Near-optimal control for time-varying linear discrete systems with additive nonlinearities and random gains

In this technical note, the near-optimal control problem is investigated for a class of time-varying linear discrete systems subject to additive nonlinearities and random gains. First, certain upper bound on the cost function is proposed to quantify the control performance. Subsequently, in virtue of the time-varying discrete Riccati-like recursions (DRLRs), the near-optimal control strategy is designed such that this upper bound is minimized over the finite horizon. To reflect the steady-state behavior of the dynamic system, the upper bound of the derived time-varying DRLRs is also analyzed over the infinite horizon by resorting to the semidefinite programming method. Finally, a numerical example is provided to verify the validity and advantages of the proposed methodology.