Akshay Rajhans

Supporting Heterogeneity in Cyber-Physical Systems Architectures

Cyber-physical systems (CPS) are heterogeneous, because they tightly couple computation, communication, and control along with physical dynamics, which are traditionally considered separately. Without a comprehensive modeling formalism, model-based development of CPS involves using a multitude of models in a variety of formalisms that capture various aspects of the system design, such as software design, networking design, physical models, and protocol design. Without a rigorous unifying framework, system integration and integration of the analysis results for various models remains ad hoc. In this paper, we propose a multi-view architecture framework that treats models as views of the underlying system structure and uses structural and semantic mappings to ensure consistency and enable system-level verification in a hierarchical and compositional manner. Throughout the paper, the theoretical concepts are illustrated using two examples: a quadrotor and an automotive intersection collision avoidance system.

Parameter Synthesis for Hybrid Systems with an Application to Simulink Models

This paper addresses a parameter synthesis problem for nonlinear hybrid systems. Considering a set of uncertain parameters and a safety property, we give an algorithm that returns a partition of the set of parameters into subsets classified as safe, unsafe, or uncertain, depending on whether respectively all, none, or some of their behaviors satisfy the safety property. We make use of sensitivity analysis to compute approximations of reachable sets and an error control mechanism to determine the size of the partition elements in order to obtain the desired precision. We apply the technique to Simulink models by combining generated code with a numerical solver that can compute sensitivities to parameter variations. We present experimental results on a non-trivial Simulink model of a quadrotor helicopter.

STRONG: a trajectory-based verification toolbox for hybrid systems

We present STRONG, a MATLAB toolbox for hybrid system verification. The toolbox addresses the problem of reachability/safety verification for bounded time. It simulates a finite number of trajectories and computes robust neighborhoods around their initial states such that any trajectory starting from these robust neighborhoods follows the same sequence of locations as the simulated trajectory does and avoids the unsafe set if the simulated trajectory does. Numerical simulation and computation of robust neighborhoods for linear dynamics scale well with the size of the problem. Moreover, the computation can be readily parallelized because the nominal trajectories can be simulated independently of each other. This paper showcases key features and functionalities of the toolbox using some examples.

Compositional heterogeneous abstraction

In model-based development, abstraction provides insight and tractability. Different formalisms are often used at different levels of abstraction to represent the variety of concerns that need to be addressed when designing complex cyber-physical systems. In this paper, we consider the problem of establishing abstraction across heterogeneous formalisms in a compositional manner. We use the framework of behavioral semantics to elucidate the general conditions that must be satisfied to assure that the composition of abstractions for individual components is an abstraction for the composition of the components. The theoretical concepts are illustrated using an example of a cooperative intersection collision avoidance system (CICAS).

Heterogeneous verification of cyber-physical systems using behavior relations

Todays complex cyber-physical systems are being built increasingly using model-based development (MBD), where mathematical models for the system behavior are checked against design specifications using analysis tools. Different types of models and analysis tools are used to address different aspects of the system. While the use of heterogeneous formalisms supports a divide-and-conquer approach to complexity and allows engineers with different types of expertise to work on various aspects of the design, system integration problems can arise due to the lack of an underlying unifying formalism. In this paper, we introduce the notion of behavior relations to address the problem of heterogeneity and propose constraints over parameters as a mechanism to manage inter-model dependencies and ensure consistency. In addition, we present structured constructs of nested conjunctive and disjunctive analyses to enable multi-model heterogeneous verification. The theoretical concepts are illustrated using an example of a cooperative intersection collision avoidance system (CICAS).

Using parameters in architectural views to support heterogeneous design and verification

Current methods for designing cyber-physical systems lack a unifying framework due to the heterogeneous nature of the constituent models and their respective analysis and verification tools. There is a need for a formal representation of the relationships between the different models. Our approach is to define these relationships at the architectural level, associating with each model a particular view of the overall system base architecture. This architectural framework captures critical structural and semantic information without including all the details of the various modeling formalisms. This paper introduces the use of logical constraints over parameters in the architectural views to represent the conditions under which the specifications verified for each model are true and imply the system-level specification. Interdependencies and connections between the constraints in the architectural views are managed in the base architecture using first-order logic of real arithmetic to ensure consistency and correct reasoning. The approach is illustrated in the context of heterogeneous verification of a leader-follower vehicle scenario.