Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Abstract

This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in sa f e − LTL F , a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discretetime dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a sa f e − LTL F formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.

Reactive and Risk-Aware Control for Signal Temporal Logic

“…A timed automata-based planning framework has been presented in our previous work [17] where we decompose the STL specification into STL subspecifications. Feedback control laws that implement such STL subspecifications, which are timed transitions, have appeared in [4,[18][19][20][21][22][23][24].…”

“…The third contribution is a planning and control framework for dynamical control systems under ReRiSITL specifications. The main elements here are a well defined timed abstraction of the control system that relies on existing feedback control laws as presented in [18][19][20][21][22][23][24]. We then propose to use a combination of a game-based approach, graph search techniques, and replanning.…”

Secure Control in Partially Observable Environments to Satisfy LTL Specifications

“…The authors used FSCs to represent the policies of the agents, and proposed an algorithm that yielded defender FSCs of fixed size satisfying the LTL formula under any adversary FSC of fixed size. The authors also broadened the scope of this problem to continuous state environments and to settings when the adversary could potentially tamper with clocks that keep track of time in the environment in [51], [52].…”

Controller Synthesis against Omega-Regular Specifications: A Funnel-based Control Approach

“…The discretization-free approaches based on control barrier functions (CBF) have shown a potential to solve the formal synthesis problem for various classes of complex logic specifications. The results in 8,9,10 search for parametric control barrier functions to synthesize controllers to enforce specifications given by deterministic forms of Automata. However, there are several limitations over the applicability of these results; for example, (i) the techniques rely on a parametric form of control barrier function (such as polynomial) that will solve the problem, which is very difficult to determine for a given system and (ii) the techniques rely on a numerical search of the unknown parameters by using sum-of-squares or counter-example guided inductive synthesis approaches which are computationally heavy and most of the time suffer from numerical errors.…”