Multi-dimensional Control Problems: Robust Approach

This book provides solutions to multi-dimensional control problems with uncertain data, including uncertain objective functionals, constraint functionals, semi-infinite constraints, dual multi-dimensional multi-objective variational control problems, and second-order PDE&PDI constrained robust optimization problems. It offers exact l1 penalty function approaches, modified objective approaches, and robust approaches to solve these complex optimization problems.

Format: Hardback
Length: 186 pages
Publication date: 01 November 2022
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the intricate realm of multi-dimensional control problems, particularly in the context of dealing with data uncertainty for vector cases. It addresses a diverse range of challenging scenarios, encompassing multi-dimensional multi-objective control problems with uncertain objective functionals, uncertain constraint functionals, uncertain objective and constraint functionals, uncertain multi-dimensional multi-objective control problems with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problems, and second-order PDE&PDI constrained robust optimization problems.

The book offers a comprehensive solution framework, presenting three distinct approaches: an exact l1 penalty function approach, a modified objective approach, and a robust approach. These approaches are designed to simplify the process of solving the recent and emerging optimization problems that arise in the realm of uncertainty.

In the first approach, the book employs an exact l1 penalty function, which is a powerful tool for regularization and optimization. It effectively handles the presence of noise and uncertainty in the data, enabling the development of robust solutions. By leveraging this approach, the book provides a clear and concise roadmap for addressing complex multi-dimensional control problems.

The second approach involves modifying the objective function to account for the uncertainty in the data. This approach allows for the development of more flexible and adaptable solutions that can handle a wide range of scenarios. By adapting the objective function, the book enables researchers and practitioners to find optimal solutions that are both effective and robust in the face of data uncertainty.

The third approach, known as the robust approach, is designed to handle the presence of uncertainties and disturbances in the system. It employs techniques such as robust optimization, which are well-suited for dealing with uncertain and challenging environments. By incorporating robustness into the solution framework, the book ensures that the solutions obtained are not sensitive to small variations in the input data or system parameters.

In conclusion, this book is a valuable resource for researchers, practitioners, and students interested in the field of multi-dimensional control problems. It provides a comprehensive and systematic treatment of the subject, covering a wide range of scenarios and offering practical solutions through three distinct approaches. By leveraging the insights and techniques presented in this book, individuals can develop robust and effective solutions to complex optimization problems in the face of data uncertainty.

Weight: 477g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811965609
Edition number: 1st ed. 2022