Cost Cumulant-Based Control for a Class of Linear-Quadratic Tracking Problems

The topic of cost-cumulant control is currently receiving substantial research from the theoretical community oriented toward stochastic control theory. For instance, the present paper extends the application of cost-cumulant controller design to control of a wide class of linear-quadratic tracking systems where output measurements of a tracker follow as closely as possible a desired trajectory via a complete statistical description of the associated integral-quadratic performance-measure. It is shown that the tracking problem can be solved in two parts: one, a feedback control whose optimization criterion representing a linear combination of finite cumulant indices of an integral-quadratic performance- measure associated to a linear tracking stochastic system over a finite horizon, is determined by a set of Riccati-type differential equations; two, an affine control which takes into account of dynamics mismatched between a desired trajectory and tracker states, is found by solving an auxiliary set of differential equations (incorporating the desired trajectory) backward from a stable final time.