Robust adaptive control for a class of semi-strict feedback systems with state and input constraints.

*(English)*Zbl 1396.93048Summary: This paper proposes a Dynamic Surface Control (DSC)-based robust adaptive control scheme for a class of semi-strict feedback systems with full-state and input constraints. In the control scheme, a constraint transformation method is employed to prevent the transgression of the full-state constraints. Specifically, the state constraints are firstly represented as the surface error constraints, then, an error transformation is introduced to convert the constrained surface errors into new equivalent variables without constraints. By ensuring the boundedness of the transformed variables, the violation of the state constraints can be prevented. Moreover, in order to obtain magnitude limited virtual control signal for the recursive design, the saturations are incorporated into the control law. The auxiliary design systems are constructed to analyze the effects of the introduced saturations and the input constraints. Rigorous theoretical analysis demonstrates that the proposed control law can guarantee that all the closed-loop signals are uniformly ultimately bounded, the tracking error converges to a small neighborhood of origin, and the full-state constraints are not violated. Compared with the existing results, the key advantages of the proposed control scheme include: (i) the utilization of the constraint transformation can handle both time-varying symmetric and asymmetric state constraints and static ones in a unified framework; (ii) the incorporation of the saturations permits the removal of a feasibility analysis step and avoids solving the constrained optimization problem; and (iii) the “explosion of complexity” in traditional backstepping design is avoided by using the DSC technique. Simulations are finally given to confirm the effectiveness of the proposed approach.

##### MSC:

93B35 | Sensitivity (robustness) |

93C40 | Adaptive control/observation systems |

93B52 | Feedback control |

93C10 | Nonlinear systems in control theory |