91 research outputs found
Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices
In this paper, we propose an approach to controller synthesis for a class of
constrained nonlinear systems. It is based on the use of a hybridization, that
is a hybrid abstraction of the nonlinear dynamics. This abstraction is defined
on a triangulation of the state-space where on each simplex of the
triangulation, the nonlinear dynamics is conservatively approximated by an
affine system subject to disturbances. Except for the disturbances, this
hybridization can be seen as a piecewise affine hybrid system on simplices for
which appealing control synthesis techniques have been developed in the past
decade. We extend these techniques to handle systems subject to disturbances by
synthesizing and coordinating local robust affine controllers defined on the
simplices of the triangulation. We show that the resulting hybrid controller
can be used to control successfully the original constrained nonlinear system.
Our approach, though conservative, can be fully automated and is
computationally tractable. To show its effectiveness in practical applications,
we apply our method to control a pendulum mounted on a cart
Reach Control on Simplices by Piecewise Affine Feedback
We study the reach control problem for affine systems on simplices, and the
focus is on cases when it is known that the problem is not solvable by
continuous state feedback. We examine from a geometric viewpoint the structural
properties of the system which make continuous state feedbacks fail. This
structure is encoded by so-called reach control indices, which are defined and
developed in the paper. Based on these indices, we propose a subdivision
algorithm and associated piecewise affine feedback. The method is shown to
solve the reach control problem in all remaining cases, assuming it is solvable
by open-loop controls
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
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
An hybrid system approach to nonlinear optimal control problems
We consider a nonlinear ordinary differential equation and want to control
its behavior so that it reaches a target by minimizing a cost function. Our
approach is to use hybrid systems to solve this problem: the complex dynamic is
replaced by piecewise affine approximations which allow an analytical
resolution. The sequence of affine models then forms a sequence of states of a
hybrid automaton. Given a sequence of states, we introduce an hybrid
approximation of the nonlinear controllable domain and propose a new algorithm
computing a controllable, piecewise convex approximation. The same way the
nonlinear optimal control problem is replaced by an hybrid piecewise affine
one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce
the global structure of the hybrid optimal control steering the system to the
target
- …