Reference trajectory management using piecewise cubic Hermite interpolating polynomials

A new reference trajectory management method is introduced to find a trade-off between the capability of the actuators and the desired performance of the controller in active fault tolerant control. The importance of this problem increases, especially when actuator faults/failures are considered. In order to handle the nonlinear optimization, the problem in transformed into nonlinear programming via dividing the state-space into several sub-intervals. Sequential quadratic programming is used as a powerful method to optimize the objective functions subject to nonlinear hard equality and inequality constraints. Due to their interesting properties, piecewise cubic hermite interpolating polynomials are used to approximate the modified reference trajectories. Several constraints, including hard nonlinear inequality and final point equality constraints are defined to ensure the asymptotic stability of the closed-loop system, even after the occurrence of a fault/failure. An adjustable parameter is introduced to explicitly take into account the graceful performance degradation. A small value of this parameter makes the controller conservative and forces the remaining actuators to accomplish the mission. On the other hand, a large value of this parameter gracefully degrades performance of the controller in favor of fewer burdens on the remaining healthy actuators. As long as the feasibility conditions are met, asymptotic stability of the closed-loop system can be assured using the proposed method. Several simulations are performed to show the capability of the proposed method in handling actuator faults/failures in the angular velocity stabilization of a rigid spacecraft. It is shown through simulations that even when severe actuator faults/failures are considered, the proposed method can render the origin an asymptotically stable point for the faulty system.