111 research outputs found
Input-to-state stability of infinite-dimensional control systems
We develop tools for investigation of input-to-state stability (ISS) of
infinite-dimensional control systems. We show that for certain classes of
admissible inputs the existence of an ISS-Lyapunov function implies the
input-to-state stability of a system. Then for the case of systems described by
abstract equations in Banach spaces we develop two methods of construction of
local and global ISS-Lyapunov functions. We prove a linearization principle
that allows a construction of a local ISS-Lyapunov function for a system which
linear approximation is ISS. In order to study interconnections of nonlinear
infinite-dimensional systems, we generalize the small-gain theorem to the case
of infinite-dimensional systems and provide a way to construct an ISS-Lyapunov
function for an entire interconnection, if ISS-Lyapunov functions for
subsystems are known and the small-gain condition is satisfied. We illustrate
the theory on examples of linear and semilinear reaction-diffusion equations.Comment: 33 page
Supervisory Control of Discrete-Event Systems Under Attacks
We consider a multi-adversary version of the supervisory control problem for discrete-event systems (DES), in which an adversary corrupts the observations available to the supervisor. The supervisor’s goal is to enforce a specific language in spite of the opponent’s actions and without knowing which adversary it is playing against. This problem is motivated by applications to computer security in which a cyber defense system must make decisions based on reports from sensors that may have been tampered with by an attacker. We start by showing that the problem has a solution if and only if the desired language is controllable (in the DES classical sense) and observable in a (novel) sense that takes the adversaries into account. For the particular case of attacks that insert symbols into or remove symbols from the sequence of sensor outputs, we show that testing the existence of a supervisor and building the supervisor can be done using tools developed for the classical DES supervisory control problem, by considering a family of automata with modified output maps, but without expanding the size of the state space and without incurring on exponential complexity on the number of attacks considered
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