95 research outputs found
Dissipativity of system abstractions obtained using approximate input-output simulation
This work focuses on the invariance of important properties between
continuous and discrete models of systems which can be useful in the control
design of large-scale systems and their software implementations. In
particular, this paper discusses the relationships between the QSR
dissipativity of a continuous state dynamical system and of its abstractions
obtained through approximate input-output simulation relations. First,
conditions to guarantee the dissipativity of the continuous system from its
abstractions are provided. The reverse problem of determining the Q, S and R
dissipativity matrices of the abstract system from that of the continuous
system is also considered. Results characterizing the change in the
dissipativity matrices are provided when the system abstraction is obtained.
Since, under certain conditions, QSR dissipative systems are known to be
stable, the results of this paper can be used to construct stable system
abstractions as well. In the second part of this paper, we analyze the
dissipativity of the approximate feedback composition of a continuous dynamical
system and a discrete controller. We present illustrative examples to
demonstrate the results of this paper.Comment: Submitted to SIAM Journal on Control and Optimizatio
From Dissipativity Theory to Compositional Abstractions of Interconnected Stochastic Hybrid Systems
In this work, we derive conditions under which compositional abstractions of
networks of stochastic hybrid systems can be constructed using the
interconnection topology and joint dissipativity-type properties of subsystems
and their abstractions. In the proposed framework, the abstraction, itself a
stochastic hybrid system (possibly with a lower dimension), can be used as a
substitute of the original system in the controller design process. Moreover,
we derive conditions for the construction of abstractions for a class of
stochastic hybrid systems involving nonlinearities satisfying an incremental
quadratic inequality. In this work, unlike existing results, the stochastic
noises and jumps in the concrete subsystem and its abstraction need not to be
the same. We provide examples with numerical simulations to illustrate the
effectiveness of the proposed dissipativity-type compositional reasoning for
interconnected stochastic hybrid systems
Approximate abstractions of control systems with an application to aggregation
Previous approaches to constructing abstractions for control systems rely on
geometric conditions or, in the case of an interconnected control system, a
condition on the interconnection topology. Since these conditions are not
always satisfiable, we relax the restrictions on the choice of abstractions,
instead opting to select ones which nearly satisfy such conditions via
optimization-based approaches. To quantify the resulting effect on the error
between the abstraction and concrete control system, we introduce the notions
of practical simulation functions and practical storage functions. We show that
our approach facilitates the procedure of aggregation, where one creates an
abstraction by partitioning agents into aggregate areas. We demonstrate the
results on an application where we regulate the temperature in three separate
zones of a building.Comment: 24 pages, 3 figures, 1 tabl
Compositional Synthesis of Finite Abstractions for Networks of Systems: A Small-Gain Approach
In this paper, we introduce a compositional scheme for the construction of
finite abstractions (a.k.a. symbolic models) of interconnected discrete-time
control systems. The compositional scheme is based on small-gain type
reasoning. In particular, we use a notion of so-called alternating simulation
functions as a relation between each subsystem and its symbolic model. Assuming
some small-gain type conditions, we construct compositionally an overall
alternating simulation function as a relation between an interconnection of
symbolic models and that of original control subsystems. In such
compositionality reasoning, the gains associated with the alternating
simulation functions of the subsystems satisfy a certain "small-gain"
condition. In addition, we introduce a technique to construct symbolic models
together with their corresponding alternating simulation functions for
discrete-time control subsystems under some stability property. Finally, we
apply our results to the temperature regulation in a circular building by
constructing compositionally a finite abstraction of a network containing
rooms for any . We use the constructed symbolic models as substitutes
to synthesize controllers compositionally maintaining room temperatures in a
comfort zone. We choose for the sake of illustrating the results. We
also apply our proposed techniques to a nonlinear example of fully connected
network in which the compositionality condition still holds for any number of
components. In these case studies, we show the effectiveness of the proposed
results in comparison with the existing compositionality technique in the
literature using a dissipativity-type reasoning
Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey
Stochastic hybrid systems have received significant attentions as a relevant
modelling framework describing many systems, from engineering to the life
sciences: they enable the study of numerous applications, including
transportation networks, biological systems and chemical reaction networks,
smart energy and power grids, and beyond. Automated verification and policy
synthesis for stochastic hybrid systems can be inherently challenging: this is
due to the heterogeneity of their dynamics (presence of continuous and discrete
components), the presence of uncertainty, and in some applications the large
dimension of state and input sets. Over the past few years, a few hundred
articles have investigated these models, and developed diverse and powerful
approaches to mitigate difficulties encountered in the analysis and synthesis
of such complex stochastic systems. In this survey, we overview the most recent
results in the literature and discuss different approaches, including
(in)finite abstractions, verification and synthesis for temporal logic
specifications, stochastic similarity relations, (control) barrier
certificates, compositional techniques, and a selection of results on
continuous-time stochastic systems; we finally survey recently developed
software tools that implement the discussed approaches. Throughout the
manuscript we discuss a few open topics to be considered as potential future
research directions: we hope that this survey will guide younger researchers
through a comprehensive understanding of the various challenges, tools, and
solutions in this enticing and rich scientific area
Passivity-Based Analysis of Sampled and Quantized Control Implementations
This paper studies the performance of a continuous controller when
implemented on digital devices via sampling and quantization, by leveraging
passivity analysis. Degradation of passivity indices from a continuous-time
