19 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
Decentralized Abstractions for Feedback Interconnected Multi-Agent Systems
The purpose of this report is to define abstractions for multi-agent systems
under coupled constraints. In the proposed decentralized framework, we specify
a finite or countable transition system for each agent which only takes into
account the discrete positions of its neighbors. The dynamics of the considered
systems consist of two components. An appropriate feedback law which guarantees
that certain performance requirements (eg. connectivity) are preserved and
induces the coupled constraints and additional free inputs which we exploit in
order to accomplish high level tasks. In this work we provide sufficient
conditions on the space and time discretization of the system which ensure that
we can extract a well posed and hence meaningful finite transition system.Comment: 15 page
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
Online Abstractions for Interconnected Multi-Agent Control Systems
In this report, we aim at the development of an online abstraction framework
for multi-agent systems under coupled constraints. The motion capabilities of
each agent are abstracted through a finite state transition system in order to
capture reachability properties of the coupled multi-agent system over a finite
time horizon in a decentralized manner. In the first part of this work, we
define online abstractions by discretizing an overapproximation of the agents'
reachable sets over the horizon. Then, sufficient conditions relating the
discretization and the agent's dynamics properties are provided, in order to
quantify the transition possibilities of each agent.Comment: 22 pages. arXiv admin note: text overlap with arXiv:1603.0478
Probabilistic constraint reasoning with Monte Carlo integration to robot localization
This work studies the combination of safe and probabilistic reasoning through the hybridization of Monte Carlo integration techniques with continuous constraint programming. In continuous constraint programming there are variables ranging over continuous domains (represented as intervals) together with constraints over them (relations between variables) and the goal is to find values for those variables that satisfy all the constraints (consistent scenarios). Constraint programming “branch-and-prune” algorithms produce safe enclosures of all consistent scenarios. Special proposed algorithms for probabilistic constraint reasoning compute the probability of sets of consistent scenarios which imply the calculation of an integral over these sets (quadrature). In this work we propose to extend the “branch-and-prune” algorithms with Monte Carlo integration techniques to compute such probabilities. This approach can be useful in robotics for localization problems. Traditional approaches are based on probabilistic techniques that search the most likely scenario, which may not satisfy the model constraints. We show how to apply our approach in order to cope with this problem and provide functionality in real time
Verification Guided Refinement of Flight Safety Assessment and Management System for Takeoff
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140668/1/1.i010408.pd
Safety verification of nonlinear hybrid systems based on invariant clusters
In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient
Flight Safety Assessment and Management.
This dissertation develops a Flight Safety Assessment and Management (FSAM) system to mitigate aircraft loss of control risk. FSAM enables switching between the pilot/nominal autopilot system and a complex flight control system that can potentially recover from high risk situations but can be hard to certify. FSAM monitors flight conditions for high risk situations and selects the appropriate control authority to prevent or recover from loss of control. The pilot/nominal autopilot system is overridden only when necessary to avoid loss of control. FSAM development is pursued using two approaches. First, finite state machines are manually prescribed to manage control mode switching. Constructing finite state machines for FSAM requires careful consideration of possible exception events, but provides a computationally-tractable and verifiable means of realizing FSAM. The second approach poses FSAM as an uncertain reasoning based decision theoretic problem using Markov Decision Processes (MDP), offering a less tedious knowledge engineering process at the cost of computational overhead. Traditional and constrained MDP formulations are presented. Sparse sampling approaches are also explored to obtain suboptimal solutions to FSAM MDPs. MDPs for takeoff and icing-related loss of control events are developed and evaluated. Finally, this dissertation applies verification techniques to ensure that finite state machine or MDP policies satisfy system requirements. Counterexamples obtained from verification techniques aid in FSAM refinement. Real world aviation accidents are used as case studies to evaluate FSAM formulations. This thesis contributes decision making and verification frameworks to realize flight safety assessment and management capabilities. Novel flight envelopes and state abstractions are prescribed to aid decision making.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133348/1/swee_1.pd