arXiv subjects

Shimin Wang

Publications and source records attributed to Shimin Wang.

At least 19 recordsLinked to original sources

arXiv2026

Nonadaptive Learning in Robust Nonlinear Output Regulation

This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting the regulation problem as the robust input-to-state stabilization of an augmented error system. Unlike adaptive schemes, the proposed method does not rely on linearly parameterized regressors and does not require the construction of Lyapunov functions having merely nonpositive derivatives. Under standard assumptions on the exosystem, including purely imaginary and simple eigenvalues, together with a minimum-phase input-to-state stability condition on the internal dynamics, we establish global asymptotic regulation and derive explicit, verifiable inequalities for selecting the design gains. The resulting nonadaptive framework guarantees convergence of the estimation and tracking errors even when the controlled-system dynamics are complex or only partially known. The effectiveness of the theoretical results is demonstrated using a benchmark controlled Duffing system.

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arXiv2025

Asymptotic Boundedness of Distributed Set-Membership Filtering

Asymptotic boundedness is a crucial property of Distributed Set-Membership Filtering (DSMFing) that prevents the unbounded growth of the set estimates caused by the wrapping effect. However, this important property remains underinvestigated, compared to its noise-free and stochastic-noise counterparts, i.e., the convergence of Distributed Observers (DOs) and the bounded error covariance of Distributed Kalman Filters (DKFs). This paper studies the asymptotic boundedness of DSMFing for linear discrete-time systems. A novel concept, termed the Collective Observation-Information Tower (COIT), is introduced to characterize the fundamental relationship between the structure of graphs and the set estimates, which enables the boundedness analysis. Leveraging the COIT, an easily verifiable sufficient condition for the asymptotic boundedness of linear DSMFing is established. Surprisingly, the sufficient condition generalizes the well-known collective detectability condition for DOs and DKFs; it links DSMFs to existing distributed estimation methods and reveals the unique characteristic of DSMFs.

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arXiv2025

Collision-Free Bearing-Driven Formation Tracking for Euler-Lagrange Systems

In this paper, we investigate the problem of tracking formations driven by bearings for heterogeneous Euler-Lagrange systems with parametric uncertainty in the presence of multiple moving leaders. To estimate the leaders' velocities and accelerations, we first design a distributed observer for the leader system, utilizing a bearing-based localization condition in place of the conventional connectivity assumption. This observer, coupled with an adaptive mechanism, enables the synthesis of a novel distributed control law that guides the formation towards the target formation, without requiring prior knowledge of the system parameters. Furthermore, we establish a sufficient condition, dependent on the initial formation configuration, that ensures collision avoidance throughout the formation evolution. The effectiveness of the proposed approach is demonstrated through a numerical example.

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arXiv2025

Reinforcement learning in pursuit-evasion differential game: safety, stability and robustness

Safety and stability are two critical concerns in pursuit-evasion (PE) problems in an obstacle-rich environment. Most existing works combine control barrier functions (CBFs) and reinforcement learning (RL) to provide an efficient and safe solution. However, they do not consider the presence of disturbances, such as wind gust and actuator fault, which may exist in many practical applications. This paper integrates CBFs and a sliding mode control (SMC) term into RL to simultaneously address safety, stability, and robustness to disturbances. However, this integration is significantly challenging due to the strong coupling between the CBF and SMC terms. Inspired by Stackelberg game, we handle the coupling issue by proposing a hierarchical design scheme where SMC and safe control terms interact with each other in a leader-follower manner. Specifically, the CBF controller, acting as the leader, enforces safety independently of the SMC design; while the SMC term, as the follower, is designed based on the CBF controller. We then formulate the PE problem as a zero-sum game and propose a safe robust RL framework to learn the min-max strategy online. A sufficient condition is provided under which the proposed algorithm remains effective even when constraints are conflicting. Simulation results demonstrate the effectiveness of the proposed safe robust RL framework.

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arXiv2025

Data-Driven Nonlinear Regulation: Gaussian Process Learning

This article addresses the output regulation problem for a class of nonlinear systems using a data-driven approach. An output feedback controller is proposed that integrates a traditional control component with a data-driven learning algorithm based on Gaussian Process (GP) regression to learn the nonlinear internal model. Specifically, a data-driven technique is employed to directly approximate the unknown internal model steady-state map from observed input-output data online. Our method does not rely on model-based observers utilized in previous studies, making it robust and suitable for systems with modelling errors and model uncertainties. Finally, we demonstrate through numerical examples and detailed stability analysis that, under suitable conditions, the closed-loop system remains bounded and converges to a compact set, with the size of this set decreasing as the accuracy of the data-driven model improves over time.

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arXiv2025

Nonadaptive Output Regulation of Second-Order Nonlinear Uncertain Systems

This paper investigates the robust output regulation problem of second-order nonlinear uncertain systems with an unknown exosystem. Instead of the adaptive control approach, this paper resorts to a robust control methodology to solve the problem and thus avoid the bursting phenomenon. In particular, this paper constructs generic internal models for the steady-state state and input variables of the system. By introducing a coordinate transformation, this paper converts the robust output regulation problem into a nonadaptive stabilization problem of an augmented system composed of the second-order nonlinear uncertain system and the generic internal models. Then, we design the stabilization control law and construct a strict Lyapunov function that guarantees the robustness with respect to unmodeled disturbances. The analysis shows that the output zeroing manifold of the augmented system can be made attractive by the proposed nonadaptive control law, which solves the robust output regulation problem. Finally, we demonstrate the effectiveness of the proposed nonadaptive internal model approach by its application to the control of the Duffing system.

