- #1
abdooo89
- 20
- 0
How to find matix K (Riccati equatin) <<<<<< pleas help me
How to solve Riccati equation for nonlinear system
In summary, the conversation is about finding matrix K for a given set of matrices using the Riccati equation. The problem is that the system is non-linear, making the equation difficult to solve.
How to find matix K (Riccati equatin) <<<<<< pleas help me
- #2
abdooo89
- 20
- 0
i need help please
- #3
- 8,938
- 2,945
abdooo89 said:
Can you post more of the original assignment? It's not very clear what the meanings of the various terms in your post are.
Last edited:
- #4
abdooo89
- 20
- 0
i need only matrix K for a given matrices
the riccati equation is
A'K-KA-Q+KBR-1 B'K=0
the riccati equation is
A'K-KA-Q+KBR-1 B'K=0
- #5
- 8,938
- 2,945
I don't understand exactly what you're doing. It looks very similar to what is described on this page:
http://en.wikipedia.org/wiki/Linear...tical_description_of_the_problem_and_solution
But they don't match up exactly.
http://en.wikipedia.org/wiki/Linear...tical_description_of_the_problem_and_solution
But they don't match up exactly.
- #6
abdooo89
- 20
- 0
the problem in this system is non-linearity that is why the riccati equation is hard to solve
1. What is a Riccati equation?
A Riccati equation is a type of differential equation that involves a quadratic term and is commonly used to model nonlinear systems in physics, engineering, and mathematics. It has the form dy/dx = f(x)y^2 + g(x)y + h(x), where f(x), g(x), and h(x) are functions of x.
2. Why do we need to solve Riccati equations for nonlinear systems?
Riccati equations are useful for studying nonlinear systems because they can capture the complex dynamics and behavior of these systems. Solving these equations allows us to analyze and predict the behavior of nonlinear systems, which are present in many real-world applications.
3. What methods can be used to solve Riccati equations for nonlinear systems?
There are various methods for solving Riccati equations, including numerical methods, analytical methods, and iterative methods. Some commonly used techniques include the substitution method, the Lie symmetry method, and the variational iteration method.
4. How do we know if a solution to a Riccati equation for a nonlinear system is valid?
A solution to a Riccati equation is considered valid if it satisfies the equation and any initial or boundary conditions that are given. In addition, the solution should also be physically meaningful and match the behavior of the system being modeled.
5. Are there any applications of Riccati equations for nonlinear systems in real life?
Yes, Riccati equations have many applications in physics, engineering, and economics. Some examples include modeling population dynamics, analyzing control systems in aerospace engineering, and predicting stock prices in finance. They are also used in the study of quantum mechanics and fluid dynamics.
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