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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Embedding Differential Dynamic Logic in PVS

Differential dynamic logic (dL) is a formal framework for specifying and reasoning about hybrid systems, i.e., dynamical systems that exhibit both continuous and discrete behaviors. These kinds of systems arise in many safety- and mission-critical applications. This paper presents a formalization of dL in the Prototype Verification System (PVS) that includes the semantics of hybrid programs and dL’s proof calculus. The formalization embeds dL into the PVS logic, resulting in a version of dL whose proof calculus is not only formally verified, but is also available for the verification of hybrid programs within PVS itself. This embedding, called Plaidypvs (Properly Assured Implementation of dL for Hybrid Program Verification and Specification), supports standard dL style proofs, but further leverages the capabilities of PVS to allow reasoning about entire classes of hybrid programs. The embedding also allows the user to import the well-established definitions and mathematical theories available in PVS.

PVS↗
NASA NTRSDate not supplied

Embedding Differential Dynamic Logic in PVS

Runtime assurance is a control framework where a complex controller operates under the observation of a monitor. If the monitor detects the controller exhibiting undesirable behavior, control is passed off to a trusted controller until a desirable state is regained. The runtime assurance architecture provides a layer of assurance to the system being controlled, but special care must be taken that the resulting overall system, consisting of the monitors and controllers, is behaving as intended. This talk aims to formally model and reason about runtime assurance-equipped systems as hybrid programs- which are models that consist of both discrete and continuous components. Using the verification tool Plaidypvs, safety properties of some examples involving RTA architectures is shown.

Formal Verification↗
NASA NTRS2022

Towards an Implementation of Differential Dynamic Logic in PVS

This paper describes an ongoing effort to embed and verify differential dynamic logic (dL) in the Prototype Verification System (PVS). dL is a logic for specifying and formally reasoning about hybrid systems, which employ both continuous and discrete dynamics. There are several benefits of this effort. First, the embedding of dL in PVS offers an independent formal verification of the semantics and rules of dL. Second, the embedding is fully operational within PVS, giving PVS practitioners the ability to use dL in the formal specification and verification process. Third, the rich specification language, type system, and powerful interactive prover of PVS can be used on dL objects. In addition to the embedding and verification of dL, a custom extension for Visual Studio Code has been developed, so that a stylized dL syntax can be used to specify hybrid programs and their properties.

Differential Dynamic Logic↗
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRSDate not supplied

A Formal Verification Framework for Runtime Assurance

The simplex architecture is an instance of Runtime Assurance (RTA) where a trusted component takes control of a safety-critical system when an untrusted component violates a safety property. This paper presents a formalization of the simplex RTA framework in the language of hybrid programs. A feature of this formal verification framework is that, for a given system, a specific instantiation can be created and its safety properties are guaranteed by construction. Instantiations may be kept at varying levels of generality, allowing for black box components, such as ML/AI-based controllers, to be modeled. The framework is written in the Prototype Verification System (PVS) using Plaidypvs, an embedding of differential dynamic logic in PVS. As a proof of concept, the framework is illustrated on an automatic vehicle braking system.

Runtime assurance↗
NASA NTRSDate not supplied

A Formal Verification Framework for Runtime Assurance

The simplex architecture is an instance of Runtime Assurance (RTA) where a trusted component takes control of a safety-critical system when an untrusted component violates a safety property. This paper presents a formalization of the simplex RTA framework in the language of hybrid programs. A feature of this formal verification framework is that, for a given system, a specific instantiation can be created and its safety properties are guaranteed by construction. Instantiations may be kept at varying levels of generality, allowing for black box components, such as ML/AI-based controllers, to be modeled. The framework is written in the Prototype Verification System (PVS) using Plaidypvs, an embedding of differential dynamic logic in PVS. As a proof of concept, the framework is illustrated on an automatic vehicle braking system.

