Nonlinear Control: Lyapunov-Based Methods

In summary, the conversation discusses different nonlinear control methods, particularly the need for a method that explicitly provides the "region of attraction." The book "Applied nonlinear control" by Slotine and Li is recommended as a good resource for beginners in this field.
  • #1
mby110
3
0
Hi all

I am looking for different nonlinear control methods based on lyapunov theory.
Indeed I should use a method which give the "region of attraction" explicitly such as CLF and Bakhstepping methods.

Can enyone help me and introduce me some otehr methods?

Many thanks in advance.
 
Engineering news on Phys.org
  • #2
I don't know much about nonlinear control theory, but I have heard that the book by Vidyasagar (same person who wrote the Robotics book) is a must read for all control engineers for non linear control.
 
  • #3
Read : Slotine J.J.E., Li, W., "Applied nonlinear control", Englewood Cliffs, NJ: Prentice-Hall, 1991.

it is a good book for starters. Not too mathematical. It will introduce you to the concepts of nonlinear controls.
 

1. What is nonlinear control?

Nonlinear control is the field of study that deals with controlling systems that exhibit nonlinear behavior. This includes systems that do not follow a direct cause and effect relationship between inputs and outputs, and may have complex dynamics that cannot be easily modeled.

2. What are Lyapunov-based methods in nonlinear control?

Lyapunov-based methods are a type of control technique used to analyze and design controllers for nonlinear systems. These methods use the concept of Lyapunov stability, which states that a system is stable if it can be shown that all trajectories starting in a certain region will remain in that region over time.

3. How do Lyapunov-based methods work?

Lyapunov-based methods work by constructing a Lyapunov function, which is a mathematical function that can be used to analyze the stability of a system. The goal is to find a Lyapunov function that satisfies certain criteria, such as being positive definite and decreasing over time, to prove the stability of the system.

4. What are some advantages of using Lyapunov-based methods?

One advantage of using Lyapunov-based methods is that they can be applied to a wide range of nonlinear systems, making them a versatile tool for control design. Additionally, these methods can provide guarantees on the stability of a system, which is important for safety-critical applications.

5. Are there any limitations to using Lyapunov-based methods?

While Lyapunov-based methods can be powerful tools for nonlinear control, they do have some limitations. One limitation is that they may not be able to handle certain types of nonlinearities, such as those that are highly oscillatory or discontinuous. Additionally, the design process can be complex and may require advanced mathematical skills.

Similar threads

Truss behaviour, load-deformation curve
    • General Engineering
Replies
3
Views
1K
Control Theory: Derivation of Controllable Canonical Form
    • General Engineering
Replies
3
Views
2K
What is the "observer" in PID control?
    • Electrical Engineering
Replies
12
Views
2K
I Attractors of a time series
    • Classical Physics
Replies
1
Views
987
Electric motor torque control based on speed interaction/instability
    • Electrical Engineering
Replies
3
Views
850
Problems with Unscented Kalman Filter
    • General Engineering
Replies
1
Views
1K
Nonlinear backstepping method and Lyapunov theory
    • General Engineering
Replies
3
Views
11K
A Intermediate Axis Theorem - Lyapunov's Indirect Method
    • Differential Equations
Replies
1
Views
1K
Applied A question about mathematics textbooks for physicists
    • Science and Math Textbooks
Replies
28
Views
2K
How to model the behavior of a closed loop position system?
    • General Engineering
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top