Eric S. Kim

A learning based approach to control synthesis of Markov decision processes for linear temporal logic specifications

We propose to synthesize a control policy for a Markov decision process (MDP) such that the resulting traces of the MDP satisfy a linear temporal logic (LTL) property. We construct a product MDP that incorporates a deterministic Rabin automaton generated from the desired LTL property. The reward function of the product MDP is defined from the acceptance condition of the Rabin automaton. This construction allows us to apply techniques from learning theory to the problem of synthesis for LTL specifications even when the transition probabilities are not known a priori. We prove that our method is guaranteed to find a controller that satisfies the LTL property with probability one if such a policy exists, and we suggest empirically that our method produces reasonable control strategies even when the LTL property cannot be satisfied with probability one.

Compositional controller synthesis for vehicular traffic networks

We tackle the issue of scalability when synthesizing controllers for large signalized vehicular traffic networks with linear temporal logic specifications. Traffic networks lend themselves to a compositional synthesis approach because they are naturally decomposed into sub-networks. However, naïvely synthesizing controllers for individual sub-networks and interconnecting them can violate the specifications on the monolithic network. By exploiting notions of supply and demand in our system dynamics, we construct contracts between sub-networks that guarantee the soundness of the overall synthesized controller. The resulting decentralized control architecture consists of controllers that rely only on local state information.

Directed Specifications and Assumption Mining for Monotone Dynamical Systems

Given a dynamical system and a specification, assumption mining is the problem of identifying the set of admissible disturbance signals and initial states that generate trajectories satisfying the specification. We first introduce the notion of a directed specification, which describes either upper or lower sets in a partially ordered signal space, and show that this notion encompasses an expressive temporal logic fragment. We next show that the order preserving nature of monotone dynamical systems makes them amenable to a systematic form of assumption mining that checks numerical simulations of system trajectories against directed specifications. The assumption set is then located with a multidimensional bisection method that converges to the boundary from above and below. Typical objectives in vehicular traffic control, such as avoiding or clearing congestion, are directed specifications. In an application to a freeway flow model with monotone dynamics, we identify the set of vehicular demand profiles that satisfy a specification that congestion be intermittent.

Sudden noise source localization system for intelligent automobile application with acoustic sensors

This paper suggests an automotive application for finding direction of sudden noise source in driving situation. The system applies sound source localization algorithm using microphone array sensor and finds the direction of the abrupt abnormal noise sources. Representative experimental results demonstrate its feasibility as new safety car electronic component.

Offset optimization for a network of signalized intersections via semidefinite relaxation

We consider the problem of coordinating the traffic signals in a network of signalized intersections to reduce accumulated queues of vehicles throughout the network. We assume that all signals have a common cycle time and a fixed actuation plan, and we propose an approach for optimizing the relative phase offsets. Unlike existing techniques, our approach accommodates networks with arbitrary topology and scales well. This is accomplished by proposing a sinusoidal approximation of the queueing processes in the network, which enables a semidefinite relaxation of the offset optimization problem that is easily solved. We demonstrate the result in a case study of a traffic network in Arcadia, California.

Constructing Control System Abstractions from Modular Components

This paper tackles the problem of constructing finite abstractions for formal controller synthesis with high dimensional systems. We develop a theory of abstraction for discrete time nonlinear systems that are equipped with variables acting as interfaces for other systems. Systems interact via an interconnection map which constrains the value of system interface variables. An abstraction of a high dimensional interconnected system is obtained by composing subsystem abstractions with an abstraction of the interconnection. System abstractions are modular in the sense that they can be rearranged, substituted, or reused in configurations that were unknown during the time of abstraction. Constructing the abstraction of the interconnection map can become computationally infeasible when there are many systems. We introduce intermediate variables which break the interconnection and the abstraction procedure apart into smaller problems. Examples showcase the abstraction of a 24-dimensional system through the composition of 24 individual systems, and the synthesis of a controller for a 6-dimensional system with a consensus objective.

Maximal persistent surveillance under safety constraints

This paper presents a method for the design of time-invariant memoryless control policies for robots tasked with persistent surveillance of an area in which there are forbidden regions. We model each robot as a controlled Markov chain whose state comprises its position on a finite two-dimensional lattice and the direction of motion. The goal is to find the minimum number of robots and an associated time-invariant memoryless control policy that guarantees that the largest number of states are persistently surveilled without ever visiting a forbidden state. We propose a design method that relies on a finitely parametrized convex program inspired by entropy maximization principles. For clarity of exposition, we focus on simple dynamics and state/control spaces, however the proposed methodology can be extended to more general cases. Numerical examples are provided.

Major Computational Breakthroughs in the Synthesis of Symbolic Controllers via Decomposed Algorithms

ACM Reference Format: Eric S. Kim, Murat Arcak and Mahmoud Khaled, Majid Zamani. 2018. Poster: Major Computational Breakthroughs in the Synthesis of Symbolic Controllers via Decomposed Algorithms. In HSCC ’18: 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week), April 11–13, 2018, Porto, Portugal. ACM, New York, NY, USA, 3 pages. https://doi.org/10.1145/3178126.3187005

Offset optimization of signalized intersections via the Burer-Monteiro method

This paper tackles the offset optimization problem which seeks to coordinate traffic signals in a large traffic network. By assuming that all signals have a common cycle time and that the arrival/departure rates at each intersection can be approximated by sinusoids, the original non-convex offset optimization problem can be relaxed into a semidefinite program (SDP). SDP solvers unfortunately run out of memory for larger networks with thousands of intersections. The Burer-Monteiro (BM) method [1] for solving large SDPs avoids conic constraints and solves a lower dimensional problem but is non-convex. A synthetic New York City example with 1771 intersections showcases the scalability of the BM method. Another example involving 420 intersections in Los Angeles demonstrates that the BM method recovers optimal solutions of the SDP. Moreover, a detailed microsimulation of the Los Angeles network shows that the optimized offsets result in reduced delay time and smaller queues.

Symbolic control design for monotone systems with directed specifications

Abstract We study the control of monotone systems when the objective is to maintain trajectories in a directed set (that is, either upper or lower set) within a signal space. We define the notion of a directed alternating simulation relation and show how it can be used to tackle common bottlenecks in abstraction-based controller synthesis. First, we develop sparse abstractions to speed up the controller synthesis procedure by reducing the number of transitions. Next, we enable a compositional synthesis approach by employing directed assume–guarantee contracts between systems. In a vehicle traffic network example, we synthesize an intersection signal controller while dramatically reducing runtime and memory requirements compared to previous approaches.