Max-Plus Methods for Nonlinear Control and Estimation

The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality.

The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HamiltonJacobiBellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches.

Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.

Examines the control of continuous-time/continuous-space nonlinear systems Several classes of nonlinear control problems are addressed, nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HamiltonJacobiBellman partial differential equations; allows for the construction of new algorithms Researchers and practitioners only tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections

Contenu
Max-Plus Analysis.- Dynamic Programming and Viscosity Solutions.- Max-Plus Eigenvector Method for the Infinite Time-Horizon Problem.- Max-Plus Eigenvector Method Error Analysis.- A Semigroup Construction Method.- Curse-of-Dimensionality-Free Method.- Finite Time-Horizon Application: Nonlinear Filtering.- Mixed L?/L2 Criteria.