Runtime assurance↗
NASA NTRSDate not supplied

A Temporal Differential Dynamic Logic Formal Embedding

Differential dynamic logic is a formal framework to specify and reason about hybrid programs (HPs). The core of dL is a proof calculus that contains a collection of axioms and rules for the rigorous verification of properties of HPs. Recently, dL has been embedded within the theorem prover Prototype Verification System (PVS) resulting in the tool Plaidypvs2. The integration of dL into PVS expands its expressive power; user defined functions, such as trigonometric and other transcendental functions, can be used inside the dL framework, and meta-reasoning about HPs can be performed, including reasoning about entire classes of HPs, specified using dependent types in PVS. The differential temporal dynamic logic (dTL2) extends dL with temporal logic operators to reason about all the states reachable during the execution of an HP. This paper presents a work in progress focusing on embedding dTL2 in PVS as an extension of Plaidypvs. Plaidypvs is expanded with the formalization of a trace semantics for HPs, the definition of the LTL temporal operators eventually and globally, and the implementation of the proof calculus for dTL2. This new embedding has the same capabilties as Plaidypvs, which allows user defined functions and meta-reasoning of properties of HPs. To the best of the authors’ knowledge this is the first implementation of dTL2.

differential dynamic logic↗
NASA NTRSDate not supplied

A Verification Framework for Runtime Assurance of Autonomous UAS

Runtime Assurance (RTA) is a design-time architecture for safety-critical systems where an internal monitor acts upon detecting a violation of a property. The simplex architecture is an instance of RTA, where the action taken is to hand control of the overall system to a trusted controller when an untrusted one violates a safety property. Simplex RTA is emerging as a method for allowing AI/ML and other unverified software to be integrated into safety-critical applications like aircraft. To this end, the American Society for Testing and Materials (ASTM) and NASA have each published guidelines on the use of RTA in such systems. In the simplex RTA framework, a system has an advanced controller (AC) and a reversionary controller (RC). The system is allowed to operate with the AC until a runtime monitor detects that some property has been violated and then the RC takes over. Assuming that the sample rate of the monitor will detect improper functioning with enough time for the RC to correct the impending problem, and that the RC is trusted, the system will operate as intended. This use of the simplex RTA framework can allow for the integration of untrusted, but possibly more performant, controllers in a safe way. This paper presents a formalization of a simplex RTA framework in the Prototype Verification System (PVS) theorem prover using an embedding of differential dynamic logic (DDL) called Plaidypvs. A novel feature of this framework is that it can be instantiated at different levels of abstraction. This feature allows for the formal verification of a system with an untrusted black box component, such as an AI/ML controller. This paper does not address the many difficulties in deploying RTA in an industrial-level system. Instead, the focus is on the formal verification of the simplex RTA framework in the language of hybrid programs. Hybrid programs are programs that include both discrete and continuous dynamics and can be used to model complex cyber-physical systems. Plaidypvs is a tool that enables formalization of hybrid programs in the PVS theorem prover. Plaidypvs enables the verification of the general simplex RTA framework and then, by specializing some components of the hybrid program, verifying instances of the framework while treating the untrusted component as a black box. A selection of Unmanned Aircraft Systems (UAS) operations are shown as instances of the general RTA framework in PVS. This offers the benefit of design time verification of relevant safety properties to the system, and it also gives requirements on the sample rate of sensors that determine the time interval in which the ‘switch’ property of the RTA framework is checked.

PVS↗
NASA NTRS1977

Dynamic response of some tentative compliant wall structures to convected turbulence fields

Some tentative compliant wall structures designed for possible skin friction drag reduction are investigated. Among the structural models considered is a ribbed membrane backed by polyurethane or PVS plastisol. This model is simplified as a beam placed on a viscoelastic foundation as well as on a set of evenly spaced supports. The total length of the beam may be either finite or infinite, and the supports may be either rigid or elastic. Another structural model considered is a membrane mounted over a series of pretensioned wires, also evenly spaced, and the entire membrane is backed by an air cavity. The forcing pressure field is idealized as a frozen random pattern convected downstream at a characteristic velocity. The results are given in terms of the frequency response functions of the system, the spectral density of the structural motion, and the spectral density of the boundary layer pressure including the effect of structural motion. These results are used in a parametric study of structural configurations capable of generating favorable wave lengths, wave amplitudes, and wave speeds in the structural motion for potential drag reduction.

Nijim, H. H.↗