Matrix Manifold-Based Performance Monitoring of Automatic Control Systems

A ``smart'' automatic feedback control system is supposed to be aware of its operational performance throughout the service time. Driven by this desire, this article addresses the problem of monitoring performance variations caused by multiplicative factors, such as components' faults, repairing, or replacement. Differing from the conventional performance indices (e.g., the quadratic value function), it detects the performance variation information from symmetric positive-definite (SPD) kernel matrices. As a carrier of performance variation information, the SPD kernel matrix is identified online. Furthermore, the performance variation is given a fresh insight in the sense that it drives the sliding of the SPD kernel matrix on a Riemannian manifold. Thus, performance variation monitoring is achieved by quantizing the geodesic between SPD kernel matrices directly on the Riemannian manifold. At last, the performance variation is visualized on the Riemannian manifold and the proposed schemes are verified via a simulation study.