Reliable State Feedback Control for Uncertain Linear Systems With Terminal Reliability Constraint

We propose a reliable state feedback control method for uncertain linear systems with a terminal reliability constraint. By modeling the uncertainties from system parameters and disturbances with multiple probabilistic intervals whose probabilities sum to 1, multiple corresponding probabilistic intervals of control responses are approximately estimated through the system dynamics as the uncertainty propagation bridge. This not only mitigates the need for large sample data required by probabilistic methods for robust control, but also avoids the large error caused by the first-order Taylor expansion required by nonprobabilistic methods in the case of large radiuses of uncertain parameters. Considering the different characteristics of transient and steady-state phases, a prescribed performance threshold function is established for the concerned control response. Based on probabilistic intervals and threshold, the failure rate model and reliability model for the concerned control response are formulated. Further, an optimization problem for the reliable state feedback control with the terminal reliability constraint is formulated and solved by the simulated annealing algorithm. An illustrative example is presented to demonstrate the feasibility and effectiveness of the reliable state feedback control.