Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators
Abstract
The robustness of optimal regulators for nonlinear, deterministic and stochastic, multiinput dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the wellknown properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1983
 Bibcode:
 1983STIN...8320003T
 Keywords:

 Control Theory;
 Nonlinear Systems;
 Regulators;
 Robustness (Mathematics);
 Stochastic Processes;
 Dynamic Programming;
 HamiltonJacobi Equation;
 Perturbation;
 Stability;
 Electronics and Electrical Engineering