We address the problem of robust permissive controller synthesis for robots operating under uncertain dynamics, modeled as Interval Markov Decision Processes (IMDPs). IMDPs generalize standard MDPs by allowing transition probabilities to vary within intervals, capturing epistemic uncertainty from sensing noise, actuation imprecision, and coarse system abstractions-common in robotics. Traditional controller synthesis typically yields a single deterministic strategy, limiting adaptability. In contrast, permissive controllers (multi-strategies) allow multiple actions per state, enabling runtime flexibility and resilience. However, prior work on permissive controller synthesis generally assumes exact transition probabilities, which is unrealistic in many robotic applications. We present the first framework for robust permissive controller synthesis on IMDPs, guaranteeing that all strategies compliant with the synthesized multi-strategy satisfy reachability or reward-based specifications under all admissible transitions. We formulate the problem as mixed-integer linear programs (MILPs) and propose two encodings: a baseline vertex-enumeration method and a scalable duality-based method that avoids explicit enumeration. Experiments on four benchmark domains show that both methods synthesize robust, maximally permissive controllers and scale to large IMDPs with up to hundreds of thousands of states.

Attitude stabilization of unmanned aerial vehicles in uncertain environments presents significant challenges due to nonlinear dynamics, parameter variations, and sensor limitations. This paper presents a comparative study of $\mathcal{H}_\infty$ and classical PID controllers for multi-rotor attitude regulation in the presence of wind disturbances and gyroscope noise. The flight dynamics are modeled using a linear parameter-varying (LPV) framework, where nonlinearities and parameter variations are systematically represented as structured uncertainties within a linear fractional transformation formulation. A robust controller based on $\mathcal{H}_\infty$ formulation is designed using only gyroscope measurements to ensure guaranteed performance bounds. Nonlinear simulation results demonstrate the effectiveness of the robust controllers compared to classical PID control, showing significant improvement in attitude regulation under severe wind disturbances.

In the game-theoretic approach to controller synthesis, we model the interaction between a system to be controlled and its environment as a game between these entities, and we seek an appropriate (e.g., winning or optimal) strategy for the system. This strategy then serves as a formal blueprint for a real-world controller. A common belief is that simple (e.g., using limited memory) strategies are better: corresponding controllers are easier to conceive and understand, and cheaper to produce and maintain. This invited contribution focuses on the complexity of strategies in a variety of synthesis contexts. We discuss recent results concerning memory and randomness, and take a brief look at what lies beyond our traditional notions of complexity for strategies.

Controller synthesis is a theoretical approach to the systematic design of discrete event systems. It constructs a controller to provide feedback and control to the system, ensuring it meets specified control specifications. Traditional controller synthesis methods often use formal languages to describe control specifications and are mainly oriented towards single-agent and non-probabilistic systems. With the increasing complexity of systems, the control requirements that need to be satisfied also become more complex. Based on this, this paper proposes a controller synthesis method for semi-cooperative semi-competitive multi-agent probabilistic discrete event systems to solve the controller synthesis problem based on temporal logic specifications. The controller can ensure the satisfaction of specifications to a certain extent. The specification is given in the form of a linear temporal logic formula. This paper designs a controller synthesis algorithm that combines probabilistic model checking. Finally, the effectiveness of this method is verified through a case study.

The inherent uncertainty of dynamic environments poses significant challenges for modeling robot behavior, particularly in tasks such as collision avoidance. This paper presents an online controller synthesis framework tailored for robots equipped with deep learning-based perception components, with a focus on addressing distribution shifts. Our approach integrates periodic monitoring and repair mechanisms for the deep neural network perception component, followed by uncertainty reassessment. These uncertainty evaluations are injected into a parametric discrete-time markov chain, enabling the synthesis of robust controllers via probabilistic model checking. To ensure high system availability during the repair process, we propose a dual-component configuration that seamlessly transitions between operational states. Through a case study on robot collision avoidance, we demonstrate the efficacy of our method, showcasing substantial performance improvements over baseline approaches. This work provides a comprehensive and scalable solution for enhancing the safety and reliability of autonomous systems operating in uncertain environments.

The central element of the paper is a (novel) algorithm that utilizes a convex optimization approach (the so-called System Level Synthesis approach, SLS) for synthesizing LQR controllers using estimated dynamics models. The SLS approach allows for an analysis of how the error in the matrix estimation affects the regret of the LQR controller. Using this controller synthesis, upper bounds on the estimation error of the dynamics matrices as well as upper and lower bounds for the expected loss are provided. The method is compared to existing approaches on a benchmark system. This computational study shows a comparable performance of all methods, with the presented method giving the nicest theoretical guarantees (e.g.

This paper considers the problem of controller synthesis of signal temporal logic (STL) specifications for large-scale multi-agent systems, where the agents are dynamically coupled and subject to collaborative tasks. A compositional framework based on continuous-time assume-guarantee contracts is developed to break the complex and large synthesis problem into subproblems of manageable sizes. We first show how to formulate the collaborative STL tasks as assume-guarantee contracts by leveraging the idea of funnel-based control. The concept of contracts is used to establish our compositionality result, which allows us to guarantee the satisfaction of a global contract by the multi-agent system when all agents satisfy their local contracts. Then, a closed-form continuous-time feedback controller is designed to enforce local contracts over the agents in a distributed manner, which further guarantees the global task satisfaction based on the compositionality result. Finally, the effectiveness of our results is demonstrated by two numerical examples.

Robots are used increasingly often in safety-critical scenarios, such as robotic surgery or human-robot interaction. To ensure stringent performance criteria, formal controller synthesis is a promising direction to guarantee that robots behave as desired. However, formally ensured properties only transfer to the real robot when the model is appropriate. We address this problem by combining the identification of a reachset-conformant model with controller synthesis. Since the reachset-conformant model contains all the measured behaviors of the real robot, the safety properties of the model transfer to the real robot. The transferability is demonstrated by experiments on a real robot, for which we synthesize tracking controllers.

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

Controller synthesis is in essence a case of model-based planning for non-deterministic environments in which plans (actually ''strategies'') are meant to preserve system goals indefinitely. In the case of supervisory control environments are specified as the parallel composition of state machines and valid strategies are required to be ''non-blocking'' (i.e., always enabling the environment to reach certain marked states) in addition to safe (i.e., keep the system within a safe zone). Recently, On-the-fly Directed Controller Synthesis techniques were proposed to avoid the exploration of the entire -and exponentially large-environment space, at the cost of non-maximal permissiveness, to either find a strategy or conclude that there is none. The incremental exploration of the plant is currently guided by a domain-independent human-designed heuristic. In this work, we propose a new method for obtaining heuristics based on Reinforcement Learning (RL). The synthesis algorithm is thus framed as an RL task with an unbounded action space and a modified version of DQN is used. With a simple and general set of features that abstracts both states and actions, we show that it is possible to learn heuristics on small versions of a problem that generalize to the larger instances, effectively doing zero-shot policy transfer. Our agents learn from scratch in a highly partially observable RL task and outperform the existing heuristic overall, in instances unseen during training.