control system to its sampled, input and output quantized model is studied
using a notion of quasi-passivity. Based on that, the passivity property of a
feedback-connected system where the continuous controller is replaced by its
sampled and quantized model is studied, and conditions that ensure the state
boundedness of the interconnected system are provided. Additionally, the
approximate bisimulation-based control implementation where the controller is
replaced by its approximate bisimilar symbolic model whose states are also
quantized is analyzed. Several examples are provided to illustrate the
theoretical results
Compositional Abstraction of Large-Scale Stochastic Systems: A Relaxed Dissipativity Approach
In this paper, we propose a compositional approach for the construction of
finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for
networks of discrete-time stochastic control subsystems that are not
necessarily stabilizable. The proposed approach leverages the interconnection
topology and a notion of finite-step stochastic storage functions, that
describes joint dissipativity-type properties of subsystems and their
abstractions, and establishes a finite-step stochastic simulation function as a
relation between the network and its abstraction. To this end, we first develop
a new type of compositionality conditions which is less conservative than the
existing ones. In particular, using a relaxation via a finite-step stochastic
simulation function, it is possible to construct finite abstractions such that
stabilizability of each subsystem is not necessarily required. We then propose
an approach to construct finite MDPs together with their corresponding
finite-step storage functions for general discrete-time stochastic control
systems satisfying an incremental passivablity property. We also construct
finite MDPs for a particular class of nonlinear stochastic control systems. To
demonstrate the effectiveness of the proposed results, we apply our results on
three different case studies.Comment: This work is accepted at Nonlinear Analysis: Hybrid Systems. arXiv
admin note: text overlap with arXiv:1712.0779
Compositional Abstraction-based Synthesis of General MDPs via Approximate Probabilistic Relations
We propose a compositional approach for constructing abstractions of general
Markov decision processes using approximate probabilistic relations. The
abstraction framework is based on the notion of -lifted relations,
using which one can quantify the distance in probability between the
interconnected gMDPs and that of their abstractions. This new approximate
relation unifies compositionality results in the literature by incorporating
the dependencies between state transitions explicitly and by allowing abstract
models to have either finite or infinite state spaces. Accordingly, one can
leverage the proposed results to perform analysis and synthesis over abstract
models, and then carry the results over concrete ones. To this end, we first
propose our compositionality results using the new approximate probabilistic
relation which is based on lifting. We then focus on a class of stochastic
nonlinear dynamical systems and construct their abstractions using both model
order reduction and space discretization in a unified framework. We provide
conditions for simultaneous existence of relations incorporating the structure
of the network. Finally, we demonstrate the effectiveness of the proposed
results by considering a network of four nonlinear dynamical subsystems
(together 12 dimensions) and constructing finite abstractions from their
reduced-order versions (together 4 dimensions) in a unified compositional
framework. We benchmark our results against the compositional abstraction
techniques that construct both infinite abstractions (reduced-order models) and
finite MDPs in two consecutive steps. We show that our approach is much less
conservative than the ones available in the literature
Compositional Abstraction-based Synthesis for Networks of Stochastic Switched Systems
In this paper, we provide a compositional approach for constructing finite
abstractions (a.k.a. finite Markov decision processes (MDPs)) of interconnected
discrete-time stochastic switched systems. The proposed framework is based on a
notion of stochastic simulation functions, using which one can employ an
abstract system as a substitution of the original one in the controller design
process with guaranteed error bounds on their output trajectories. To this end,
we first provide probabilistic closeness guarantees between the interconnection
of stochastic switched subsystems and that of their finite abstractions via
stochastic simulation functions. We then leverage sufficient small-gain type
conditions to show compositionality results of this work. Afterwards, we show
that under standard assumptions ensuring incremental input-to-state stability
of switched systems (i.e., existence of common incremental Lyapunov functions,
or multiple incremental Lyapunov functions with dwell-time), one can construct
finite MDPs for the general setting of nonlinear stochastic switched systems.
We also propose an approach to construct finite MDPs for a particular class of
nonlinear stochastic switched systems. To demonstrate the effectiveness of our
proposed results, we first apply our approaches to a road traffic network in a
circular cascade ring composed of 200 cells, and construct compositionally a
finite MDP of the network. We employ the constructed finite abstractions as
substitutes to compositionally synthesize policies keeping the density of the
traffic lower than 20 vehicles per cell. We then apply our proposed techniques
to a fully interconnected network of 500 nonlinear subsystems (totally 1000
dimensions), and construct their finite MDPs with guaranteed error bounds. We
compare our proposed results with those available in the literature.Comment: This work is accepted as a regular paper at Automatica. arXiv admin
note: text overlap with arXiv:1902.01223, arXiv:1808.0089
Compositional abstractions of networks of stochastic hybrid systems under randomly switched topologies
In this work, we derive conditions under which abstractions of networks of
stochastic hybrid systems can be constructed compositionally. Proposed
conditions leverage the interconnection topology, switching randomly between P
different interconnection topologies, and the joint dissipativity-type
properties of subsystems and their abstractions. The random switching of the
interconnection is modelled by a Markov chain. In the proposed framework, the
abstraction, itself a stochastic hybrid system (possibly with a lower
dimension), can be used as a substitute of the original system in the
controller design process. Finally, we provide an example illustrating the
effectiveness of the proposed results by designing a controller enforcing some
logic properties over the interconnected abstraction and then refining it to
the original interconnected system.Comment: arXiv admin note: substantial text overlap with arXiv:1805.0881
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