H Infinity Control for Nonlinear and Linear Systems

Abstract

Abstract : The design of a system or circuit in which stability is a key constraint frequently leads to an optimization problem over the space of functions analytic on the right half plane (R.H.P.) Mathematical techniques for solving such optimization problems for mean square error (L2 error) criteria have been widespread in engineering since the time of Wiener. Much of this research goes to developing techniques for handling worst case error (L infinity error) criteria. These occur naturally in design of control systems and amplifiers. Practically speaking there is evidence that frequency domain L infinity criteria control system designs have desirable robustness properties. The ultimate objective is to develop a new CAD approach to MIMO control design which has the flavor of classical control as well as a systematic approach to worst case frequency domain design as it occurs in many areas. The promise of this approach is sufficient to have attracted many investigators and it is currently the focus of much attention. This research addresses many aspects of the problem. They range from the development of computer algorithms of a radically different type to the discovery of theoretical methods for understanding computational design. Also considerable progress was made in extending existing H infinity control to nonlinear plants. Another major effort involves computer algebra for systems research. The objective is to treat (on a computer) systems formulas of the type an investigator would manipulate by hand. Considerable software was developed along these lines.