The problem of quickly reducing operating errors during recovery from a feedback disruption is considered. The objective is to design controllers that reduce operating errors as quickly as possible, once feedback has been restored. It is shown that robust optimal feedback controllers that achieve this objective do exist. Furthermore, it is shown that the performance of optimal controllers can be approximated as closely as desired by controllers that generate bang–bang input signals for the controlled system. Controllers that generate bang–bang signals are relatively easy to derive and implement, since bang–bang signals are characterised by a finite list of scalars – their switching times.

Fastest recovery after feedback disruption

The problem of maintaining low operating errors during feedback outages is considered for a class of nonlinear systems with time-delays in the input channel. It is shown that there are optimal controllers that keep operating errors below a specified bound for the longest time possible. Furthermore, it is shown that optimal performance can be approximated as closely as desired by using bang-bang controllers – controllers that are relatively easy to calculate and implement.

Optimal Robust Control of Nonlinear Time-Delay Systems: Maintaining Low Operating Errors During Feedback Outages

The problem of reducing operating errors after a feedback disruption is considered for a class of nonlinear delay-differential systems. It is shown that there are optimal controllers that reduce such errors in minimal time, once feedback has been restored. It is further shown that optimal performance can be approximated by bang-bang controllers – controllers that are easy to design and implement.

Fastest recovery after feedback disruption: nonlinear delay-differential systems

The problem of designing robust optimal controllers to reduce in minimal time operating errors that had accumulated during a period of feedback loss is revisited, with the objective of impo...

Fastest recovery from feedback loss: Bounded overshoot

Recovering from Feedback Failure in Minimal Time

The problem of finding the minimum input norm required to bring a dynamical system from an arbitrary initial state to a given end-point constraint set under specified state constraints, in a finite time interval, is considered. Even when there exists a control input which achieves the constraints, there may not be one with a minimum norm. For input-affine systems, it is shown that there is an admissible bang-bang control input whose norm is arbitrarily close to the minimum-norm. Since bang-bang functions are completely specified by their amplitude and switching times, the optimal norm can be numerically estimated by performing a finite dimensional search.

/pdf/an-approximate-solution-to-the-norm-optimal-control-problem-3fe4o45611.pdf

C. Shaikshavali

Papers

An approximate solution to the norm optimal control problem