35 research outputs found
Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics
Automated synthesis of provably correct controllers for cyber-physical
systems is crucial for deployment in safety-critical scenarios. However, hybrid
features and stochastic or unknown behaviours make this problem challenging. We
propose a method for synthesising controllers for Markov jump linear systems
(MJLSs), a class of discrete-time models for cyber-physical systems, so that
they certifiably satisfy probabilistic computation tree logic (PCTL) formulae.
An MJLS consists of a finite set of stochastic linear dynamics and discrete
jumps between these dynamics that are governed by a Markov decision process
(MDP). We consider the cases where the transition probabilities of this MDP are
either known up to an interval or completely unknown. Our approach is based on
a finite-state abstraction that captures both the discrete (mode-jumping) and
continuous (stochastic linear) behaviour of the MJLS. We formalise this
abstraction as an interval MDP (iMDP) for which we compute intervals of
transition probabilities using sampling techniques from the so-called 'scenario
approach', resulting in a probabilistically sound approximation. We apply our
method to multiple realistic benchmark problems, in particular, a temperature
control and an aerial vehicle delivery problem.Comment: 14 pages, 6 figures, under review at QES
Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels
The performance of a noisy linear time-invariant (LTI) plant, controlled over
a noiseless digital channel with transmission delay, is investigated in this
paper. The rate-limited channel connects the single measurement output of the
plant to its single control input through a causal, but otherwise arbitrary,
coder-controller pair. An infomation-theoretic approach is utilized to analyze
the minimal average data rate required to attain the quadratic performance when
the channel imposes a known constant delay on the transmitted data. This
infimum average data rate is shown to be lower bounded by minimizing the
directed information rate across a set of LTI filters and an additive white
Gaussian noise (AWGN) channel. It is demonstrated that the presence of time
delay in the channel increases the data rate needed to achieve a certain level
of performance. The applicability of the results is verified through a
numerical example. In particular, we show by simulations that when the optimal
filters are used but the AWGN channel (used in the lower bound) is replaced by
a simple scalar uniform quantizer, the resulting operational data rates are at
most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for
publication in the proceedings of ACC 201
SOLUTION APPROXIMATIONS FOR LYAPUNOV TYPE EQUATIONS ASSOCIATED WITH LINEAR STOCHASTIC EQUATIONS WITH UNBOUNDED COEFFICIENTS AND COUNTABLY INFINITE MARKOV JUMPS
This paper discuses solution properties of the Lyapunov-type equations (LEs),
associated with a class of linear stochastic equations with unbounded coefficients and countably
infinite Markov jumps. It is proved that the mild solutions of these LEs can be obtained as weak
limits of sequences of strong solutions of certain approximating systems of LEs. Unlike the case of
linear stochastic equations without jumps [4], where the LEs acts on Banach spaces of linear and
bounded operators and the mild solutions are strong limits of approximating strong solutions, in
our case the LEs are defined on Banach spaces of infinite sequences of operators and the strong
convergence is replaced by the weak convergence
Robust Performance Analysis for Time-Varying Multi-Agent Systems with Stochastic Packet Loss
Recently, a scalable approach to system analysis and controller synthesis for
homogeneous multi-agent systems with Bernoulli distributed packet loss has been
proposed. As a key result of that line of work, it was shown how to obtain
upper bounds on the -norm that are robust with respect to uncertain
interconnection topologies. The main contribution of the current paper is to
show that the same upper bounds hold not only for uncertain but also
time-varying topologies that are superimposed with the stochastic packet loss.
Because the results are formulated in terms of linear matrix inequalities that
are independent of the number of agents, multi-agent systems of any size can be
analysed efficiently. The applicability of the approach is demonstrated on a
numerical first-order consensus example, on which the obtained upper bounds are
compared to estimates from Monte-Carlo simulations.Comment: 8 pages, 4 figures. Extended version of a paper to be published at
IFAC World Congress 202
Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version)
In most real cases transition probabilities between operational modes of
Markov jump linear systems cannot be computed exactly and are time-varying. We
take into account this aspect by considering Markov jump linear systems where
the underlying Markov chain is polytopic and time-inhomogeneous, i.e. its
transition probability matrix is varying over time, with variations that are
arbitrary within a polytopic set of stochastic matrices. We address and solve
for this class of systems the infinite-horizon optimal control problem. In
particular, we show that the optimal controller can be obtained from a set of
coupled algebraic Riccati equations, and that for mean square stabilizable
systems the optimal finite-horizon cost corresponding to the solution to a
parsimonious set of coupled difference Riccati equations converges
exponentially fast to the optimal infinite-horizon cost related to the set of
coupled algebraic Riccati equations. All the presented concepts are illustrated
on a numerical example showing the efficiency of the provided solution.Comment: Extended version of the paper accepted for the presentation at the
European Control Conference (ECC 2019