9813182 Kelkar The main objective of this research project is to develop a unified framework for the stabilization and control of underactuated linear and nonlinear nonholonomic systems. In particular, it is aimed to develop a methodology for the control of nonlinear underactuated nonholonomic systems which will include open-loop unstable and/or non-minimum phase systems. As a special case, the methodology will be applicable to linear systems as well. Similarly, the methodology will also be applicable to holonomic systems. The proposed research will yield a methodology to obtain a class of controllers (and not a specific controller) for stabilization and control of underactuated nonlinear systems. The proposed method has great potential in the design of robust controllers and fault-tolerant controllers for difficult-to-control nonlinear systems, leading to the development of a software tool (toolbox) which can generate controllers for a given underactuated system. The methodology is based on the construction of a class of auxiliary stable systems each of which will be equivalent to the original system with a proper choice of controller. The simulation results for an underactuated 2-d.o.f. inverted pendulum-cart system are included and compared with the existing recent results as a validation of the theory. The methodology will advance the state-of-the-art in the area of control of nonlinear systems as well as nonlinear controllers. The results of this research will enhance ability to control a large class of real life systems, for example, aircraft and spacecraft in actuator failure mode, underwater vehicles, and biped locomotion. To demonstrate the viability of this methodology, a series of control experiments will be developed. Each apparatus will represent a class of underactuated nonlinear mechanical systems with two or higher degrees-of-freedom. ***
