Konsep Inti
This paper analyzes the closed-loop stability of predictive cost adaptive control (PCAC) for output-feedback of a discrete-time Lur'e system using absolute stability criteria, namely the circle criterion and the Tsypkin test.
Abstrak
The paper considers a discrete-time Lur'e (DTL) system, which consists of a linear system G connected in a feedback loop with a memoryless nonlinearity γ. The goal is to evaluate the effectiveness of PCAC for stabilizing the DTL system.
Key highlights:
- PCAC performs online closed-loop linear system identification using recursive least squares (RLS) with variable-rate forgetting. The identified model is then used as the basis for receding-horizon optimization.
- The closed-loop Lur'e system, comprising the positive feedback interconnection of the DTL system and the PCAC-based controller, is derived. This allows the application of absolute stability theory for analyzing the stability of the closed-loop system.
- The discrete-time circle and Tsypkin criteria are used to evaluate the absolute stability of the closed-loop Lur'e system, where the adaptive controller is viewed as instantaneously linear time-invariant.
- A numerical example demonstrates that, under additional excitation, the circle and Tsypkin criteria are satisfied, suggesting that PCAC globally asymptotically stabilizes the DTL system.
- The effectiveness of PCAC in stabilizing the nonlinear system, despite the modeling mismatch between the linearized system and the actual self-oscillating behavior, is an interesting observation that warrants further research.