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      Shrinking Horizon Model Predictive Control with Signal Temporal Logic Constraints under Stochastic Disturbances

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          Abstract

          We present Shrinking Horizon Model Predictive Control (SHMPC) for discrete-time linear systems with Signal Temporal Logic (STL) specification constraints under stochastic disturbances. The control objective is to maximize an optimization function under the restriction that a given STL specification is satisfied with high probability against stochastic uncertainties. We formulate a general solution, which does not require precise knowledge of the probability distributions of the (possibly dependent) stochastic disturbances; only the bounded support intervals of the density functions and moment intervals are used. For the specific case of disturbances that are independent and normally distributed, we optimize the controllers further by utilizing knowledge of the disturbance probability distributions. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for an HVAC system.

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          The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial

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            Monitoring Temporal Properties of Continuous Signals

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              Robustness of temporal logic specifications for continuous-time signals

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                Author and article information

                Journal
                2017-05-05
                Article
                1705.02152
                ed813a8a-049a-44e6-a8a5-95cf799d4015

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                11 pages, 1 figure, 1 table, Submitted to IEEE Transaction on Automatic Control. A limited subset of the results of this paper is accepted for presentation at American Control Conference 2017
                cs.SY cs.LO math.OC math.PR

                Numerical methods,Theoretical computer science,Performance, Systems & Control,Probability

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