Robust relatively optimal trajectory tracking control for a class of uncertain nonlinear control affine systems with state and input constraints

This paper proposes a robust relatively optimal trajectory tracking control strategy for a class of uncertain nonlinear control affine systems under the effect of external disturbances. The class of systems considered operates from a specific initial condition with state and input constraints. Simultaneous fulfillment of optimal trajectory tracking, constraint satisfaction, and robustness is a complex control problem. To address this, a control strategy is proposed by integrating the uncertainty and disturbance estimator (UDE) with a feedforward control as well as a relatively optimal trajectory tracking control (ROTTC). In this strategy, the estimate of equivalent disturbance from UDE and the feedforward control help to derive a nominal linear error dynamics of the system. The ROTTC minimizes this tracking error by satisfying the state and input constraints. Overall, the proposed strategy has the potential benefit on constraint satisfaction and robustness. A measure of the rate of change of input is incorporated in the performance measure (PM) along with that of state and input in the ROTTC design to assure reduced oscillations in the input signal. The estimation error due to the non-ideal filter in UDE is addressed in the stability analysis, and the ultimate boundedness of the tracking error is proved. The proposed control strategy is experimentally validated on the 3-DOF helicopter under aggressive maneuver. The superiority of the proposed method over a robust linear quadratic regulator (LQR) and feedback linearization-based relatively optimal control schemes in terms of the input energy as well as integral absolute errors is established in real-time.