In our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each sequence in order to maximize a reward equal to the expected value of the sum of the selections from all sequences. The decision on which element to pick is irrevocable, i.e., rejected observations cannot be revisited. Furthermore, the procedure terminates upon having a single selection from each sequence. Our observation constraint is that we cannot observe the current realization of all sequences at each time instant. Instead, we can observe only a smaller, yet arbitrary, subset of them. Thus, together with a stopping rule that determines whether we choose or reject the sample, the solution requires a sampling rule that determines which sequence to observe at each instant. The problem can be solved via dynamic programming, but with an exponential complexity in the length of the sequences. In order to make the solution computationally tractable, we introduce a decoupling approach and determine each stopping time using either a single-sequence dynamic programming, or a Prophet Inequality inspired threshold method, with polynomial complexity in the length of the sequences. We prove that the decoupling approach guarantees at least 0.745 of the optimal expected reward of the joint problem. In addition, we describe how to efficiently compute the optimal number of samples for each sequence, and its' dependence on the variances.

The problem of sequential anomaly detection is considered, where multiple data sources are monitored in real time and the goal is to identify the “anomalous” ones among them, when it is not possible to sample all sources at all times. A detection scheme in this context requires specifying not only when to stop sampling and which sources to identify as anomalous upon stopping, but also which sources to sample at each time instance until stopping. A novel formulation for this problem is proposed, in which the number of anomalous sources is not necessarily known in advance and the number of sampled sources per time instance is not necessarily fixed. Instead, an arbitrary lower bound and an arbitrary upper bound are assumed on the number of anomalous sources, and the fraction of the expected number of samples over the expected time until stopping is required to not exceed an arbitrary, user-specified level. In addition to this sampling constraint, the probabilities of at least one false alarm and at least one missed detection are controlled below user-specified tolerance levels. A general criterion is established for a policy to achieve the minimum expected time until stopping to a first-order asymptotic approximation as the two familywise error rates go to zero. Moreover, the asymptotic optimality is established of a family of policies that sample each source at each time instance with a probability that depends on past observations only through the current estimate of the subset of anomalous sources. This family includes, in particular, a novel policy that requires minimal computation under any setup of the problem.

The problem of sequential anomaly detection is considered under sampling constraints and generalized error control. It is assumed that there is no prior information on the number of anomalies. It is required to control the probability at least k errors, of any kind, upon stopping, where k is a user specified integer. It is possible to sample only a fixed number of processes at each sampling instance. The processes to be sampled are determined based on the already acquired observations. The goal is to find a procedure that consists of a stopping rule and a decision rule and a sampling rule that satisfy the sampling and error constraints, and have as small as possible average sample size for every possible scenario regarding the subset of anomalous processes. We characterize the optimal expected sample size for this problem to a first order approximation as the error probability vanishes to zero, and we propose procedures that achieve it. The performance of those procedures is compared in a simulation study for different values of k.

The problem of anomaly detection is considered when multiple processes are observed sequentially, but it is possible to sample only a subset of them at a time according to an adaptive sampling policy. The problem is to stop sampling as soon as possible and identify the anomalous processes, while controlling appropriate error probabilities. We consider two versions of this problem: in the first one there is no assumption regarding the anomalous processes, in the second their number is assumed to be known a priori. For each version, we obtain the optimal asymptotic performance as the error probabilities vanish and characterize the sampling rules that lead to asymptotic optimality. Moreover, we present two sampling rules for each setup, which differ in terms of the computational complexity and the actual performance they imply.

We present the design of a backstepping controller for a triangular over-actuated marine platform, controlled by three rotating jets. Our goal is the stabilization of the position and the orientation of the platform, under realistic environmental disturbances, such as wind forces, wave forces and hydrodynamic forces. Actuator thrust and angle dynamics, as well as settling delays, in the rotation of the jets and in the response of the desired thrust, are included in the algorithm, despite the presence of an allocation scheme. Thrust and angle velocity, limitations are also taken into account. A Thrust Upper Limit (TUL) manipulation heuristic is introduced in order to reduce the thrust requirements and the energy consumed. The performance of the developed backstepping controller is compared to the case with and without the TUL. Simulation results show that the use of the heuristic reduces energy consumption.