Dynamical systems with active singularities: Input/state/output modeling and control

Controller synthesis setting for systems with active, or controlled, singularities is extended to the case of incomplete information. The general physically-based description of mechanical systems with controlled singularities and sensing in the singular phase that also admits control over observations is developed. An example is presented that demonstrates the computation of a singular phase sensor-based optimal control law. It is found that optimal control of this class of systems should, in general, be sought in the class of complex signals termed temporal multi-impacts - very short duration isolated sets of temporally sequenced impulses. The system subject to these impacts is shown to exhibit a novel mode of controlled dynamic behavior - the interlaced singular phase.