Optimal Control Of A Double Integrator

Optimal Control of a Double Integrator

This book provides an introductory yet rigorous treatment of Pontryagin’s Maximum Principle and its application to optimal control problems when simple and complex constraints act on state and control variables, the two classes of variable in such problems. The achievements resulting from first-order variational methods are illustrated with reference to a large number of problems that, almost universally, relate to a particular second-order, linear and time-invariant dynamical system, referred to as the double integrator. The book is ideal for students who have some knowledge of the basics of system and control theory and possess the calculus background typically taught in undergraduate curricula in engineering. Optimal control theory, of which the Maximum Principle must be considered a cornerstone, has been very popular ever since the late 1950s. However, the possibly excessive initial enthusiasm engendered by its perceived capability to solve any kind of problem gave way to its equally unjustified rejection when it came to be considered as a purely abstract concept with no real utility. In recent years it has been recognized that the truth lies somewhere between these two extremes, and optimal control has found its (appropriate yet limited) place within any curriculum in which system and control theory plays a significant role.

Optimal Control of a Double Integrator

Advanced Motion Control and Navigation of Robots in Extreme Environments

Advances in robotics and autonomous systems have opened new horizons for the scientists by creating new opportunities to explore extreme environments that would previously not have been possible. For example, robots that are deployed to study environmental processes such remote volcanos, monitor the climate variables under the adverse weather conditions, understand underground mines, and explore deep oceans which are all inaccessible or hazardous for the human. Industrial applications can also often be situated in extreme environments such as offshore oil and gas and nuclear industries. In such applications the autonomous robot is expected to complete tasks such as repair and maintenance, exploration, reconnaissance, inspection, and transportation which is either done in isolation or as a team of cooperative robots. Due to the harsh and severe conditions of such environments, designing an advanced robotic system that can endure them is a challenging task. The robot needs to cope with the time-varying, restricted, uncertain, and unstructured nature of the environment to achieve the planning and execution of the tasks. This in turn demands development of advanced, robust and adaptive motion control and navigation algorithms along with machine learning and deep learning algorithms with high cognitive capability for the robot to perceive the surrounding environment effectively. The use of both single and multi-robot platforms can be advantageous depending on the specific application and environment.