3,654 research outputs found
Computing control invariant sets in high dimension is easy
In this paper we consider the problem of computing control invariant sets for
linear controlled high-dimensional systems with constraints on the input and on
the states. Set inclusions conditions for control invariance are presented that
involve the N-step sets and are posed in form of linear programming problems.
Such conditions allow to overcome the complexity limitation inherent to the set
addition and vertices enumeration and can be applied also to high dimensional
systems. The efficiency and scalability of the method are illustrated by
computing approximations of the maximal control invariant set, based on the
10-step operator, for a system whose state and input dimensions are 30 and 15,
respectively.Comment: arXiv admin note: substantial text overlap with arXiv:1708.0479
Computing control invariant sets is easy
In this paper we consider the problem of computing control invariant sets for
linear controlled systems with constraints on the input and on the states. We
focus in particular on the complexity of the computation of the N-step
operator, given by the Minkowski addition of sets, that is the basis of many of
the iterative procedures for obtaining control invariant sets. Set inclusions
conditions for control invariance are presented that involve the N-step sets
and are posed in form of linear programming problems. Such conditions are
employed in algorithms based on LP problems that allow to overcome the
complexity limitation inherent to the set addition and can be applied also to
high dimensional systems. The efficiency and scalability of the method are
illustrated by computing in less than two seconds an approximation of the
maximal control invariant set, based on the 15-step operator, for a system
whose state and input dimensions are 20 and 10 respectively
Attenuation of Persistent L∞-Bounded Disturbances for Nonlinear Systems
A version of nonlinear generalization of the L1-control problem, which deals with the attenuation of persistent bounded disturbances in L∞-sense, is investigated in this paper. The methods used in this paper are motivated by [23]. The main idea in the L1-performance analysis and synthesis is to construct a certain invariant subset of the state-space such that achieving disturbance rejection is equivalent to restricting the state-dynamics to this set. The concepts from viability theory, nonsmooth analysis, and set-valued analysis play important roles. In addition, the relation between the L1-control of a continuous-time system and the l1-control of its Euler approximated discrete-time systems is established
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
We introduce the framework of path-complete graph Lyapunov functions for
approximation of the joint spectral radius. The approach is based on the
analysis of the underlying switched system via inequalities imposed among
multiple Lyapunov functions associated to a labeled directed graph. Inspired by
concepts in automata theory and symbolic dynamics, we define a class of graphs
called path-complete graphs, and show that any such graph gives rise to a
method for proving stability of the switched system. This enables us to derive
several asymptotically tight hierarchies of semidefinite programming
relaxations that unify and generalize many existing techniques such as common
quadratic, common sum of squares, and maximum/minimum-of-quadratics Lyapunov
functions. We compare the quality of approximation obtained by certain classes
of path-complete graphs including a family of dual graphs and all path-complete
graphs with two nodes on an alphabet of two matrices. We provide approximation
guarantees for several families of path-complete graphs, such as the De Bruijn
graphs, establishing as a byproduct a constructive converse Lyapunov theorem
for maximum/minimum-of-quadratics Lyapunov functions.Comment: To appear in SIAM Journal on Control and Optimization. Version 2 has
gone through two major rounds of revision. In particular, a section on the
performance of our algorithm on application-motivated problems has been added
and a more comprehensive literature review is presente
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