Total sum of squares

Y Stability and performance verification of optimization-based controllers

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

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

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

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