An efficient preconditioning technique used earlier for two-by-two block matrix systems with square matrix blocks is shown to be applicable also for a state variable box-constrained optimal control problem. The problem is penalized by a standard regularization term for the control variable and for the box-constraint, using a Moreau–Yosida penalization method. It is shown that there occur very few nonlinear iteration steps and also few iterations to solve the arising linearized equations on the fine mesh. This holds for a wide range of the penalization and discretization parameters. The arising nonlinearity can be handled with a hybrid nonlinear-linear procedure that raises the computational efficiency of the overall solution method.
An adaptive revisit interval selection (RIS) in multifunction radars is an integral part of efficient time budget management (TBM). In this paper, the RIS problem is formulated as a Markov decision process (MDP) with unknown state transition probabilities and reward distributions. A reward function is proposed to minimize the tracking load (TL) while maintaining the track loss probability (TLP) at a tolerable level. The reinforcement learning (RL) problem is solved using the Qlearning algorithm with an epsilon-greedy policy. Compared to a baseline algorithm, the RL approach was capable of maintaining the tracks while reducing the tracking load significantly.
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