Nonlinear Control of Underactuated Systems Subject to Both Actuated and Unactuated State Constraints With Experimental Verification

In practice, underactuated systems are widely used, and their control problems have attracted much attention in recent years. For safety concerns or transient performance requirements, some state constraints should be guaranteed both theoretically and practically, particularly those exerted on unactuated states. To the best of our knowledge, there are few closed-loop control methods that can treat unactuated state constraints with theoretical guarantees (i.e., that can theoretically guarantee unactuated state variables to be always within the preset ranges). For this purpose, in this article, we propose a new control strategy for a class of underactuated systems that can treat the various constraints including actuated and unactuated state constraints and the constraints on some specific composite variables. Specifically, we elaborately design some new auxiliary terms that are composed of constrained variable signals and actuated velocity signals. These terms can enhance the couplings between unactuated and actuated states that are further utilized to tackle the unactuated state and composite variable constraints. Then, the performance of the designed method is proven by rigorous analysis. Finally, the proposed method is applied to a double pendulum crane system and a tower crane system to verify its superior performance by experiments.