Mixed Control Strategy for a Class of Sector-Bounded Nonlinear Systems.

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Deterministic state-feedback control is widely used.
• Stochastic control, particularly state-multiplicative noise, is less common but applicable in areas like Stochastic Anti Resonance (SAR).
• Mixed strategies combine deterministic and stochastic elements for potentially enhanced control.

Purpose of the Study:

• To investigate a mixed-strategy control approach for systems with sector-bounded nonlinearities.
• To analyze the benefits of combining deterministic and stochastic state feedback.
• To ensure exponential LP-stability and weighted L2-gain for the closed-loop system.

Main Methods:

• Development of a stochastic state feedback control strategy with both deterministic and white noise components.
• Derivation of matrix inequality conditions for stability and gain analysis.
• Application of the mixed control strategy to systems with sector-bounded nonlinearities.

Main Results:

• The mixed-strategy control is shown to be effective for systems with sector-bounded nonlinearities.
• Matrix inequalities provide conditions for achieving weighted L2-gain and exponential LP-stability.
• A numerical example demonstrates the advantages of the mixed control over purely deterministic control.

Conclusions:

• Mixed-strategy control offers a viable and potentially superior alternative to purely deterministic control for certain nonlinear systems.
• The proposed method allows for separate quantification of the mean and variance of the control signal.
• The derived conditions ensure robust stability and performance in the closed-loop system.