Related papers: PolyOCP.jl -- A Julia Package for Stochastic OCPs …
A surrogate model approximates a computationally expensive solver. Polynomial Chaos is a method to construct surrogate models by summing combinations of carefully chosen polynomials. The polynomials are chosen to respect the probability…
The paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimizes a discounted cost…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
Model predictive control (MPC) is of increasing interest in applications for constrained control of multivariable systems. However, one of the major obstacles to its broader use is the computation time and effort required to solve a…
Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a…
In this paper, a new python package (optipoly) is described that solves box-constrained optimization problem over multivariate polynomial cost functions. The principle of the algorithm is described before its performance is compared to…
Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…
The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
We present a stochastic model predictive control (MPC) method for linear discrete-time systems subject to possibly unbounded and correlated additive stochastic disturbance sequences. Chance constraints are treated in analogy to robust MPC…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based…
An integrated optimization method based on the constrained multi-objective evolutionary algorithm (MOEA) and non-intrusive polynomial chaos expansion (PCE) is proposed, which solves robust multi-objective optimization problems under…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…
Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named…
Stochastic expansion-based methods of uncertainty quantification, such as polynomial chaos and separated representations, require basis functions orthogonal with respect to the density of random inputs. Many modern engineering problems…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the…