Dual Perturbation Control.
Abstract
Optimal control laws are investigated for minimizing the expected value of a quadratic criterion with linear dynamics and state measurements, both perturbed by additive white Gaussian noise processes whose intensities depend weakly and linearly on the instantaneous state and control. A dynamic programing approach is used to derive expressions for the optimal control and cost function that are accurate to first order in the noise intensity variations and are given in terms of initial value systems of ordinary differential equations. As compared to the classical 'linear-quadratic-Gaussian' control problem without noise-intensity variations, the first-order optimal control law modifications here are found to be the inclusion of the state covariance matrix as a measurement-driven variable in the state estimator, the appearance of deterministic skewness variables in this estimator, and the addition of a deterministic term to the control. Part of the additive control term can be interpreted as the 'dual control' effect, and it is coupled to the control through a matrix time function whose properties are investigated. A useful refinement of the certainty-equivalence principle is made. When the measurement noise is state-dependent, the differential equations for state estimation have a random driving term containing the scatter matrix of the measurements, which imposes some additional restrictions on the validity of the analysis. Some aspects of the results are shown to generalize to the case of a quadratic exponential criterion, although that situation is more complicated. A method for including the effects of noise intensity gradients in iterative optimization algorithms is described, and a numerical example is given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 15, 1977
- Accession Number
- ADA037065
Entities
People
- Warren W. Willman
Organizations
- United States Naval Research Laboratory