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

Authors:
Eugenio Cinquemani;Mayank Agarwal;Debasish Chatterjee;John Lygeros
Affiliations:
INRIA Grenoble-Rhône-Alpes, 655 avenue de l'Europe, Montbonnot, 38334 Saint Ismier cedex, France;Department of Electrical Engineering, Stanford University, CA, USA;Automatic Control Laboratory, Physikstrasse 3, ETH Zürich, 8092 Zürich, Switzerland;Automatic Control Laboratory, Physikstrasse 3, ETH Zürich, 8092 Zürich, Switzerland
Venue:
Automatica (Journal of IFAC)
Year:
2011

Citing 14
Cited 3

Rolling horizon procedures in nonhomogeneous Markov decision processes

Operations Research - Supplement to Operations Research: stochastic processes
Adjustable robust solutions of uncertain linear programs

Mathematical Programming: Series A and B
Probabilistically Constrained Linear Programs and Risk-Adjusted Controller Design

SIAM Journal on Optimization
Tractable Approximations to Robust Conic Optimization Problems

Mathematical Programming: Series A and B
Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

Mathematical Programming: Series A and B
Convex Approximations of Chance Constrained Programs

SIAM Journal on Optimization
Technical Communique: Input-to-state stability of robust receding horizon control with an expected value cost

Automatica (Journal of IFAC)
Brief paper: Constrained linear system with disturbance: Convergence under disturbance feedback

Automatica (Journal of IFAC)
Brief paper: Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints

Automatica (Journal of IFAC)
Brief paper: Convergence properties of constrained linear system under MPC control law using affine disturbance feedback

Automatica (Journal of IFAC)
Stochastic MPC with inequality stability constraints

Automatica (Journal of IFAC)
Randomized algorithms for robust controller synthesis using statistical learning theory

Automatica (Journal of IFAC)
Optimization over state feedback policies for robust control with constraints

Automatica (Journal of IFAC)
Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications

Randomized Algorithms for Analysis and Control of Uncertain Systems: With Applications

Stochastic receding horizon control with output feedback and bounded controls

Automatica (Journal of IFAC)
Lyapunov-based model predictive control of stochastic nonlinear systems

Automatica (Journal of IFAC)
Stochastic model predictive control of LPV systems via scenario optimization

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.15

Visualization

Abstract

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.