Time-Constrained Temporal Logic Control of Multi-Affine Systems

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution

An Efficient Formula Synthesis Method with Past Signal Temporal Logic

In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided formula synthesis framework. In particular, we combine optimized formulas iteratively to describe the causes of the labeled events while bounding the error. We illustrate the proposed framework on two examples.Comment: 8 pages, 5 figures, conference pape

A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems

Traffic Network Control from Temporal Logic Specifications

We propose a framework for generating a signal control policy for a traffic network of signalized intersections to accomplish control objectives expressible using linear temporal logic. By applying techniques from model checking and formal methods, we obtain a correct-by-construction controller that is guaranteed to satisfy complex specifications. To apply these tools, we identify and exploit structural properties particular to traffic networks that allow for efficient computation of a finite state abstraction. In particular, traffic networks exhibit a componentwise monotonicity property which allows reach set computations that scale linearly with the dimension of the continuous state space

A Novel MDP Based Decision Support Framework to Restore Earthquake Damaged Distribution Systems

Electric power network expanded rapidly in recent decades due of the excessive need of electricity in every aspect of life, including critical infrastructures such as medical services, and transportation and communication systems. Natural disasters are one of the major reasons of electricity outage. It is extremely important to restore electrical energy in the shortest time possible after a disaster. This paper proposes a decision support method for electric system operators to restore electricity to the critical loads in a distribution system after an earthquake. The proposed method employs Markov Decision Process to find the optimal restoration scheme based on the Probability of Failure of critical structures determined by using the Peak Ground Acceleration values recorded by observatories and earthquake research centers during earthquakes.Comment: Presented in ISGT 201

MDP based Decision Support for Earthquake Damaged Distribution System Restoration

As the society becomes more dependent on the presence of electricity, the resilience of the power systems gains more importance. This paper develops a decision support method for distribution system operators to restore electricity after an earthquake to the maximum number of customers in the minimum expected duration. The proposed method employs Markov Decision Process (MDP) to determine the optimal restoration scheme. In order to determine the probability of the field component damage due to the earthquake, the Probability of Failure ($P_f$) of structures are calculated using the Peak Ground Acceleration (PGA) values recorded by observatories and earthquake research centers during the earthquake

Temporal logic model predictive control

This paper proposes an optimal control strategy for a discrete-time linear system constrained to satisfy a temporal logic specification over a set of linear predicates in its state variables. The cost is a quadratic function that penalizes the distance from desired state and control trajectories. The specification is a formula of syntactically co-safe Linear Temporal Logic (scLTL), which can be satisfied in finite time. To incorporate dynamic environments, it is assumed that the reference trajectories are only available over a finite horizon and a model predictive control (MPC) approach is employed. The MPC controller solves a set of convex optimization problems guided by the specification and subject to progress constraints. The constraints ensure that progress is made towards the satisfaction of the formula with guaranteed satisfaction by the closed-loop trajectory. The algorithms proposed in this paper were implemented as a software package that is available for download. Illustrative case studies are included

Language-guided controller synthesis for linear systems

This paper considers the problem of controlling discrete-time linear systems from specifications given as formulas of syntactically co-safe linear temporal logic over linear predicates in the state variables. A systematic procedure is developed for the automatic computation of sets of initial states and feedback controllers such that all the resulting trajectories of the closed-loop system satisfy the given specifications. The procedure is based on the iterative construction and refinement of an automaton that enforces the satisfaction of the formula. Linear programming based approaches are proposed to compute the polytope-to-polytope controllers that label the transitions of the automaton. Extensions to discrete-time piecewise affine systems and specifications given as formulas of full linear temporal logic are included. The algorithms developed in this paper were implemented as a software package that is available for download. Their application and effectiveness are demonstrated for several case studies