Stochastic control for a class of overtaking tracking problems: Risk-averse feedback design for performance robustness

Among of important results herein is the performance information analysis of forecasting higher-order characteristics of a general criterion of performance associated with a stochastic tracking system which is closely supervised by a reference command input and a desired trajectory. Both compactness from logic of state-space model description and quantitativity from probabilistic knowledge of stochastic disturbances are exploited to therefore allow accurate prediction of the effects of Chi-squared randomness on performance distribution of the optimal tracking problem. Information about performance-measure statistics is further utilized in the synthesis of optimal cumulant-based controllers which are thus capable of shaping the distribution of tracking performance without reliance on computationally intensive Monte Carlo analysis as needed in post-design performance assessment. As a by-product, the recent results can potentially be applicable to another substantially larger class of optimal tracking systems whereby local representations with only first two statistics for non-Gaussian random distributions of exogenous disturbances and uncertain environments may be sufficient.