arXiv subjects

Zhiyong Sun

Publications and source records attributed to Zhiyong Sun.

At least 19 recordsLinked to original sources

arXiv2026

Opinion-Guided Layered Strategies for Decentralized Coordination

Autonomous agents increasingly interact with other independent agents, and such interactions typically admit multiple joint behaviors. When two agents prefer different ones, their independent strategies may be mutually incompatible and fail to reach a coordinated outcome; when they are identical, neither can differentiate its role when needed. Ideally, an agent should coordinate with any agent it encounters, regardless of which admissible joint behavior that agent aims to realize. We therefore propose a new form of strategy, the opinion-guided strategy, which keeps all the admissible joint behaviors available and postpones the selection to execution time, when the other agent's behavior reveals which one to realize. To realize this, nonlinear opinion dynamics are leveraged in a layered realization to guide the agent to a common admissible joint behavior in response to the other agent's evolving behavior, even without communication. We formally establish the conditions under which the strategy remains robust to every preference the other agent may hold. This robustness has an important implication: two agents running identical strategies can break symmetry when needed, a capability that conventional strategies lack. Three case studies across different applications show that the opinion-guided strategy coordinates with every randomly encountered agent, as long as it is willing to realize one of the admissible joint behaviors. One of them corresponds to a general-sum game: unlike conventional approaches devoted to finding a unique Nash equilibrium in advance, the opinion-guided strategy keeps every equilibrium open and guarantees the agents reach one, decided by their runtime interaction.

cs.MA↗

arXiv2026

Characterizing Robustness in Nonlinear Optimal Control: From Stability to Optimality

In nonlinear optimal control, uncertainties in system dynamics may affect not only closed-loop stability but also the achieved optimality properties of the resulting solutions. This paper develops a systematic robustness analysis for nonlinear optimal control beyond the conventional focus on stability in robust control theory. First, we demonstrate that the optimal value function retains its Lyapunov property under a quantifiable criterion, thereby guaranteeing the preservation of closed-loop stability. Building upon this foundation, we establish explicit characterizations for optimality deviations induced by model mismatch in both closed-loop performance and optimal controllers, and further reveal their consistency with classical linear-quadratic regulator (LQR) results. In addition, the robustness analysis admits a unified computational formulation that gives rise to an iterative scheme with guaranteed convergence, enabling quantitative assessment of optimality robustness in nonlinear control systems. Numerical examples validate the theoretical analysis.

math.OC↗

arXiv2026

Unraveling tensor structures in correct-by-design controller synthesis

Formal safety guarantees on the synthesis of controllers for stochastic systems can be obtained using correct-by-design approaches. These approaches often use abstractions as finite-state Markov Decision Processes. As the state space of these MDPs grows, the curse of dimensionality makes the computational and memory cost of the probabilistic guarantees, quantified with dynamic programming, scale exponentially. In this work, we leverage decoupled dynamics and unravel, via dynamic programming operations, a tree structure in the Canonical Polyadic Decomposition (CPD) of the value functions. For discrete-time stochastic systems with syntactically co-safe linear temporal logic (scLTL) specifications, we provide provable probabilistic safety guarantees and significantly alleviate the computational burden. We provide an initial validation of the theoretical results on several typical case studies and showcase that the uncovered tree structure enables efficient reductions in the computational burden.

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arXiv2026

Correct-by-Design Control Synthesis of Stochastic Multi-agent Systems: a Robust Tensor-based Solution

Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that deliver control strategies with provable lower bounds on temporal-logic satisfaction, quantified via approximate stochastic simulation relations. Exploiting decoupled dynamics, we reveal a Canonical Polyadic Decomposition tensor structure in value functions that makes dynamic programming scalable. The proposed method provides correct-by-design probabilistic guarantees for temporal logic specifications. We validate our results on continuous-state linear stochastic systems.

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arXiv2026

Unifying Controller Design for Stabilizing Nonlinear Systems with Norm-Bounded Control Inputs

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag's universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system.

