Real-time optimal control and observation

A survey of the results obtained by authors and their coworkers (mainly in 2000-2003) on realization of modern principles of optimal control and observations in real time was made. Optimal control problems and the problems of observation of deterministic systems, problems under the conditions of set-membership uncertainty; perfect and imperfect measurements, feedforward, feedback, and combined loop cases, inertial and inertialess controls; and special and dynamical regulators for indirect control, linear piecewise linear, and nonlinear models are considered consecutively. The presentation focuses mainly on linear models, since the optimal control of nonlinear systems is based on linear or piecewise linear approximations of the initial model. For the realization of the positional solutions of the optimal control and observation problems, fast dual methods taking into account the dynamical nature of the problems being investigated are justified. The application of the results on optimal control in real time for the solution of classical control problems (problems of regulating, stabilizing, tracking, etc.) is discussed. The presentation is accompanied by computational examples.