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In this paper, a new controller framework incorporating an L1 adaptive control and an online optimization scheme is presented. This framework provides a method for maintaining output constraints in the presence of non-linear time-varying matched uncertainties by predicting future output trajectories within a finite time horizon. The stability conditions of the system are derived, and the prediction error is characterized. The online optimization is formulated into a linear program problem for which many efficient algorithms exist. Simulation results demonstrate the effectiveness of the controller framework.

SUMMARYRecently, an adaptive control algorithm was proposed to handle time‐varying parameters with transient characterization. Using fast and robust adaptation, the unknown time‐varying parameters are no longer restricted to having slow change rates. As unknown nonlinear functions can be simply expressed by a few time‐varying parameters, they can be handled by the adaptive framework easily without resorting to learning techniques such as artificial neural networks. This motivates a fundamental question about whether learning is still useful in algorithms using fast adaptation. This paper provides an answer to this question. An adaptive controller is presented that uses a radial basis function neural network in addition to the currently used piecewise constant adaptive law of the algorithm to approximate uncertainties. Even though the fast and robust adaptation of control can handle unknown nonlinear functions, there is still an advantage to using neural networks. This advantage is that certain design parameters related to the adaptation rate can be relaxed while still achieving good performance. It is shown that performance improves with better function approximation, and the inclusion of the neural network in the control architecture cannot degrade performance but only improve it. Fast adaptation requires a small integration step size. In the presence of artificial neural network learning, the same performance can be achieved at a lower adaptation rate or enlarged integration step size. This benefit is important for practical implementation of fast adaptation algorithms by relaxing the often stringent constraints on hardware CPU speed. Theoretical results are supported by simulations. Copyright © 2013 John Wiley & Sons, Ltd.

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