class of convex expectation-type constraints that provide tractable approximations of the so-called integrated chance constraints. Performance of these methods and of existing convex approximation methods for probabilistic constraints is compared on a numerical example.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.01.023