Compositional safety analysis using barrier certificates

Sloth, Christoffer; Pappas, George J.; Wisniewski, Rafael

doi:10.1145/2185632.2185639

Cited by 71 publications

(44 citation statements)

References 17 publications

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“…Dual decomposition and the projected subgradient method as presented in [7] was used in [18] to certify stability of an interconnected system and in [15] to verify the safety of a system using barrier certificates. Applying dual decomposition to (7), the projected subgradient method has the form:…”

Section: Decomposition Techniquesmentioning

confidence: 99%

Performance certification of interconnected systems using decomposition techniques

Meissen

Lessard

Packard

2014

2014 American Control Conference

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We propose a unified framework for the certification of stability and input-output performance of interconnected dynamical systems. In our approach, we seek local dissipativity certificates for each subsystem such that when they are combined, the performance of the entire interconnected system is certified. We also demonstrate, by the use of numerical simulations, that the Alternating Direction Method of Multipliers (ADMM) is a promising computational approach for solving such problems.

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Section: Decomposition Techniquesmentioning

confidence: 99%

Performance certification of interconnected systems using decomposition techniques

Meissen

Lessard

Packard

2014

2014 American Control Conference

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“…Furthermore, a decision matrix of this size has 5.2 million decision variables. In the following, the problem is divided into subproblems, which are solved individually [7].…”

Section: Sos Program 1 Complete Wind Turbine Systemmentioning

confidence: 99%

“…Consequently, the search of a sum of squares decomposition becomes numerically tractable. In [7], the safety verification with barrier certificates is divided into subproblems with interconnections, which can be solved independently. Using this approach, the computational requirements are reduced [7].…”

Section: Introductionmentioning

confidence: 99%

Certificate for safe emergency shutdown of wind turbines

Wisniewski

Svenstrup

Pedersen

et al. 2013

2013 American Control Conference

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Abstract-To avoid damage to a wind turbine in the case of a fault or a large wind gust, a detection scheme for emergency shutdown is developed. Specifically, the concept of a safety envelope is introduced. Within the safety envelope, the system can be shutdown without risking structural damage to the turbine. To demarcate the boundary of the safety envelope, a protection certificate, is computed. To this end, a modelbased framework of barrier certificates is used. As a result, the protection certificate problem is formulated as a sum-ofsquares program with the optimisation criterion related to the volume of the safety envelope. The framework enables the inclusion of a bounded wind disturbance and the a priori known emergency shutdown procedure. For this purpose, the model of a wind turbine is developed that includes structural safety critical components.

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“…In the past decades, various solutions have been proposed to verify the safety of dynamical systems. The solution approaches often fall into the following two categories: (i) reachable set methods [10][11][12], and (ii) Lyapunov function methods [13][14][15][16]. Essentially, reachable set methods aim to find a set containing all possible states at a given time, for a given set of initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Safety Verification of Nonlinear Polynomial System via Occupation Measures

Chen

Preciado

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper, we introduce a flexible notion of safety verification for nonlinear autonomous systems by measuring how much time the system spends in given unsafe regions. We consider this problem in the particular case of nonlinear systems with a polynomial dynamics and unsafe regions described by a collection of polynomial inequalities. In this context, we can quantify the amount of time spent in the unsafe regions as the solution to an infinite-dimensional linear program (LP). This LP measures the volume of the unsafe region with respect to the occupation measure of the system trajectories. Using Lasserre hierarchy, we approximate the solution to the infinite-dimensional LP using a sequence of finitedimensional semidefinite programs (SDPs). The solutions to the SDPs in this hierarchy provide monotonically converging upper bounds on the optimal solution to the infinite-dimensional LP. Finally, we validate the performance of our framework using numerical simulations.

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Compositional safety analysis using barrier certificates

Cited by 71 publications

References 17 publications

Performance certification of interconnected systems using decomposition techniques

Performance certification of interconnected systems using decomposition techniques

Certificate for safe emergency shutdown of wind turbines

Safety Verification of Nonlinear Polynomial System via Occupation Measures

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