Introduction

Abstract

Constraints on inputs and other variables of a dynamic system are ubiquitous. Often they occur in the form of magnitude as well as rate saturation of a variable. Clearly, the capacity of every device is capped. Valves can only be operated between fully open and fully closed states, pumps and compressors have a finite throughput capacity, and tanks can only hold a certain volume. Force, torque, thrust, stroke, voltage, current, flow rate, and so on, are limited in their activation range in all physical systems. Servers can serve only so many consumers. In circuits, transistors and amplifiers are saturating components. Saturation and other physical limitations are dominant in maneuvering systems like aircrafts. Every physically conceivable actuator, sensor, or transducer has bounds on the magnitude as well as on the rate of change of its output. Thus, the saturation of a device presents a hard constraint.