Incremental Design of Simplex Basis Function Model for Dynamic System Identification.

Area of Science:

• Control Engineering
• Computational Mathematics
• Signal Processing

Background:

• Dynamic system identification is crucial for understanding and controlling complex systems.
• Existing methods often struggle with model complexity and generalization, especially with noisy data.
• Optimizing basis function structure presents a challenge in function approximation.

Purpose of the Study:

• To propose a novel adaptive piecewise linear model for dynamic system identification.
• To enhance generalization ability and reduce model complexity through a new basis function design.
• To develop an efficient and robust identification strategy that handles noisy system outputs.

Main Methods:

• Design of a novel basis function with uniform shape for improved generalization and complexity tradeoff.
• Optimization of basis function structure as decision variables, differing from coefficient-based approaches.
• Implementation of an incremental design strategy solving Lipschitz continuous optimization problems for efficiency.
• Introduction of a smoothing mechanism to mitigate overfitting in the presence of noise.

Main Results:

• The proposed model demonstrates effective function approximation with a balance between generalization and complexity.
• Optimizing basis function structure proved more effective than traditional coefficient optimization.
• The incremental design strategy significantly reduced estimation costs.
• The smoothing mechanism successfully addressed overfitting issues caused by system output noise.

Conclusions:

• The novel adaptive piecewise linear model offers a promising approach to dynamic system identification.
• The unique features, including basis function design and incremental strategy, provide significant advantages.
• The model shows potential for application in various benchmark dynamic systems, especially under noisy conditions.