Converse Barrier Certificate Theorems

Wisniewski, Rafael; Sloth, Christoffer

doi:10.1109/tac.2015.2476155

Cited by 54 publications

(52 citation statements)

References 17 publications

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“…, T }. Proof: SOS conditions (20) and (21) are a direct application of Propositions 1 and 2 in Appendix A to verify conditions (5) and (6), respectively. Furthermore, condition (7) for system (18) can be re-written as…”

Section: B Privacy Verification For Pomdps Via Sospmentioning

confidence: 99%

Privacy Verification in POMDPs via Barrier Certificates

Ahmadi

Lin

Topcu

2018

2018 IEEE Conference on Decision and Control (CDC)

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Privacy is an increasing concern in cyber-physical systems that operates over a shared network. In this paper, we propose a method for privacy verification of cyberphysical systems modeled by Markov decision processes (MDPs) and partially-observable Markov decision processes (POMDPs) based on barrier certificates. To this end, we consider an opacity-based notion of privacy, which is characterized by the beliefs in system states. We show that the belief update equations can be represented as discrete-time switched systems, for which we propose a set of conditions for privacy verification in terms of barrier certificates. We further demonstrate that, for MDPs and for POMDPs, privacy verification can be computationally implemented by solving a set of semi-definite programs and sum-of-squares programs, respectively. The method is illustrated by an application to privacy verification of an inventory management system.

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Section: B Privacy Verification For Pomdps Via Sospmentioning

confidence: 99%

Privacy Verification in POMDPs via Barrier Certificates

Ahmadi

Lin

Topcu

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…Less restrictive barrier functions and barrier certificates must decrease only at the boundary [6]-the sub-level set of zero. Barrier functions have been extended to PDEs [7], and dynamical segregation in arbitrary manifolds [8]. Barrier Lyapunov functions can be constructed from a Lyapunov function and a barrier function [9], but finding such functions is the classical art of nonlinear control practitioners.…”

Section: Introductionmentioning

confidence: 99%

Safety Control Synthesis with Input Limits: a Hybrid Approach

Thomas

Sentis

2018

2018 Annual American Control Conference (ACC)

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We introduce a hybrid (discrete-continuous) safety controller which enforces strict state and input constraints on a system-but only acts when necessary, preserving transparent operation of the original system within some safe region of the state space. We define this space using a Min-Quadratic Barrier function, which we construct along the equilibrium manifold using the Lyapunov functions which result from linear matrix inequality controller synthesis for locally valid uncertain linearizations. We also introduce the concept of a barrier pair, which makes it easy to extend the approach to include trajectory-based augmentations to the safe region, in the style of LQR-Trees. We demonstrate our controller and barrier pair synthesis method in simulation-based examples.

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“…Exponential barrier functions were proposed in [15] for finite-time regional verification of stochastic nonlinear systems. Moreover, compositional barrier certificates and converse results were studied in [16] and [17,18], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…) = 2x 2 (1 − x) 2 0(x) = 0.4x(e x − e) 0(x) = x(1 − x) 0(x) = 1 6 (1 − cos(2πx)) 0(x) = ln(0.55x(1 − x) + 1) PSfrag replacements t u0 = 2x 2 (1 − x) 2 u0 = 0.4x(e x − e) u0 = x(1 − x) u0 = ln(11 20 x(1 − x) + 1) The evolution of H 1 (0,1) -norm of solutions to(18) with λ = 1.2π 2 for different initial conditions. The red and green lines show the boundaries of Yu and U 0 , respectively.…”

mentioning

confidence: 99%

Safety verification for distributed parameter systems using barrier functionals

Ahmadi

Valmórbida

Papachristodoulou

2017

Systems & Control Letters

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We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (integral) inequalities, then the solutions of the system do not enter the unsafe set. Therefore, the proposed method does not require finite-dimensional approximations of the distributed parameter system. Furthermore, for PDEs with polynomial data, we solve the associated integral inequalities using semi-definite programming (SDP) based on a method that relies on a quadratic representation of the integrands of integral inequalities. The proposed method is illustrated through examples.

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Converse Barrier Certificate Theorems

Cited by 54 publications

References 17 publications

Privacy Verification in POMDPs via Barrier Certificates

Privacy Verification in POMDPs via Barrier Certificates

Safety Control Synthesis with Input Limits: a Hybrid Approach

Safety verification for distributed parameter systems using barrier functionals

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