Adaptive control systems can be vulnerable to disturbances and uncertainties. Robustness improvement techniques like dead-zones, projection operators, and leakage terms help address these issues by modifying adaptive laws and constraining parameter estimates.
Robust adaptive control combines adaptive and robust methods for better stability and performance. Techniques like normalization, composite control, and multiple model approaches enhance convergence and handling of uncertainties, making systems more reliable in real-world applications.
Robustness Improvement Techniques in Adaptive Control
Dead-zones and projection operators
- Dead-zones suspend adaptation around zero error preventing parameter drift from noise or disturbances
- Region where adaptation halts when error falls within threshold
- Modifies adaptive law stopping updates for small errors (±0.1 units)
- Projection operators constrain parameter estimates within bounds ensuring stability
- Componentwise projection limits individual parameters
- Norm-based projection restricts overall parameter vector magnitude
- Modifies adaptive law projecting estimates onto feasible set (unit sphere)
Robust vs traditional adaptive control
- Robust adaptive control combines adaptive and robust techniques maintaining stability under uncertainties
- Advantages over traditional approaches:
- Improved stability guarantees for wider range of disturbances
- Better handling of unmodeled dynamics (high-frequency resonances)
- Reduced sensitivity to measurement noise (sensor inaccuracies)
- Faster convergence of parameter estimates to true values
- Key features incorporate a priori knowledge about uncertainties and use Lyapunov-based design for stability analysis
Techniques for enhanced adaptive control
- Parameter projection keeps estimates within known bounds
- Projects estimates onto convex set after each update (unit cube)
- Normalization improves convergence and robustness to high-frequency inputs
- Divides adaptive law by time-varying normalization signal
- Prevents parameter drift and enhances transient performance
- Leakage adds damping term to adaptive law preventing drift and improving robustness
- $\sigma$-modification introduces constant leakage term
- $e_1$-modification uses error-dependent leakage
Design of robust adaptive systems
- Composite adaptive control combines direct and indirect approaches improving convergence and transient performance
- Multiple model adaptive control uses model set for uncertainties
- Switches between models or blends outputs (weighted average)
- Adaptive backstepping provides recursive design for nonlinear systems handling unmatched uncertainties
- L1 adaptive control decouples adaptation and robustness using fast adaptation with guaranteed time-delay margin
- Sliding mode adaptive control combines sliding mode with adaptive techniques providing robustness against matched uncertainties (friction, disturbances)