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arXiv2026

Risk-Aware Autonomous Driving with Linear Temporal Logic Specifications

Human drivers naturally balance the risks of different concerns while driving, including traffic rule violations, minor accidents, and fatalities. However, achieving the same behavior in autonomous driving systems remains an open problem. This paper extends a risk metric that has been verified in human-like driving studies to encompass more complex driving scenarios specified by linear temporal logic (LTL) that go beyond just collision risks. This extension incorporates the timing and severity of events into LTL specifications, thereby reflecting a human-like risk awareness. Without sacrificing expressivity for traffic rules, we adopt LTL specifications composed of safety and co-safety formulas, allowing the control synthesis problem to be reformulated as a reachability problem. By leveraging occupation measures, we further formulate a linear programming (LP) problem for this LTL-based risk metric. Consequently, the synthesized policy balances different types of driving risks, including both collision risks and traffic rule violations. The effectiveness of the proposed approach is validated by three typical traffic scenarios in Carla simulator.

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arXiv2026

Deep Koopman Iterative Learning and Stability-Guaranteed Control for Unknown Nonlinear Time-Varying Systems

This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying systems, upon which a robust controller is designed to ensure that the resulting closed-loop system is input-to-state stable with respect to the Koopman approximation error. The error of the lifted system model learned through the Koopman-based method increases over time due to the time-varying nature of the nonlinear time-varying system. To address this issue, an online iterative update scheme is incorporated into the learning process to update the lifted system model, aligning it more precisely with the time-varying nonlinear system by integrating the updated data and discarding the outdated data. A necessary condition for the feasibility of the proposed iterative learning method is derived. In order to reduce unnecessary system updates while ensuring the prediction accuracy of the lifted system, the update mechanism is enhanced to determine whether to update the lifted system and meanwhile to reduce updates that deteriorate the fitting performance. Furthermore, based on the online-updated lifted system, a controller is designed to ensure the closed-loop controlled system be input-to-state stable with respect to the Koopman approximation error. Numerical simulations on the Duffing oscillator, the serial manipulator, and the synthetic biological network system are presented to demonstrate the effectiveness of the proposed method for the approximation and control of unknown nonlinear time-varying systems. The results show that the proposed approach outperforms existing methods in terms of approximation accuracy and computational efficiency, even under significant system variations.

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arXiv2026

Adaptive Robust Control for Uncertain Systems with Ellipsoid-Set Learning

Despite the celebrated success of stochastic control approaches for uncertain systems, such approaches are limited in the ability to handle non-Gaussian uncertainties. This work presents an adaptive robust control for linear uncertain systems, whose process noise, observation noise, and system states are depicted by ellipsoid sets rather than Gaussian distributions. We design an ellipsoid-set learning method to estimate the boundaries of state sets, and incorporate the learned sets into the control law derivation to reduce conservativeness in robust control. Further, we consider the parametric uncertainties in state-space matrices. Particularly, we assign finite candidates for the uncertain parameters, and construct a bank of candidate-conditional robust control problems for each candidate. We derive the final control law by aggregating the candidate-conditional control laws. In this way, we separate the control scheme into parallel robust controls, decoupling the learning and control, which otherwise renders the control unattainable. We demonstrate the effectiveness of the proposed control in numerical simulations in the cases of linear quadratic regulation and tracking control.

math.OC↗

arXiv2025

Fault Tolerant Control of Mecanum Wheeled Mobile Robots

Mecanum wheeled mobile robots (MWMRs) are highly susceptible to actuator faults that degrade performance and risk mission failure. Current fault tolerant control (FTC) schemes for MWMRs target complete actuator failures like motor stall, ignoring partial faults e.g., in torque degradation. We propose an FTC strategy handling both fault types, where we adopt posterior probability to learn real-time fault parameters. We derive the FTC law by aggregating probability-weighed control laws corresponding to predefined faults. This ensures the robustness and safety of MWMR control despite varying levels of fault occurrence. Simulation results demonstrate the effectiveness of our FTC under diverse scenarios.

cs.RO↗

arXiv2025

Curvature-Constrained Vector Field for Motion Planning of Nonholonomic Robots

Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the design of the curvature-bounded vector field and the tracking controller under underactuation. In this paper, we present a novel framework to co-develop the vector field and the control laws, guiding the nonholonomic robot to the target configuration with curvature-bounded trajectory. First, we formulate the problem by introducing the target positive limit set, which allows the robot to converge to or pass through the target configuration, depending on different dynamics and tasks. Next, we construct a curvature-constrained vector field (CVF) via blending and distributing basic flow fields in workspace and propose the saturated control laws with a dynamic gain, under which the tracking error's magnitude decreases even when saturation occurs. Under the control laws, kinematically constrained nonholonomic robots are guaranteed to track the reference CVF and converge to the target positive limit set with bounded trajectory curvature. Numerical simulations show that the proposed CVF method outperforms other vector-field-based algorithms. Experiments on Ackermann UGVs and semi-physical fixed-wing UAVs demonstrate that the method can be effectively implemented in real-world scenarios.

