Safety control of monotone systems with bounded uncertainties

Monotone systems are prevalent in models of engineering applications such as transportation and biological networks. In this paper, we investigate the problem of finding a control strategy for a discrete time positive monotone system with bounded uncertainties such that the evolution of the system is guaranteed to be confined to a safe set in the state space for all times. By exploiting monotonicity, we propose an approach to this problem which is based on constraint programming. We find control strategies that are based on repetitions of finite sequences of control actions. We show that, under assumptions made in the paper, safety control of monotone systems does not require state measurement. We demonstrate the results on a signalized urban traffic network, where the safety objective is to keep the traffic flow free of congestion.This work was partially supported by the NSF under grants CPS-1446151 and CMMI-1400167. (CPS-1446151 - NSF; CMMI-1400167 - NSF

Robust Temporal Logic Model Predictive Control

Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints given as formulas of signal temporal logic (STL). We introduce a (conservative) computationally efficient framework to synthesize control strategies based on mixed integer programs. The designed controllers satisfy the temporal logic requirements, are robust to all possible realizations of the disturbances, and optimal with respect to a cost function. In case the temporal logic constraint is infeasible, the controller satisfies a relaxed, minimally violating constraint. An illustrative case study is included.Comment: This work has been accepted to appear in the proceedings of 53rd Annual Allerton Conference on Communication, Control and Computing, Urbana-Champaign, IL (2015

Formal Synthesis of Control Strategies for Positive Monotone Systems

We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances. Such systems are widely used to model the dynamics of transportation and biological networks. The specifications are described using signal temporal logic (STL), which can express a broad range of temporal properties. We formulate the problem as a mixed-integer linear program (MILP) and show that under the assumptions made in this paper, which are not restrictive for traffic applications, the existence of open-loop control policies is sufficient and almost necessary to ensure the satisfaction of STL formulas. We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions. We also develop a robust model predictive framework to plan controls optimally while ensuring the satisfaction of the specification. Illustrative examples and a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16 pages, double colum