Fully Actuated System Approaches: Predictive Elimination Control for Discrete-Time Nonlinear Time-Varying Systems With Full State Constraints and Time-Varying Delays

This paper concentrates on the optimal tracking control for a discrete-time nonlinear time-varying fully-actuated system (FAS) with full state constraints and time-varying delays. An explicit analytical predictive controller is constructed by incorporating the predictive control scheme and the constraint elimination technique into FAS approaches. The proposed PEC-FAS scheme dexterously eliminates full state constraints without introducing new constraints and uncertainties, makes full use of full-actuation property to compensate the time-delay actively. Especially, it reduces the coupling degree of the states, and eliminates the nonlinearities arising from the original system and constraints elimination process simultaneously. These efforts largely improve the solvability of the strongly nonlinear and coupled optimization problem with constraints and time-delay. Meanwhile, by analytically expressing the predictive information by off-line calculation, the nonlinear optimization problem is converted into a series of linear convex optimization problems without constraints and time-delay, which fundamentally mitigates the computational burden and the design complexity compared with the previous nonlinear predictive control approaches. Theoretically, it is demonstrated that the proposed controller is recursively feasible, which also owns a recursive explicit analytical predictive controller sequence in each predictive horizon, and the tracking error system is asymptotically stable under the certain condition with predictive parameters. Finally, the simulation of a benchmark under-actuated application of a rotational translational actuator (RTAC) system, demonstrates the effectiveness and the simplicity of the proposed PEC-FAS scheme.