Robust Optimization-Based Affine Abstractions for Uncertain Affine Dynamics
Cyber-physical systems such as smart grids, autonomous vehicles, and smart buildings are becoming increasingly complex, integrated, and interconnected. One of the difficulties in designing cyber-physical systems is their complex dynamics, which are almost always nonlinear, uncertain, or hybrid. For this reason, the past few years have seen increased popularity in abstraction approaches for cyber-physical systems for approximating original complex dynamics with simpler dynamics. The abstraction approaches compute a simple but conservative approximation that can be used to represent the original dynamics, allowing the application of well-developed controller or observer design methods. This is especially useful in cases requiring reachability and safety specifications for controller synthesis or guarantees for estimator design.
Researchers at Arizona State University have developed a robust optimization-based affine abstraction approach to conservatively approximate uncertain affine discrete-time systems. Specifically, system uncertainties are represented by a pair of affine functions to include all possible trajectories over the entire domain. Because the affine abstraction problem involves robust optimization with nonlinear uncertainties, conversion of nonlinear uncertainties to linear uncertainties makes this problem practically solvable. This is accomplished by exploiting the fact that the system uncertainties are hyperrectangles; thus, only the vertices of the hyperrectangles (instead of the entire uncertainty sets) need to be considered. Consequently, affine abstraction can be solved efficiently by computing its corresponding robust counterpart to obtain a linear programming problem. The effectiveness of the proposed approach for abstracting uncertain driver intention models has been demonstrated in an intersection-crossing scenario.
• Cyber-physical systems
• Autonomous systems
• Power grids
• Smart buildings
Benefits and Advantages
• Provides a practical method for solving complex nonlinear uncertainties through conversion to linear uncertainties