Fixed-Time Convergent Control Barrier Functions for Coupled Multi-Agent Systems Under STL Tasks

This paper presents a control strategy based on a new notion of time-varying fixed-time convergent control barrier functions (TFCBFs) for a class of coupled multi-agent systems under signal temporal logic (STL) tasks. In this framework, each agent is assigned a local STL task regradless of the tasks of other agents. Each task may be dependent on the behavior of other agents which may cause conflicts on the satisfaction of all tasks. Our approach finds a robust solution to guarantee the fixed-time satisfaction of STL tasks in a least violating way and independent of the agents' initial condition in the presence of undesired violation effects of the neighbor agents. Particularly, the robust performance of the task satisfactions can be adjusted in a user-specified way.Comment: Accepted in ECC 202

Communication-Constrained STL Task Decomposition through Convex Optimization

In this work, we propose a method to decompose signal temporal logic (STL) tasks for multi-agent systems subject to constraints imposed by the communication graph. Specifically, we propose to decompose tasks defined over multiple agents which require multi-hop communication, by a set of sub-tasks defined over the states of agents with 1-hop distance over the communication graph. To this end, we parameterize the predicates of the tasks to be decomposed as suitable hyper-rectangles. Then, we show that by solving a constrained convex optimization, optimal parameters maximising the volume of the predicate's super-level sets can be computed for the decomposed tasks. In addition, we provide a formal definition of conflicting conjunctions of tasks for the considered STL fragment and a formal procedure to exclude such conjunctions from the solution set of possible decompositions. The proposed approach is demonstrated through simulations.Comment: This paper is accepted at 2024 American Control Conference (ACC

Multi-Agent Robust Control Synthesis from Global Temporal Logic Tasks

This paper focuses on the heterogeneous multi-agent control problem under global temporal logic tasks. We define a specification language, called extended capacity temporal logic (ECaTL), to describe the required global tasks, including the number of times that a local or coupled signal temporal logic (STL) task needs to be satisfied and the synchronous requirements on task satisfaction. The robustness measure for ECaTL is formally designed. In particular, the robustness for synchronous tasks is evaluated from both the temporal and spatial perspectives. Mixed-integer linear constraints are designed to encode ECaTL specifications, and a two-step optimization framework is further proposed to realize task-satisfied motion planning with high spatial robustness and synchronicity. Simulations are conducted to demonstrate the expressivity of ECaTL and the efficiency of the proposed control synthesis approach.Comment: 7 pages, 3 figure

Formal Synthesis of Controllers for Safety-Critical Autonomous Systems: Developments and Challenges

In recent years, formal methods have been extensively used in the design of autonomous systems. By employing mathematically rigorous techniques, formal methods can provide fully automated reasoning processes with provable safety guarantees for complex dynamic systems with intricate interactions between continuous dynamics and discrete logics. This paper provides a comprehensive review of formal controller synthesis techniques for safety-critical autonomous systems. Specifically, we categorize the formal control synthesis problem based on diverse system models, encompassing deterministic, non-deterministic, and stochastic, and various formal safety-critical specifications involving logic, real-time, and real-valued domains. The review covers fundamental formal control synthesis techniques, including abstraction-based approaches and abstraction-free methods. We explore the integration of data-driven synthesis approaches in formal control synthesis. Furthermore, we review formal techniques tailored for multi-agent systems (MAS), with a specific focus on various approaches to address the scalability challenges in large-scale systems. Finally, we discuss some recent trends and highlight research challenges in this area

Signal Temporal Logic Control Synthesis among Uncontrollable Dynamic Agents with Conformal Prediction

The control of dynamical systems under temporal logic specifications among uncontrollable dynamic agents is challenging due to the agents' a-priori unknown behavior. Existing works have considered the problem where either all agents are controllable, the agent models are deterministic and known, or no safety guarantees are provided. We propose a predictive control synthesis framework that guarantees, with high probability, the satisfaction of signal temporal logic (STL) tasks that are defined over the system and uncontrollable stochastic agents. We use trajectory predictors and conformal prediction to construct probabilistic prediction regions for each uncontrollable agent that are valid over multiple future time steps. Specifically, we reduce conservatism and increase data efficiency compared to existing works by constructing a normalized prediction region over all agents and time steps. We then formulate a worst-case mixed integer program (MIP) that accounts for all agent realizations within the prediction region to obtain control inputs that provably guarantee task satisfaction with high probability. To efficiently solve this MIP, we propose an equivalent MIP program based on KKT conditions of the original one. We illustrate our control synthesis framework on two case studies

Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet

In this paper, we consider the problem of learning a neural network controller for a system required to satisfy a Signal Temporal Logic (STL) specification. We exploit STL quantitative semantics to define a notion of robust satisfaction. Guaranteeing the correctness of a neural network controller, i.e., ensuring the satisfaction of the specification by the controlled system, is a difficult problem that received a lot of attention recently. We provide a general procedure to construct a set of trainable High Order Control Barrier Functions (HOCBFs) enforcing the satisfaction of formulas in a fragment of STL. We use the BarrierNet, implemented by a differentiable Quadratic Program (dQP) with HOCBF constraints, as the last layer of the neural network controller, to guarantee the satisfaction of the STL formulas. We train the HOCBFs together with other neural network parameters to further improve the robustness of the controller. Simulation results demonstrate that our approach ensures satisfaction and outperforms existing algorithms.Comment: Submitted to CDC 202

Resilience for satisfaction of temporal logic specifications by dynamical systems

The increased adoption and deployment of cyber-physical systems in critical infrastructure in recent years have led to challenging questions about safety and reliability. These systems usually operate in uncertain environments and are required to satisfy a broad spectrum of specifications. Thus, automated tools are necessary to alleviate the need for manual design and proof of their correct behaviors. This thesis studies mathematical and computational frameworks to design correct and optimal control strategies for discrete-time and continuous-time systems with temporal and spatial specifications. Signal Temporal Logic (STL) is employed as a rich and expressive language to impose temporal constraints and deadlines on system performance. The first part of the thesis introduces a novel quantitative semantics for STL that improves the evaluation of temporal logic specifications. Furthermore, an extension of STL, called Weighted Signal Temporal Logic (wSTL), is defined in order to formalize satisfaction priorities of multiple specifications and time preferences in a high-level specification. Learning-based frameworks are proposed to infer quantitative semantics, and satisfaction priorities and preferences from data. The second part develops optimization frameworks to determine control strategies enforcing the satisfaction of wSTL specifications by different classes of systems. Mixed-integer programming and gradient-based optimization techniques are studied to solve the control synthesis problem. Further evaluation and optimization algorithms are presented based on Control Barrier Functions to guarantee continuous-time satisfaction of safety-critical specifications in a system. The third part of this thesis focuses on utilizing STL to express spatio-temporal specifications that are widely used in networks of locally interacting dynamical systems. Machine learning techniques are used to derive spatio-temporal quantitative semantics, which is employed in automated frameworks for evaluation and synthesis of complex spatial and temporal properties. Case studies illustrating the synthesis of spatio-temporal patterns in biological cell networks are presented