Impulsive Observer of Linear Systems: An Adaptive Impulsive Gain Approach

Area of Science:

• Control Systems Engineering
• Adaptive Control Theory
• System Identification

Background:

• Continuous-time adaptive observers often require real-time data, posing practical challenges.
• Existing adaptive observation frameworks can be computationally intensive and lack flexibility.
• Accurate state estimation is crucial for effective control of dynamic systems.

Purpose of the Study:

• To introduce a novel impulsive adaptive observation (IAO) approach for linear systems.
• To develop a discrete-time adaptive rule for observer gain using only output data at impulsive instants.
• To design an IAO-based feedback controller for stabilizing controlled plants.

Main Methods:

• A discrete-time adaptive rule for impulsive observer gain was designed.
• The impulsive adaptive observer (IAO) was implemented to estimate system states.
• Stability criteria for IAO protocols were established.
• An IAO-based feedback controller was designed and applied.

Main Results:

• The IAO effectively estimates continuous-time system states with outstanding tracking performance.
• The discrete-time approach overcomes the real-time data requirement of continuous-time methods.
• IAO protocols demonstrate improved performance, reduced computational load, and enhanced control flexibility.
• Simulations on an electrical system confirmed the IAO's effectiveness.

Conclusions:

• The proposed impulsive adaptive observation (IAO) provides an efficient method for state estimation in linear systems.
• IAO overcomes real-time data limitations and offers enhanced control flexibility.
• The IAO-based control strategy ensures system stabilization with improved performance metrics.