Search

Contractive nonlinear systems possess numerous desirable properties, which have drawn considerable attention from the control community. The work proposes an extended HGO based output feedback strategy, which can assure contraction of a class of uncertain singularly perturbed (SP) systems. The analysis differs from the conventional Lyapunov approach in two aspects: the convergence bounds explicitly depend on the singular perturbation parameter (SPP); and the sufficient conditions for contraction do not require any interconnection conditions. Moreover, it is observed that the requirement of the smallness of SPP can be relaxed for certain classes of nonlinear systems. The derived bounds also reveal a particular trade-off between the contraction rates and condition numbers associated with the transformation metric. These bounds offer additional degree of freedom in tuning the closed loop performances apart from reducing the SPP. Multiple numerical simulations point to the veracity of the claims. [ABSTRACT FROM AUTHOR]

This work is inspired by motion control of cleaning robots, operating in certain endogenous environments, and performing various tasks like door cleaning, wall sanitizing, etc. The base platform's motion for these robots is generally similar to the motion of four-wheel cars. Most of the cleaning and maintenance tasks require detection, path planning, and control. The motion controller's job is to ensure the robot follows the desired path or a set of points, pre-decided by the path planner. This control loop generally requires some feedback from the on-board sensors, and odometry modules, to compute the necessary velocity inputs for the wheels. As the sensors and odometry modules are prone to environmental noise, dead-reckoning errors, and calibration errors, the control input may not provide satisfactory performance in a closed-loop. This paper develops a robust-observer based sliding mode controller to fulfill the motion control task in the presence of incomplete state measurements and sensor inaccuracies. A robust intrinsic observer design is proposed to estimate the input matrix, which is used for dynamic feedback linearization. The resulting uncertain dynamics are then stabilized through a sliding mode controller. The proposed robust-observer based sliding mode technique assures asymptotic trajectory tracking in the presence of measurement uncertainties. Lyapunov based stability analysis is used to guarantee the convergence of the closed-loop system, and the proposed strategy is successfully validated through numerical simulations.