Max-Plus Methods for Nonlinear Control and Estimation [Hardcover]

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.

The control and estimation of continuous-time/continuous-space nonlinear systems continues to be a challenging problem, and this is one of the c- tral foci of this book. A common approach is to use dynamic programming; this typically leads to solution of the control or estimation problem via the solution of a corresponding HamiltonJacobi (HJ) partial di?erential eq- tion (PDE). This approach has the advantage of producing the optimal control. (The term optimal has a somewhat more complex meaning in the class of H problems. However, we will freely use the term for such controllers ? throughout, and this meaning will be made more precise when it is not ob- ous. )Thus,insolvingthecontrol/estimationproblem,wewillbesolvingsome nonlinear HJ PDEs. One might note that a second focus of the book is the solution of a class of HJ PDEs whose viscosity solutions havelc<