相关论文: Inner approximations of the region of attraction f…
We address the long-standing problem of computing the region of attraction (ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a controlled nonlinear system with polynomial dynamics and semialgebraic state and input…
This work presents a method to obtain inner and outer approximations of the region of attraction of a given target set as well as an admissible controller generating the inner approximation. The method is applicable to constrained…
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…
Motivated by stability analysis of large scale power systems, we describe how the Lasserre (moment-sums of squares, SOS) hierarchy can be used to generate outer approximations of the region of attraction (ROA) of sparse polynomial…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
This paper presents a method for calculating the Region of Attraction (ROA) of nonlinear dynamical systems, both with and without control. The ROA is determined by solving a hierarchy of semidefinite programs (SDPs) defined on a splitting…
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…
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on…
Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we…
We consider the problem of nonlinear system identification when prior knowledge is available on the region of attraction (ROA) of an equilibrium point. We propose an identification method in the form of an optimization problem, minimizing…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach…
This paper focuses on the analysis of the Region of Attraction (RoA) for unknown autonomous dynamical systems. A data-driven approach based on the moment-Sum-of-Squares (SoS) hierarchy is proposed, enabling novel RoA outer approximations…
We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear…
In this paper we propose a convex programming based method for computing robust regions of attraction for state-constrained perturbed discrete-time polynomial systems. The robust region of attraction of interest is a set of states such that…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…