[en] This paper develops a new methodology for robust control of uncertain nonlinear systems. Two different controllers are developed and combined to accurately satisfy control requirements in the presence of (a) system uncertainties in our knowledge of the exact physical system, and (b) uncertainties in the given forces acting on the system. The methodology is developed in two steps. First, a controller is designed for the nominal system, which is our best assessment of the actual physical system, and no uncertainties are considered at this step. This controller is realized using a recent finding in the field of analytical dynamics. The control requirements are recast as constraints on the dynamical system, and use of the analytical dynamics result enables us to find the required generalized forces to exactly satisfy the control requirements while simultaneously minimizing a control cost. The discrepancies caused by ignoring the uncertainties are next compensated for by adding a second controller that is obtained by generalizing the concept of sliding mode control. Unlike conventional sliding mode controllers, this additive controller does not suffer from a chattering problem; it also leads to much smaller errors, and faster response. In addition, it allows many different forms of control functions to be used, depending on practical considerations of implementation. A numerical example of a three-degree-of-freedom pendulum is simulated to demonstrate the control strategy developed herein, in which there are uncertainties both in the description of the physical system’s parameters and in the description of the gravity field acting on the pendulum. The example illustrates the accuracy, efficiency, and ease of implementation of the new control methodology.
