Extending H^∞ Control to Nonlinear Systems: Control of Nonlinear Systems to Achieve Performance Objectives

Explicit Solution to a Robust Queueing Control Problem

“…The two players are antagonistic, with thē rst player attempting to maintain good system performance. Di®erential game formulations provide a powerful tool for the design of robust controls [3,14]. In many situations knowledge of the true system is limited.…”

“…Equations (18) and (19) imply that R=c is a (classical) supersolution to (13) and (14). Standard arguments based on dynamic programming can then be used to show that V + (x) · R(x)=c.…”

Measurement feedback controller design to achieve input to state stability

“…(ii) We consider possibly dynamic feedback controller design where the dimension of the controller is not given before the design. (iii) This requirement is compatible with definitions of nonlinear H ∞ problems ( [5]) and the ULIB problems that are stated next.…”

“…This trend has been driven by several major breakthroughs over the past 15 years that occurred in nonlinear H ∞ control (e.g. [3], [21], [5]) and the input to state stability (ISS) related literature (e.g. [19], [16], [2]).…”

“…Moreover, this literature often aims at designing controllers that achieve minimum (optimal) gains from disturbance inputs to plant outputs and, hence, controller design often requires a solution of an appropriate dynamic programming equation (DPE) or inequality (DPI). An advantage of this approach is that it can be applied to a very broad class of plants and its main drawback is the heavy computation required to solve DPE/DPI [5]. Nevertheless, the methodology is fundamental and provides useful conceptual insights.…”