96M. MARWAHA AND J. VALASEK the concepts of feedback linearization, dynamic inversion, and structured model reference adaptive control. Because dynamic inversion assumes perfect knowledge of all the system parameters which are used to solve for the control, but is approximate in the actual implementation due to inaccurate modeling of system parameters, in SAMI an adaptive controller is wrapped around the dynamic inversion to handle the uncertainties in system parameters. Specific to the Mars entry problem, Restrepo and Valasek in [5] conducted the modeling and SAMI adaptive control formulation for a potential planetary entry vehicle that has 18 discrete reaction control system (RCS) jets.Another challenge during operation is recovery or tolerance in the case of actuator faults. Actuator faults can be due to any malfunction in the physical system or subsystem of the controller which results in its failure to perform as designed. The fault-tolerant control problem belongs to the domain of complex control systems in which inter-control-disciplinary information and expertise are required, with most application studies based upon aerospace systems [6]. Patton provides a thorough review of fault-tolerant control systems in [6]. When combined with adaptive control, control allocation algorithms provide the capability to recover from actuator faults. In their basic form control allocation algorithms are useful for finding solutions to meet the desired control objectives by delivering the desired moments [7]. Bodson provides a comprehensive survey of constrained, numerical-based optimization methods for control allocation in [8], and Page and Steinberg in [9] compare the closed and open-loop performance for 16 different control allocation approaches. Numerous linear control allocation algorithms are currently available. In [10] a faulttolerant control allocation scheme is introduced to handle actuator failures in discrete systems and is validated with a numerical example of a disturbance-free case. Tjonnas and Johansen [11] considers a dynamic approach by constructing actuator reference adaptive laws for over-actuated nonlinear time-varying systems. Shertzer et al. [12] discusses control allocation algorithms specifically in the context of next generation entry vehicles. Recently, Bolender and Doman have used a concept in which control allocation is used for aerodynamic surfaces, and dynamic inversion-based adaptive control is used for system identification, which helps in identifying any failure [13]. The control variable rates or moments are nonlinear functions of control positions. These schemes are applied to different aerovehicles and are shown to have good performance for continuous controls. However, this approach has not been applied to discrete controls, since they require a different allocation algorithm from aerodynamic surfaces [14].This paper introduces a novel use of fault-tolerant control allocation for discrete controls to nonlinear, time-varying systems. Specifically, we address the problem of discrete c...

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This paper introduces the Global-Local Mapping Approximation algorithm as a candidate for identifying nonlinear, six degree-of-freedom rigid body aircraft dynamics. The technique models the nonlinear dynamical model as a sum of linear model and nonlinear model. The linear model dynamics are assumed to be perturbed by a nonlinear term which represents the system nonlinearities that are not captured by the linear model. Lyapunov stability analysis is used to derive the learning laws. To demonstrate the suitability of the algorithm for nonlinear system identification of aircraft dynamics, a longitudinal and a lateral/directional example using nonlinear simulation data, and flight test data are conducted. The true nonlinear model is generated using both the six degree-of-freedom nonlinear equations of motion of an aircraft, and by flight test data. Results presented in the paper demonstrate the utility of the Global-Local Mapping Approximation for the realistic cases of an unknown control distribution matrix B and unknown influence coefficient matrix C.