Class Of Discrete-time Control Systems Research Articles

Abstraction-Based Verification of Approximate Preopacity for Control Systems

In this letter, we consider the problem of verifying pre-opacity for discrete-time control systems. Pre-opacity is an important information-flow security property that secures the intention of a system to execute some secret behaviors in the future. Existing works on pre-opacity only consider non-metric discrete systems, where it is assumed that intruders can distinguish different output behaviors precisely. However, for continuous-space control systems whose output sets are equipped with metrics (which is the case for most real-world applications), it is too restrictive to assume precise measurements from outside observers. In this letter, we first introduce a concept of approximate pre-opacity by capturing the security level of control systems with respect to the measurement precision of the intruder. Based on this new notion of pre-opacity, we propose a verification approach for continuous-space control systems by leveraging abstraction-based techniques. In particular, a new concept of approximate pre-opacity preserving simulation relation is introduced to characterize the distance between two systems in terms of preserving pre-opacity. This new system relation allows us to verify pre-opacity of complex continuous-space control systems using their finite abstractions. We also present a method to construct pre-opacity preserving finite abstractions for a class of discrete-time control systems under certain stability assumptions.

Verification of Approximate Opacity via Barrier Certificates

This paper is motivated by the increasing security concerns of cyber-physical systems. Here, we develop a discretization-free verification scheme targeting an information-flow security property, called approximate initial-state opacity, for the class of discrete-time control systems. We propose notions of so-called augmented control barrier certificates in conjunction with specified regions of interest capturing the initial and secret sets of the system. Sufficient conditions for (the lack of) approximate initial-state opacity of discrete-time control systems are proposed based on the existence of the proposed barrier certificates. We further present an efficient computation method by casting the conditions for barrier certificates as sum-of-squares programming problems. The effectiveness of the proposed results is illustrated through two numerical examples.

On Approximate Opacity of Cyber-Physical Systems

Opacity is an important information-flow security property in the analysis of cyber-physical systems. It captures the plausible deniability of the system's secret behavior in the presence of an intruder that may access the information flow. Existing works on opacity only consider nonmetric systems by assuming that the intruder can always distinguish between two different outputs precisely. In this article, we extend the concept of opacity to systems whose output sets are equipped with metrics. Such systems are widely used in the modeling of many real-world systems whose measurements are physical signals. A new concept called approximate opacity is proposed in order to quantitatively evaluate the security guarantee level with respect to the measurement precision of the intruder. Then, we propose a new simulation-type relation, called approximate opacity-preserving simulation relation, which characterizes how close two systems are in terms of the satisfaction of approximate opacity. This allows us to verify approximate opacity for large-scale, or even infinite, systems using their abstractions. We also discuss how to construct approximate opacity-preserving symbolic models for a class of discrete-time control systems. Our results extend the definitions and analysis techniques for opacity from nonmetric systems to metric systems.

Frequency condition for the stochastic stability of a class of discrete-time control systems

This letter concerns the nonlinear discrete closed-loop control system with a randomly time-varying parameter. For such a system, a frequency criterion of asymptotic stochastic stability in mean square is presented. A simple example is included for illustration.

Approximation of the asymptotic stability boundary of discrete-time control systems using an inverse transformation approach

The objective of this paper is to describe the use of the direct method of Lyapunov together with an inverse transformation process as a basis for determining the stability domain and for estimating the stability boundary of the null solution of a set of autonomous difference equations which describe the dynamics of a class of discrete-time control systems. Two theorems are developed which give sufficient conditions for the existence of an asymptotic stability boundary, which is a hypersurface enclosing a simply-connected domain, provided that a Lyapunov function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon(x)</tex> exists in a neighborhood of the origin. The proofs of these theorems indicate that an original subdomain of asymptotic stability, obtained by using a Lyapunov function, can be enlarged by applying an inverse transformation to the boundary of the subdomain. The inverse transformation is defined from the given set of difference equations as giving the state at the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> th instant in terms of the state at the ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</tex> )th instant. The exact boundary of asymptotic stability is theoretically obtained in the limit by carrying out the inverse transformation an infinite number of times. Analogous to the work on stability, two theorems give sufficient conditions for the existence of an instability boundary which is a hypersurface surrounding a simply connected domain that includes the origin. It is shown that a known domain of instability found by using a Lyapunov function can be increased in size by applying the inverse transformation to its boundary. An important property of this approach is that each time the inverse transformation is applied, an enlarged region of known asymptotic stability or instability is found. In addition to giving stability information, the successive plots of the boundaries can also be used to give the settling time of the system.