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arXiv2025

Virtual Contraction Approach to Decentralized Adaptive Stabilization of Nonlinear Time-Delayed Networks

In this paper, we exploit a diagonally dominant structure for the decentralized stabilization of unknown nonlinear time-delayed networks. To this end, we first introduce a novel generalization of virtual contraction analysis to diagonally dominant time-delayed control systems. We then show that nonlinear time-delayed networks can be stabilized using diagonal high-gains, provided that the input matrices satisfy certain generalized (column/row) diagonally dominant conditions. To enable stabilization of unknown networks, we further propose a distributed adaptive tuning rule for each individual gain function, guaranteeing that all closed-loop trajectories converge to the origin while the gains converge to finite values. The effectiveness of the proposed decentralized adaptive control is illustrated through a case study on epidemic spreading control in SIS networks with transmission delays.

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arXiv2025

Integrating Uncertainties for Koopman-Based Stabilization

Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in data-driven control via the Koopman operator, fully accounting for three uncertainties: projection error, estimation error, and process disturbance. It comprehensively investigates both direct and indirect data-driven control approaches, facilitating flexible methodology selection for analysis and control. For the direct approach, considering process disturbances, the lifted-state feedback controller, designed via a linear matrix inequality (LMI), robustly stabilizes all lifted bilinear systems consistent with noisy data. For the indirect approach requiring system identification, the feedback controller, designed using a nonlinear matrix inequality convertible to an LMI, ensures closed-loop stability under worst-case process disturbances. Numerical simulations via cross-validation validate the effectiveness of both approaches, highlighting their theoretical significance and practical utility.

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arXiv2025

Integrating Opinion Dynamics into Safety Control for Decentralized Airplane Encounter Resolution

As the airspace becomes increasingly congested, decentralized conflict resolution methods for airplane encounters have become essential. While decentralized safety controllers can prevent dangerous midair collisions, they do not always ensure prompt conflict resolution. As a result, airplane progress may be blocked for extended periods in certain situations. To address this blocking phenomenon, this paper proposes integrating bio-inspired nonlinear opinion dynamics into the airplane safety control framework, thereby guaranteeing both safety and blocking-free resolution. In particular, opinion dynamics enable the safety controller to achieve collaborative decision-making for blocking resolution and facilitate rapid, safe coordination without relying on communication or preset rules. Extensive simulation results validate the improved flight efficiency and safety guarantees. This study provides practical insights into the design of autonomous controllers for airplanes.

eess.SY↗

arXiv2025

Multi-Robot Cooperative Herding through Backstepping Control Barrier Functions

We propose a novel cooperative herding strategy through backstepping control barrier functions (CBFs), which coordinates multiple herders to herd a group of evaders safely towards a designated goal region. For the herding system with heterogeneous groups involving herders and evaders, the behavior of the evaders can only be influenced indirectly by the herders' motion, especially when the evaders follow an inverse dynamics model and respond solely to repulsive interactions from the herders. This indirect interaction mechanism inherently renders the overall system underactuated. To address this issue, we first construct separate CBFs for the dual objectives of goal reaching and collision avoidance, which ensure both herding completion and safety guarantees. Then, we reformulate the underactuated herding dynamics into a control-affine structure and employ a backstepping approach to recursively design control inputs for the hierarchical barrier functions, avoiding taking derivatives of the higher-order system. Finally, we present a cooperative herding strategy based on backstepping CBFs that allow herders to safely herd multiple evaders into the goal region. In addition, centralized and decentralized implementations of the proposed algorithm are developed, further enhancing its flexibility and applicability. Extensive simulations and real-world experiments validate the effectiveness and safety of the proposed strategy in multi-robot herding.

