PostDoc Project
Title:
Observer based stabilisation of a class of coupled non linear PDE systems
Dates:
2024/09/01 - 2024/12/31
Supervisor(s):
Description:
Context and Justification
In many real-world models, systems are modeled by partial differential equations (PDEs), particularly coupled nonlinear PDEs, which complicates the
task of state feedback stabilization, especially when a part of the state vector is not directly measurable. An observer is therefore necessary to estimate
these states and enable effective control. Observer-based controllers are often used to stabilize unstable systems or improve system performance. While
the stabilization problem based on observers for linear systems is well-studied, there is limited research on coupled nonlinear PDEs.
Project Objectives
1. Develop a Comprehensive Theory: Establish a complete theoretical framework for designing observers and observer-based controllers for systems
modeled by coupled nonlinear PDEs.
2. Design Innovative Algorithms: Propose innovative algorithms for designing observers and controllers specifically tailored to coupled nonlinear PDEs.
3. Validate Theoretical Methods: Use numerical simulations to validate theoretical results on benchmark problems and real-world applications.
References
1. Krstic, Miroslav, Luke Bhan, and Yuanyuan Shi (2024). Neural operators of backstepping controller and observer gain functions for reaction-
diffusion PDEs.Automatica 164 : 111649.
2. Krstic, M., & Smyshlyaev, A. (2008). Boundary Control of PDEs: A Course on Backstepping Designs. SIAM.
3. Meurer, T. (2012). Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs. Springer.
4. Prieur, C., & Vazquez, R. (2019). Robust nonlinear control of a class of coupled hyperbolic and parabolic
systems. IEEE Transactions on Automatic Control, 64(5), 1905-1919.
In many real-world models, systems are modeled by partial differential equations (PDEs), particularly coupled nonlinear PDEs, which complicates the
task of state feedback stabilization, especially when a part of the state vector is not directly measurable. An observer is therefore necessary to estimate
these states and enable effective control. Observer-based controllers are often used to stabilize unstable systems or improve system performance. While
the stabilization problem based on observers for linear systems is well-studied, there is limited research on coupled nonlinear PDEs.
Project Objectives
1. Develop a Comprehensive Theory: Establish a complete theoretical framework for designing observers and observer-based controllers for systems
modeled by coupled nonlinear PDEs.
2. Design Innovative Algorithms: Propose innovative algorithms for designing observers and controllers specifically tailored to coupled nonlinear PDEs.
3. Validate Theoretical Methods: Use numerical simulations to validate theoretical results on benchmark problems and real-world applications.
References
1. Krstic, Miroslav, Luke Bhan, and Yuanyuan Shi (2024). Neural operators of backstepping controller and observer gain functions for reaction-
diffusion PDEs.Automatica 164 : 111649.
2. Krstic, M., & Smyshlyaev, A. (2008). Boundary Control of PDEs: A Course on Backstepping Designs. SIAM.
3. Meurer, T. (2012). Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs. Springer.
4. Prieur, C., & Vazquez, R. (2019). Robust nonlinear control of a class of coupled hyperbolic and parabolic
systems. IEEE Transactions on Automatic Control, 64(5), 1905-1919.
Department(s):
| Control Identification Diagnosis |