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Online monitoring aims to evaluate or to predict, at runtime, whether or not the behaviors of a system satisfy some desired specification. It plays a key role in safety-critical cyber-physical systems. In this work, we propose a new monitoring approach, called model predictive monitoring, for specifications described by Signal Temporal Logic (STL) formulae. Specifically, we assume that the observed state traces are generated by an underlying dynamic system whose model is known. The main idea is to use the dynamic of the system to predict future states when evaluating the satisfaction of the STL formulae. To this end, effective approaches for the computation of feasible sets of STL formulae are provided. We show that, by explicitly utilizing the model information of the dynamic system, the proposed online monitoring algorithm can falsify or certify of the specification in advance compared with existing algorithms, where no model information is used. We also demonstrate the proposed monitoring algorithm by several real world case studies., arXiv admin note: substantial text overlap with arXiv:2203.16267

The goal of Inverse Optimal Control (IOC) is to identify the underlying objective function based on observed optimal trajectories. It provides a powerful framework to model expert's behavior, and a data-driven way to design an objective function so that the induced optimal control is adapted to a contextual environment. In this paper, we design an IOC algorithm for linear-quadratic tracking problems with random time horizon, and prove the statistical consistency of the algorithm. More specifically, the proposed estimator is the solution to a convex optimization problem, which means that the estimator does not suffer from local minima. This enables the proven statistical consistency to actually be achieved in practice. The algorithm is also verified on simulated data as well as data from a real world experiment, both in the setting of identifying the objective function of human tracking locomotion. The statistical consistency is illustrated on the synthetic data set, and the experimental results on the real data shows that we can get a good prediction on human tracking locomotion based on estimating the objective function. It shows that the theory and the model have a good performance in real practice. Moreover, the identified model can be used as a control target in personalized rehabilitation robot controller design, since the identified objective function describes personal habit and preferences.