cs.MA↗

arXiv2025

Avoiding Deadlocks Is Not Enough: Analysis and Resolution of Blocked Airplanes

This paper is devoted to the analysis and resolution of a pathological phenomenon in airplane encounters called blocking mode. As autonomy in airplane systems increases, a pathological phenomenon can be observed in two-aircraft encounter scenarios, where airplanes stick together and fly in parallel for an extended period. This parallel flight results in a temporary blocking that significantly delays progress. In contrast to widely studied deadlocks in multi-robot systems, such transient blocking is often overlooked in existing literature. Since such prolonged parallel flying places high-speed airplanes at elevated risks of near-miss collisions, encounter conflicts must be resolved as quickly as possible in the context of aviation. We develop a mathematical model for a two-airplane encounter system that replicates this blocking phenomenon. Using this model, we analyze the conditions under which blocking occurs, quantify the duration of the blocking period, and demonstrate that the blocking condition is significantly less restrictive than that of deadlock. Based on these analytical insights, we propose an intention-aware strategy with an adaptive priority mechanism that enables efficient resolution of ongoing blocking phenomena while also incidentally eliminating deadlocks. Notably, the developed strategy does not rely on central coordination and communications that can be unreliable in harsh situations. The analytical findings and the proposed resolution strategy are validated through extensive simulations.

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arXiv2025

A Tunable Universal Formula for Safety-Critical Control

Sontag's universal formula is a widely used technique for stabilizing control through control Lyapunov functions. Recently, it has been extended to address safety-critical control by incorporating control barrier functions (CBFs). However, deriving a universal formula that satisfies requirements on essential properties, including safety, smoothness, and robustness against input disturbances, is still an open problem. To address this challenge, this paper introduces a novel solution - a tunable universal formula - by incorporating a (state-dependent) tunable term into Sontag's formula. This tunable term enables the regulation of safety-critical control performances, allowing the attainment of desired properties through a proper selection of tunable terms. Generally, the tunable universal formula can be seen as a controller that improves the quadratic program (QP)-synthesized controllers in terms of robustness and smoothness, while also reducing the conservatism (corresponding to robustness) in Sontag's formula. Furthermore, we extend the tunable universal formula to address safety-critical control problems with norm-bounded input constraints, showcasing its applicability across diverse control scenarios. Finally, we demonstrate the efficacy of our method through a two-link manipulator safe tracking example, investigating the essential properties including safety, smoothness, and robustness against input disturbances under various tunable terms.

eess.SY↗

arXiv2025

Moving Obstacle Collision Avoidance via Chance-Constrained MPC with CBF

Model predictive control (MPC) with control barrier functions (CBF) is a promising solution to address the moving obstacle collision avoidance (MOCA) problem. Unlike MPC with distance constraints (MPC-DC), this approach facilitates early obstacle avoidance without the need to increase prediction horizons. However, the existing MPC-CBF method is deterministic and fails to account for perception uncertainties. This paper proposes a generalized MPC-CBF approach for stochastic scenarios, which maintains the advantages of the deterministic method for addressing the MOCA problem. Specifically, the chance-constrained MPC-CBF (CC-MPC-CBF) technique is introduced to ensure that a user-defined collision avoidance probability is met by utilizing probabilistic CBFs. However, due to the potential empty intersection between the reachable set and the safe region confined by CBF constraints, the CC-MPC-CBF problem can pose challenges in achieving feasibility. To address this issue, we propose a sequential implementation approach that involves solving a standard MPC optimization problem followed by a predictive safety filter optimization, which leads to improved feasibility. Furthermore, we introduce an iterative convex optimization scheme to further expedite the resolution of the predictive safety filter, which results in an efficient approach to tackling the non-convex CC-MPC-CBF problem. We apply our proposed algorithm to a double integrator system for MOCA, and we showcase its resilience to obstacle measurement uncertainties and favorable feasibility properties.

eess.SY↗

arXiv2025

A Comparative Study of Artificial Potential Fields and Reciprocal Control Barrier Function-based Safety Filters

In this paper, we demonstrate that controllers designed by artificial potential fields (APFs) can be derived from reciprocal control barrier function quadratic program (RCBF-QP) safety filters. By integrating APFs within the RCBF-QP framework, we explicitly establish the relationship between these two approaches. Specifically, we first introduce the concepts of tightened control Lyapunov functions (T-CLFs) and tightened reciprocal control barrier functions (T-RCBFs), each of which incorporates a flexible auxiliary function. We then utilize an attractive potential field as a T-CLF to guide the nominal controller design, and a repulsive potential field as a T-RCBF to formulate an RCBF-QP safety filter. With appropriately chosen auxiliary functions, we show that controllers designed by APFs and those derived by RCBF-QP safety filters are equivalent. Based on this insight, we further generalize the APF-based controllers (equivalently, RCBF-QP safety filter-based controllers) to more general scenarios without restricting the choice of auxiliary functions. Finally, we present a collision avoidance example to clearly illustrate the connection and equivalence between the two methods.

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