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Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that minimizes the expected time to complete the control task while satisfying syntactically co-safe Linear Temporal Logic (scLTL) specifications. First, we present an exact dynamic programming update to compute the value function. Afterwards, we propose a point-based approximation, which allows us to compute a lower bound of the closed-loop probability of satisfying the specifications. The effectiveness of the proposed approach and comparisons with standard strategies are shown on high-fidelity navigation tasks with partially observable static obstacles.
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The community integrated energy system (CIES) is an essential energy internet carrier that has recently been the focus of much attention. A scheduling model based on chance-constrained programming is proposed for integrated demand response (IDR)-enabled CIES in uncertain environments to minimize the system operating costs, where an IDR program is used to explore the potential interaction ability of electricity-gas-heat flexible loads and electric vehicles. Moreover, power to gas (P2G) and micro-gas turbine (MT), as links of multi-energy carriers, are adopted to strengthen the coupling of different energy subsystems. Sequence operation theory (SOT) and linearization methods are employed to transform the original model into a solvable mixed-integer linear programming model. Simulation results on a practical CIES in North China demonstrate an improvement in the CIES operational economy via the coordination of IDR and renewable uncertainties, with P2G and MT enhancing the system operational flexibility and user comprehensive satisfaction. The CIES operation is able to achieve a trade-off between economy and system reliability by setting a suitable confidence level for the spinning reserve constraints. Besides, the proposed solution method outperforms the Hybrid Intelligent Algorithm in terms of both optimization results and calculation efficiency.
We present a robust control framework for time-critical systems in which satisfying real-time constraints is of utmost importance for the safety of the system. Signal Temporal Logic (STL) provides a formal means to express a variety of real-time constraints over signals and is suited for planning and control purposes as it allows us to reason about the time robustness of such constraints. The time robustness of STL particularly quantifies the extent to which timing uncertainties can be tolerated without violating real-time specifications. In this paper, we first pose a control problem in which we aim to find an optimal input sequence to a control system that maximizes the time robustness of an STL constraint. We then propose a Mixed Integer Linear Program (MILP) encoding and provide correctness guarantees and a complexity analysis of the encoding. We also show in two case studies that maximizing STL time robustness allows to account for timing uncertainties of the underlying control system.
This paper studies the robust satisfiability check and online control synthesis problems for uncertain discrete-time systems subject to signal temporal logic (STL) specifications. Different from existing techniques, this work proposes an approach based on STL, reachability analysis, and temporal logic trees. Firstly, a real-time version of STL semantics and a tube-based temporal logic tree are proposed. We show that such a tree can be constructed from every STL formula. Secondly, using the tube-based temporal logic tree, a sufficient condition is obtained for the robust satisfiability check of the uncertain system. When the underlying system is deterministic, a necessary and sufficient condition for satisfiability is obtained. Thirdly, an online control synthesis algorithm is designed. It is shown that when the STL formula is robustly satisfiable and the initial state of the system belongs to the initial root node of the tube-based temporal logic tree, it is guaranteed that the trajectory generated by the controller satisfies the STL formula. The effectiveness of the proposed approach is verified by an automated car overtaking example.
This paper investigates an optimal consensus problem for a group of uncertain linear multi-agent systems. All agents are allowed to possess parametric uncertainties that range over an arbitrarily large compact set. The goal is to collectively minimize a sum of local costs in a distributed fashion and finally achieve an output consensus on this optimal point using only output information of agents. By adding an optimal signal generator to generate the global optimal point, we convert this problem to several decentralized robust tracking problems. Output feedback integral control is constructively given to achieve an optimal consensus under a mild graph connectivity condition. The efficacy of this control is verified by a numerical example.
We propose a new framework to solve online optimization and learning problems in unknown and uncertain dynamical environments. This framework enables us to simultaneously learn the uncertain dynamical environment while making online decisions in a quantifiably robust manner. The main technical approach relies on the theory of distributional robust optimization that leverages adaptive probabilistic ambiguity sets. However, as defined, the ambiguity set usually leads to online intractable problems, and the first part of our work is directed to find reformulations in the form of online convex problems for two sub-classes of objective functions. To solve the resulting problems in the proposed framework, we further introduce an online version of the Nesterov accelerated-gradient algorithm. We determine how the proposed solution system achieves a probabilistic regret bound under certain conditions. Two applications illustrate the applicability of the proposed framework.
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