1,281 research outputs found
Compositional abstraction and safety synthesis using overlapping symbolic models
In this paper, we develop a compositional approach to abstraction and safety
synthesis for a general class of discrete time nonlinear systems. Our approach
makes it possible to define a symbolic abstraction by composing a set of
symbolic subsystems that are overlapping in the sense that they can share some
common state variables. We develop compositional safety synthesis techniques
using such overlapping symbolic subsystems. Comparisons, in terms of
conservativeness and of computational complexity, between abstractions and
controllers obtained from different system decompositions are provided.
Numerical experiments show that the proposed approach for symbolic control
synthesis enables a significant complexity reduction with respect to the
centralized approach, while reducing the conservatism with respect to
compositional approaches using non-overlapping subsystems
From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems
This paper is concerned with a compositional approach for the construction of
control barrier certificates for large-scale interconnected stochastic systems
while synthesizing hybrid controllers against high-level logic properties. Our
proposed methodology involves decomposition of interconnected systems into
smaller subsystems and leverages the notion of control sub-barrier certificates
of subsystems, enabling one to construct control barrier certificates of
interconnected systems by employing some -type small-gain conditions. The
main goal is to synthesize hybrid controllers enforcing complex logic
properties including the ones represented by the accepting language of
deterministic finite automata (DFA), while providing probabilistic guarantees
on the satisfaction of given specifications in bounded-time horizons. To do so,
we propose a systematic approach to first decompose high-level specifications
into simple reachability tasks by utilizing automata corresponding to the
complement of specifications. We then construct control sub-barrier
certificates and synthesize local controllers for those simpler tasks and
combine them to obtain a hybrid controller that ensures satisfaction of the
complex specification with some lower-bound on the probability of satisfaction.
To compute control sub-barrier certificates and corresponding local
controllers, we provide two systematic approaches based on sum-of-squares (SOS)
optimization program and counter-example guided inductive synthesis (CEGIS)
framework. We finally apply our proposed techniques to two physical case
studies
Compositional Synthesis of Control Barrier Certificates for Networks of Stochastic Systems against -Regular Specifications
This paper is concerned with a compositional scheme for the construction of
control barrier certificates for interconnected discrete-time stochastic
systems. The main objective is to synthesize switching control policies against
-regular properties that can be described by accepting languages of
deterministic Streett automata (DSA) along with providing probabilistic
guarantees for the satisfaction of such specifications. The proposed framework
leverages the interconnection topology and a notion of so-called control
sub-barrier certificates of subsystems, which are used to compositionally
construct control barrier certificates of interconnected systems by imposing
some dissipativity-type compositionality conditions. We propose a systematic
approach to decompose high-level -regular specifications into simpler
tasks by utilizing the automata corresponding to the complement of
specifications. In addition, we formulate an alternating direction method of
multipliers (ADMM) optimization problem in order to obtain suitable control
sub-barrier certificates of subsystems while satisfying compositionality
conditions. We also provide a sum-of-squares (SOS) optimization problem for the
computation of control sub-barrier certificates and local control policies of
subsystems. Finally, we demonstrate the effectiveness of our proposed
approaches by applying them to a physical case study
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