Publications de Milan Korda | EPFL Graph Search

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates polynomial under-approximations to the value function of the optimal ...

Elsevier Science Bv2017

Solving the Infinite-horizon Constrained LQR Problem using Accelerated Dual Proximal Methods

Georgios Stathopoulos, Colin Neil Jones, Milan Korda

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting (FBS), and prov ...

Institute of Electrical and Electronics Engineers2017

Technical Report: Control of Nonlinear Systems with Explicit-MPC-like Controllers

Colin Neil Jones, Milan Korda, Ivan Pejcic

This paper describes synthesis of controllers involving Quadratic Programming (QP) optimization problems for control of nonlinear systems. The QP structure allows an implementation of the controller as a piecewise affine function, pre-computed offline, whi ...

2017

Y Stability and performance verification of optimization-based controllers

Colin Neil Jones, Milan Korda

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include g ...

Pergamon-Elsevier Science Ltd2017

On turnpike and dissipativity properties of continuous-time optimal control problems

Dominique Bonvin, Colin Neil Jones, Milan Korda, Timm Faulwasser

This paper investigates the relations between three different properties, which are of importance in optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnp ...

Pergamon-Elsevier Science Ltd2017

Controller design and value function approximation for nonlinear dynamical systems

Colin Neil Jones, Milan Korda

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of th ...

Pergamon-Elsevier Science Ltd2016

Moment-sum-of-squares hierarchies for set approximation and optimal control

Milan Korda

This thesis uses the idea of lifting (or embedding) a nonlinear controlled dynamical system into an infinite-dimensional space of measures where this system is equivalently described by a linear equation. This equation and problems involving it are subsequ ...

EPFL2016

Certification of fixed computation time first-order optimization-based controllers for a class of nonlinear dynamical systems

Colin Neil Jones, Milan Korda

This paper proposes a stability verification method for systems controlled by an early terminated first-order method (e.g., an MPC problem approximately solved by a fixed number of iterations of the fast gradient method). The method is based on the observa ...

Ieee2014

Solving the infinite-horizon constrained LQR problem using splitting techniques

Georgios Stathopoulos, Colin Neil Jones, Milan Korda

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR proble ...

Elsevier2014

Turnpike and dissipativity properties in dynamic real-time optimization and economic MPC

Dominique Bonvin, Colin Neil Jones, Milan Korda, Timm Faulwasser

We investigate the turnpike and dissipativity properties of continuous-time optimal control problems. These properties play a key role in the analysis and design of schemes for dynamic real-time optimization and economic model predictive control. We show i ...

2014

Stochastic MPC framework for controlling the average constraint violation

Colin Neil Jones, Milan Korda

This paper considers linear discrete-time systems with additive, bounded, disturbances subject to hard control input bounds and a stochastic constraint on the amount of state-constraint violation averaged over time. The amount of violations is quantified b ...

Institute of Electrical and Electronics Engineers2014

Convex computation of the maximum controlled invariant set for polynomial control systems

Colin Neil Jones, Milan Korda

We characterize the maximum controlled invariant (MCI) set for discrete- as well as continuous-time nonlinear dynamical systems as the solution of an infinite-dimensional linear programming problem. For systems with polynomial dynamics and compact semialge ...

Society for Industrial and Applied Mathematics2014

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

Institute of Electrical and Electronics Engineers2014

On the selection of the most appropriate MPC problem formulation for buildings

Colin Neil Jones, Milan Korda

Model Predictive Control (MPC) for buildings has gained a lot of attention recently. It has been shown that MPC can achieve significant energy savings in the range between 15-30 % compared to a conventional control strategy, e.g., to a rule-based controlle ...

2013

Convex computation of the maximum controlled invariant set for discrete-time polynomial control systems

Colin Neil Jones, Milan Korda

We characterize the maximum controlled invariant (MCI) set for discrete-time systems as the solution of an infinite-dimensional linear programming problem. In the case of systems with polynomial dynamics and semialgebraic state and control constraints, we ...

2013

Convex computation of the region of attraction of polynomial control systems

Milan Korda

We address the long-standing problem of computing the region of attraction (ROA) of a target set (typically a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input constraints. We ...

2013

Nonquadratic Stochastic Model Predictive Control: A Tractable Approach

Milan Korda

This paper deals with the nite horizon stochastic optimal control problem with the expectation of the p-norm as the objective function and jointly Gaussian, although not necessarily independent, additive disturbance process. We develop an approximation str ...

Pergamon-Elsevier Science Ltd2012

Stochastic Model Predictive Control: Controlling the Average Number of Constraint Violations

Colin Neil Jones, Milan Korda

This paper considers linear discrete-time systems with additive bounded disturbances subject to hard control input bounds and constraints on the expected number of state-constraint violations averaged over time, or, equivalently, constraints on the probabi ...

2012