LMIs in Control/pages/Algebraic Riccati Equation
Algebraic Riccati Equations are particularly significant in Optimal Control, filtering and estimation problems. The need to solve such equations is common in the analysis and linear quadratic Gaussian control along with general Control problems. In one form or the other, Riccati Equations play significant roles in optimal control of multivariable and large-scale systems, scattering theory, estimation, and detection processes. In addition, closed forms solution of Riccti Equations are intractable for two reasons namely; one, they are nonlinear and two, are in matrix forms.
The System
editThe Data
editFollowing matrices are needed as Inputs:.
- .
The Optimization Problem
editIn control systems theory, many analysis and design problems are closely related to Riccati algebraic equations or inequalities. Find
The LMI: Algebraic Riccati Inequality
editTitle and mathematical description of the LMI formulation.
Conclusion:
editIf the solution exists, LMIs give a unique, stabilizing, symmetric matrix P.
Implementation:
editMatlab code for this LMI in the Github repository:
- REDIRECT [[1]]- CODE
External links
edit- [2]-Optimal Solution to Matrix Riccati Equation
- https://https://arxiv.org/abs/1903.08599/ LMI Properties and Applications in Systems, Stability, and Control Theory.- - A List of LMIs by Ryan Caverly and James Forbes