Unfalsified adaptive control: Controller switching algorithms for nonmonotone cost functions

Controller switching algorithms used for adaptive control are investigated. The concept of interfalsification, a generalization of the existing epsilon-hysteresis algorithm, is defined; a new concept of self-falsification is introduced, and the two concepts are compared. On the basis of the idea of self-falsification, new controller switching algorithms are designed and two new convergence theorems are proved. These new results allow for removal of the assumption that the cost function associated with each controller be monotonically nondecreasing in time, thus opening the possibility of safe data-driven adaptive control designs with fading-memory cost functions. Theoretical analysis and simulations illustrate that the self-falsification algorithms can also decrease insertions of destabilizing controllers and improve the transient properties. Copyright (c) 2012 John Wiley & Sons, Ltd.