We present a method to find an optimal policy with respect to a reward function for a discounted Markov decision process under general linear temporal logic (LTL) specifications. Previous work has either focused on maximizing a cumulative reward objective under finite-duration tasks, specified by syntactically co-safe LTL, or maximizing an average reward for persistent (e.g., surveillance) tasks. This paper extends and generalizes these results by introducing a pair of occupancy measures to express the LTL satisfaction objective and the expected discounted reward objective, respectively. These occupancy measures are then connected to a single policy via a novel reduction resulting in a mixed integer linear program whose solution provides an optimal policy. Our formulation can also be extended to include additional constraints with respect to secondary reward functions. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.
This paper discusses the functional stability of closed-loop Markov Chains under optimal policies resulting from a discounted optimality criterion, forming Markov Decision Processes (MDPs). We investigate the stability of MDPs in the sense of probability measures (densities) underlying the state distributions and extend the dissipativity theory of Economic Model Predictive Control in order to characterize the MDP stability. This theory requires a so-called storage function satisfying a dissipativity inequality. In the probability measures space and for the discounted setting, we introduce new …
Boston University（波士顿大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）
In this paper, we propose a learning-based framework to simultaneously learn the communication and distributed control policies for a heterogeneous multi-agent system (MAS) under complex mission requirements from Capability Temporal Logic plus (CaTL+) specifications. Both policies are trained, implemented, and deployed using a novel neural network model called CatlNet. Taking advantage of the robustness measure of CaTL+, we train CatlNet centrally to maximize it where network parameters are shared among all agents, allowing CatlNet to scale to large teams easily. CatlNet can then be deployed d…
This paper investigates a class of optimal control problems associated with Markov processes with local state information. The decision-maker has only local access to a subset of a state vector information as often encountered in decentralized control problems in multi-agent systems. Under this information structure, part of the state vector cannot be observed. We leverage ab initio principles and find a new form of Bellman equations to characterize the optimal policies of the control problem under local information structures. The dynamic programming solutions feature a mixture of dynamics as…
Characterization and Computation of Feedback Nash Equilibria in Scalar Discounted N-Player Linear Quadratic Games
IMT School for Advanced Studies Lucca（卢卡高等研究院）；Research Unit DYSCO (Dynamical Systems, Control, and Optimization) at IMT School for Advanced Studies Lucca（卢卡高等研究院动态系统、控制与优化研究单元）
This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against $ω$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called \emph{control sub-barrier certificates} of subsystems, which are used to composition…
IMT School for Advanced Studies Lucca（卢卡IMT高等研究院）；Gran Sasso Science Institute - GSSI（格兰萨索科学研究院（GSSI））
In this paper, we consider solving discounted Markov Decision Processes (MDPs) under the constraint that the resulting policy is stabilizing. In practice MDPs are solved based on some form of policy approximation. We will leverage recent results proposing to use Model Predictive Control (MPC) as a structured policy in the context of Reinforcement Learning to make it possible to introduce stability requirements directly inside the MPC-based policy. This will restrict the solution of the MDP to stabilizing policies by construction. The stability theory for MPC is most mature for the undiscounted…
This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. The search for policies is limited to the space of finite state controllers, which leads to a tractable approach to determine policies. We relate the satisfaction …
Compositional Policy Learning in Stochastic Control Systems with Formal Guarantees
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所（ISTA））；Massachusetts Institute of Technology（麻省理工学院）；The Pennsylvania State University（宾夕法尼亚州立大学）
In this paper, we use concepts from supervisory control theory of discrete event systems to propose a method to learn optimal control policies for a finite-state Markov Decision Process (MDP) in which (only) certain sequences of actions are deemed unsafe (respectively safe). We assume that the set of action sequences that are deemed unsafe and/or safe are given in terms of a finite-state automaton; and propose a supervisor that disables a subset of actions at every state of the MDP so that the constraints on action sequence are satisfied. Then we present a version of the Q-learning algorithm f…
In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of control policies by using a notation of control barrier functions without requiring any knowledge of the estimation accuracy. Our goal is to synthesize an offline control policy providing (potentially maximizing) a lower bound on the probability that the trajectories of the partially observed jump-diffusion system satisfy some complex specifications expressed by…
Decision-making policies for agents are often synthesized with the constraint that a formal specification of behaviour is satisfied. Here we focus on infinite-horizon properties. On the one hand, Linear Temporal Logic (LTL) is a popular example of a formalism for qualitative specifications. On the other hand, Steady-State Policy Synthesis (SSPS) has recently received considerable attention as it provides a more quantitative and more behavioural perspective on specifications, in terms of the frequency with which states are visited. Finally, rewards provide a classic framework for quantitative p…
