We describe an efficient method for solving an optimal control problem that arises in robust model-predictive control. The problem is to design the input sequence that minimizes the peak tracking error between the ouput of a linear dynamical system and a desired target output, subject to inequality constraints on the inputs.

Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the …

1.1 Robust linear programming In this section, we will be looking at the basic case of robust linear programming. We will consider two types of uncertainty sets: polytopic and ellipsoidal. A robust LP is a problem of the form: min. x cTx (1) s.t. aT i x b i; 8a i2U a i; 8b i2U b i;i= 1;:::;m; where U a i Rn and U b i R are given uncertainty ...

Robust Optimization • definitions of robust optimization • robust linear programs • robust cone programs • chance constraints EE364b, Stanford University

We propose an approach to two-stage linear optimization with recourse that does not in-volve a probabilistic description of the uncertainty and allows the decision-maker to adjust the degree of conservativeness of the model, while preserving its linear properties.

Jan 1, 2002 · Numerical algorithms for linear and quadratic programming have been applied to optimal control since the 60s, and are widely used in model-predictive control, see (Morari and Lee 1999, Rawlings 2000).

Mar 24, 2009 · We propose an approach to linear optimization with recourse that does not involve a probabilistic description of the uncertainty, and allows the decision-maker to adjust the degree of robustness of the model while preserving its linear properties.

This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified

Jul 1, 2017 · We propose a randomized, distributed algorithm working under time-varying, asynchronous and directed communication topology. The algorithm is based on a local computation and communication paradigm.

We also outline a semidefinite programming based algorithm for providing upper bounds on robust-to-dynamics linear programs. Index Terms—Robust optimization, linear programming, semidefinite programming, dynamical systems.