This paper treats the geometric formulation of optimal control problems for rigid bodies and it presents computational procedures based on this geometric formulation that can be used for numerical solution of these optimal control problems. The dynamics of each rigid body is viewed as evolving on a configuration manifold that is a Lie group. Discrete time dynamics of each rigid body are develop...

The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The maximum principle changes the problem of optimal control to a two point boundary value problem which can be completely solved only in special tasks. It was probably the reaso...

this paper presents a discrete-time robust control for electrically driven robot manipulators in the task space. a novel discrete-time model-free control law is proposed by employing an adaptive fuzzy estimator for the compensation of the uncertainty including model uncertainty, external disturbances and discretization error. parameters of the fuzzy estimator are adapted to minimize the estimat...

A linear-like discrete-time fuzzy controller was designed to control and stabilize a single-pool irrigation canal. Saint Venant equations for open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear partial differential equations. Using the linear optimal control theory, a traditional linear quadratic regulator (LQR) was first dev...

Certain types of adaptive algorithms used for repetitive control are input/output equivalent to linear time-invariant controllers. This paper concerns the consequences of this equivalence for analysis and design of these types of adaptive controllers. Specifically, the role of zero placement in the linear time-invariant equivalent is closely examined using root locus analysis, and a modificatio...