Accommodating Sensor Bias in MRAC for State Tracking

The problem of accommodating unknown sensor bias is considered in a direct model reference adaptive control (MRAC) setting for state tracking using state feedback. Sensor faults can occur during operation, and if the biased state measurements are directly used with a standard MRAC control law, neither closed-loop signal boundedness, nor asymptotic tracking can be guaranteed and the resulting tracking errors may be unbounded or unacceptably large. A modified MRAC law is proposed, which combines a bias estimator with control gain adaptation, and it is shown that signal boundedness can be accomplished, although the tracking error may not go to zero. Further, for the case wherein an asymptotically stable sensor bias estimator is available, an MRAC control law is proposed to accomplish asymptotic tracking and signal boundedness. Such a sensor bias estimator can be designed if additional sensor measurements are available, as illustrated for the case wherein bias is present in the rate gyro and airspeed measurements. Numerical example results are presented to illustrate each of the schemes

On Using Exponential Parameter Estimators with an Adaptive Controller

Typical adaptive controllers are restricted to using a specific update law to generate parameter estimates. This paper investigates the possibility of using any exponential parameter estimator with an adaptive controller such that the system tracks a desired trajectory. The goal is to provide flexibility in choosing any update law suitable for a given application. The development relies on a previously developed concept of controller/update law modularity in the adaptive control literature, and the use of a converse Lyapunov-like theorem. Stability analysis is presented to derive gain conditions under which this is possible, and inferences are made about the tracking error performance. The development is based on a class of Euler-Lagrange systems that are used to model various engineering systems including space robots and manipulators

Decentralized Adaptive Control of Systems with Uncertain Interconnections, Plant-Model Mismatch and Actuator Failures

Decentralized adaptive control is considered for systems consisting of multiple interconnected subsystems. It is assumed that each subsystem s parameters are uncertain and the interconnection parameters are not known. In addition, mismatch can exist between each subsystem and its reference model. A strictly decentralized adaptive control scheme is developed, wherein each subsystem has access only to its own state but has the knowledge of all reference model states. The mismatch is estimated online for each subsystem and the mismatch estimates are used to adaptively modify the corresponding reference models. The adaptive control scheme is extended to the case with actuator failures in addition to mismatch

Composite Adaptive Control for Euler-Lagrange Systems with Additive Disturbances

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error.Ideally, the adaptive update law would also include some feedback of the parameter estimation error.The desire to include some measurable form of the parameter estimation error in the adaptation lawresulted in the development of composite adaptive update laws that are functions of a prediction errorand the state feedback. In all previous composite adaptive controllers, the formulation of the predictionerror is predicated on the critical assumption that the system uncertainty is linear in the uncertainparameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy theprediction error formulation and stability analysis arguments in previous results. In this paper, a newprediction error formulation is constructed through the use of a recently developed Robust Integral ofthe Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis isthat the prediction error can be developed even with disturbances that do not satisfy the LP assumption(e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMOEuler–Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-basedstability analysis is used to derive sufficient gain conditions under which the proposed controller yieldssemi-global asymptotic tracking. Experimental results are presented to illustrate the approach