A hierarchical reinforcement learning method for persistent time-sensitive tasks

Reinforcement learning has been applied to many interesting problems such as the famous TD-gammon and the inverted helicopter flight. However, little effort has been put into developing methods to learn policies for complex persistent tasks and tasks that are time-sensitive. In this paper, we take a step towards solving this problem by using signal temporal logic (STL) as task specification, and taking advantage of the temporal abstraction feature that the options framework provide. We show via simulation that a relatively easy to implement algorithm that combines STL and options can learn a satisfactory policy with a small number of training cases

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

Negotiating the Probabilistic Satisfaction of Temporal Logic Motion Specifications

We propose a human-supervised control synthesis method for a stochastic Dubins vehicle such that the probability of satisfying a specification given as a formula in a fragment of Probabilistic Computational Tree Logic (PCTL) over a set of environmental properties is maximized. Under some mild assumptions, we construct a finite approximation for the motion of the vehicle in the form of a tree-structured Markov Decision Process (MDP). We introduce an efficient algorithm, which exploits the tree structure of the MDP, for synthesizing a control policy that maximizes the probability of satisfaction. For the proposed PCTL fragment, we define the specification update rules that guarantee the increase (or decrease) of the satisfaction probability. We introduce an incremental algorithm for synthesizing an updated MDP control policy that reuses the initial solution. The initial specification can be updated, using the rules, until the supervisor is satisfied with both the updated specification and the corresponding satisfaction probability. We propose an offline and an online application of this method.Comment: 9 pages, 4 figures; The results in this paper were presented without proofs in IEEE/RSJ International Conference on Intelligent Robots and Systems November 3-7, 2013 at Tokyo Big Sight, Japa

Control with probabilistic signal temporal logic

Autonomous agents often operate in uncertain environments where their decisions are made based on beliefs over states of targets. We are interested in controller synthesis for complex tasks defined over belief spaces. Designing such controllers is challenging due to computational complexity and the lack of expressivity of existing specification languages. In this paper, we propose a probabilistic extension to signal temporal logic (STL) that expresses tasks over continuous belief spaces. We present an efficient synthesis algorithm to find a control input that maximises the probability of satisfying a given task. We validate our algorithm through simulations of an unmanned aerial vehicle deployed for surveillance and search missions

Distributed Robust Set-Invariance for Interconnected Linear Systems

We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invariance-inducing control policy. Illustrative examples, including one on platooning, are presented.Comment: 8 Pages. Submitted to American Control Conference (ACC), 201

Control with Probabilistic Signal Temporal Logic

Autonomous agents often operate in uncertain environments where their decisions are made based on beliefs over states of targets. We are interested in controller synthesis for complex tasks defined over belief spaces. Designing such controllers is challenging due to computational complexity and the lack of expressivity of existing specification languages. In this paper, we propose a probabilistic extension to signal temporal logic (STL) that expresses tasks over continuous belief spaces. We present an efficient synthesis algorithm to find a control input that maximises the probability of satisfying a given task. We validate our algorithm through simulations of an unmanned aerial vehicle deployed for surveillance and search missions.Comment: 7 pages, submitted to the 2016 American Control Conference (ACC 2016) on September, 30, 2015 (under review

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

Automata guided hierarchical reinforcement learning for zero-shot skill composition

An obstacle that prevents the wide adoption of (deep) reinforcement learning (RL) in control systems is its need for a large amount of interactions with the environment in order to master a skill. The learned skill usually generalizes poorly across domains and re-training is often necessary when presented with a new task. We present a framework that combines methods in formal methods with hierarchical reinforcement learning (HRL). The set of techniques we provide allows for convenient specification of tasks with complex logic, learn hierarchical policies (meta-controller and low-level controllers) with well-defined intrinsic rewards using any RL methods and is able to construct new skills from existing ones without additional learning. We evaluate the proposed methods in a simple grid world simulation as well as simulation on a Baxter robot