Co-Simulation of Algebraically Coupled Dynamic Subsystems Without Disclosure of Proprietary Subsystem Models

A method for simultaneously running a collection of dynamic simulators coupled by algebraic boundary conditions is presented. Dynamic interactions between subsystems are simulated without disclosing proprietary information about the subsystem models, as all the computations are performed based on input-output numerical data of encapsulated subsystem simulators coded by independent groups. First, this paper describes a system of interacting subsystems with a causal conflict as a high-index, Differential-Algebraic Equation (DAE), and develops a systematic solution method using Discrete-Time Sliding Mode control. Stability and convergence conditions as well as error bounds are analyzed by using nonlinear control theory. Second, the algorithm is modified such that the subsystem simulator does not have to disclose its internal model and state variables for solving the overall DAE. The new algorithm is developed based on the generalized Kirchhoff Laws that allow us to represent algebraic boundary constraints as linear equations of the subsystems' outputs interacting to each other. Third, a multi-rate algorithm is developed for improving efficiency, accuracy, and convergence characteristics. Numerical examples verify the major theoretical results and illustrate features of the proposed method.