OUTPUT ZEROING WITH INTERNAL STABILITY BY LEARNING

We formulate a novel learning algorithm for output zeroing of linear f inite-dimensional, control systems. As in classical control systems th eory, we start from the knowledge of a nominal plant to develop a feed back algorithm that achieves the control objective by means of success ive trials on the plant. Algorithm convergence in the face of linear p lant perturbations is proved, and performance in the face of small non linear perturbations is discussed. The proposed algorithm does not req uire output differentiation, and is based upon the learning of the ini tial conditions that allow the output to remain identically zero, whil e the state of the system, dynamically extended, freely evolves comply ing with an internal stability constraint. Implementation of this algo rithm requires state initialization at an arbitrary point of the state space. Therefore, for those systems for which direct state initializa tion is not feasible, we develop a learning procedure that automatical ly accomplishes this task. By means of a control input generated by th e algorithm, the state of the system is steered, during an initial pha se, from a point where it is easily initialized to the point from whic h the output zeroing task starts. An illustrative example is included.