On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems

Area of Science:

• Control Theory
• Systems Engineering
• Mathematical Modeling

Background:

• Discrete-time controlled bilinear systems are crucial in various engineering applications.
• Characterizing the maximal output set under state and output constraints is a fundamental problem.
• Existing methods may not efficiently handle complex constraint sets or provide algorithmic solutions.

Purpose of the Study:

• To investigate and determine the maximal output set for discrete-time controlled bilinear systems.
• To develop a method for characterizing this set using a finite number of inequalities.
• To provide an algorithmic approach for generating the maximal output set.

Main Methods:

• Utilizing stability hypotheses to derive theoretical properties of the maximal output set.
• Developing a finite set of inequalities to define the maximal output set.
• Implementing an algorithmic process for the computation and generation of the maximal output set.
• Applying the developed methodology to SI and SIR epidemic models.

Main Results:

• Demonstrated that the maximal output set can be determined by a finite number of inequalities under stability conditions.
• Presented a concrete algorithmic process for generating the maximal output set.
• Validated the theoretical approach with numerical simulations and examples.
• Showcased the practical applicability of the method through epidemic modeling.

Conclusions:

• The proposed method provides an effective way to determine and generate the maximal output set for discrete-time controlled bilinear systems.
• The algorithmic approach offers a computationally feasible solution for practical problems.
• The application to epidemic models highlights the versatility and effectiveness of the developed framework in real-world scenarios.