1,517 research outputs found
Optimal Control of MDPs with Temporal Logic Constraints
In this paper, we focus on formal synthesis of control policies for finite
Markov decision processes with non-negative real-valued costs. We develop an
algorithm to automatically generate a policy that guarantees the satisfaction
of a correctness specification expressed as a formula of Linear Temporal Logic,
while at the same time minimizing the expected average cost between two
consecutive satisfactions of a desired property. The existing solutions to this
problem are sub-optimal. By leveraging ideas from automata-based model checking
and game theory, we provide an optimal solution. We demonstrate the approach on
an illustrative example.Comment: Technical report accompanying the CDC 2013 pape
Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints
We consider synthesis of control policies that maximize the probability of
satisfying given temporal logic specifications in unknown, stochastic
environments. We model the interaction between the system and its environment
as a Markov decision process (MDP) with initially unknown transition
probabilities. The solution we develop builds on the so-called model-based
probably approximately correct Markov decision process (PAC-MDP) methodology.
The algorithm attains an -approximately optimal policy with
probability using samples (i.e. observations), time and space that
grow polynomially with the size of the MDP, the size of the automaton
expressing the temporal logic specification, ,
and a finite time horizon. In this approach, the system
maintains a model of the initially unknown MDP, and constructs a product MDP
based on its learned model and the specification automaton that expresses the
temporal logic constraints. During execution, the policy is iteratively updated
using observation of the transitions taken by the system. The iteration
terminates in finitely many steps. With high probability, the resulting policy
is such that, for any state, the difference between the probability of
satisfying the specification under this policy and the optimal one is within a
predefined bound.Comment: 9 pages, 5 figures, Accepted by 2014 Robotics: Science and Systems
(RSS
Toward Specification-Guided Active Mars Exploration for Cooperative Robot Teams
As a step towards achieving autonomy in space exploration missions, we consider a cooperative robotics system consisting of a copter and a rover. The goal of the copter is to explore an unknown environment so as to maximize knowledge about a science mission expressed in linear temporal logic that is to be executed by the rover. We model environmental uncertainty as a belief space Markov decision process and formulate the problem as a two-step stochastic dynamic program that we solve in a way that leverages the decomposed nature of the overall system. We demonstrate in simulations that the robot team makes intelligent decisions in the face of uncertainty
Deception in Optimal Control
In this paper, we consider an adversarial scenario where one agent seeks to
achieve an objective and its adversary seeks to learn the agent's intentions
and prevent the agent from achieving its objective. The agent has an incentive
to try to deceive the adversary about its intentions, while at the same time
working to achieve its objective. The primary contribution of this paper is to
introduce a mathematically rigorous framework for the notion of deception
within the context of optimal control. The central notion introduced in the
paper is that of a belief-induced reward: a reward dependent not only on the
agent's state and action, but also adversary's beliefs. Design of an optimal
deceptive strategy then becomes a question of optimal control design on the
product of the agent's state space and the adversary's belief space. The
proposed framework allows for deception to be defined in an arbitrary control
system endowed with a reward function, as well as with additional
specifications limiting the agent's control policy. In addition to defining
deception, we discuss design of optimally deceptive strategies under
uncertainties in agent's knowledge about the adversary's learning process. In
the latter part of the paper, we focus on a setting where the agent's behavior
is governed by a Markov decision process, and show that the design of optimally
deceptive strategies under lack of knowledge about the adversary naturally
reduces to previously discussed problems in control design on partially
observable or uncertain Markov decision processes. Finally, we present two
examples of deceptive strategies: a "cops and robbers" scenario and an example
where an agent may use camouflage while moving. We show that optimally
deceptive strategies in such examples follow the intuitive idea of how to
deceive an adversary in the above settings
- …