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arXiv2025

Learning-Based Tracking Perimeter Control for Two-region Macroscopic Traffic Dynamics

Leveraging the concept of the macroscopic fundamental diagram (MFD), perimeter control can alleviate network-level congestion by identifying critical intersections and regulating them effectively. Considering the time-varying nature of travel demand and the equilibrium of accumulation state, we extend the conventional set-point perimeter control (SPC) problem for the two-region MFD system as an optimal tracking perimeter control problem (OTPCP). Unlike the SPC schemes that stabilize the traffic dynamics to the desired equilibrium point, the proposed tracking perimeter control (TPC) scheme regulates the traffic dynamics to a desired trajectory in a differential framework. Due to the inherent network uncertainties, such as heterogeneity of traffic dynamics and demand disturbance, the system dynamics could be uncertain or even unknown. To address these issues, we propose an adaptive dynamic programming (ADP) approach to solving the OTPCP without utilizing the well-calibrated system dynamics. Numerical experiments demonstrate the effectiveness of the proposed ADP-based TPC. Compared with the SPC scheme, the proposed TPC scheme achieves a 20.01% reduction in total travel time and a 3.15% improvement in cumulative trip completion. Moreover, the proposed adaptive TPC approach can regulate the accumulation state under network uncertainties and demand disturbances to the desired time-varying equilibrium trajectory that aims to maximize the trip completion under a nominal demand pattern. These results validate the robustness of the adaptive TPC approach.

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arXiv2025

Strategic learning for disturbance rejection in multi-agent systems: Nash and Minmax in graphical games

This article investigates the optimal control problem with disturbance rejection for discrete-time multi-agent systems under cooperative and non-cooperative graphical games frameworks. Given the practical challenges of obtaining accurate models, Q-function-based policy iteration methods are proposed to seek the Nash equilibrium solution for the cooperative graphical game and the distributed minmax solution for the non-cooperative graphical game. To implement these methods online, two reinforcement learning frameworks are developed, an actor-disturber-critic structure for the cooperative graphical game and an actor-adversary-disturber-critic structure for the non-cooperative graphical game. The stability of the proposed methods is rigorously analyzed, and simulation results are provided to illustrate the effectiveness of the proposed methods.

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arXiv2025

Optimal Output Feedback Learning Control for Discrete-Time Linear Quadratic Regulation

This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for solving the LQR problem requires an implicit condition on the convergence of the state observer. Moreover, due to unknown system matrices and the existence of observer error, it is difficult to analyze the convergence and stability of most existing output feedback learning-based control methods. To tackle these issues, we propose a generalized dynamic output feedback learning control approach with guaranteed convergence, stability, and optimality performance for solving the LQR problem of unknown discrete-time linear systems. In particular, a dynamic output feedback controller is designed to be equivalent to a state feedback controller. This equivalence relationship is an inherent property without requiring convergence of the estimated state by the state observer, which plays a key role in establishing the off-policy learning control approaches. By value iteration and policy iteration schemes, the adaptive dynamic programming based learning control approaches are developed to estimate the optimal feedback control gain. In addition, a model-free stability criterion is provided by finding a nonsingular parameterization matrix, which contributes to establishing a switched iteration scheme. Furthermore, the convergence, stability, and optimality analyses of the proposed output feedback learning control approaches are given. Finally, the theoretical results are validated by two numerical examples.

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arXiv2025

Partial Excitation in Parameter Learning

This paper investigates parameter learning problems under Partial Persistent Excitation (PPE). The PPE condition is a rank-deficient, and therefore, a more general evolution of the well-known Persistent Excitation (PE) condition. Under the PPE condition, a proposed online algorithm is able to calculate the PE and non-PE subspaces, and finally gives an optimal parameter estimate in the sense of least squares. In particular, the learning error within the PE subspace exponentially converges to zero in the noise-free case. The PPE condition also provides a new perspective for solving distributed parameter learning problems, where the challenge is posed by local regressors that are often insufficiently excited. To improve knowledge of the unknown parameters, a cooperative learning protocol is proposed for a group of estimators that collect measured information under complementary PPE condition. This protocol allows each local estimator to operate locally in its PE subspace, and reach a consensus with neighbors in its non-PE subspace. As a result, the task of estimating unknown parameters can be achieved in a distributed way using cooperative local estimators. Application examples in system identification are given to demonstrate the effectiveness of the theoretical results developed in this paper.

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arXiv2025

Safe Learning Control with Optimality and Stability Guarantees

Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.

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arXiv2024

A nonparametric learning framework for nonlinear robust output regulation

A nonparametric learning solution framework is proposed for the global nonlinear robust output regulation problem. We first extend the assumption that the steady-state generator is linear in the exogenous signal to the more relaxed assumption that it is polynomial in the exogenous signal. Additionally, a nonparametric learning framework is proposed to eliminate the construction of an explicit regressor, as required in the adaptive method, which can potentially simplify the implementation and reduce the computational complexity of existing methods. With the help of the proposed framework, the robust nonlinear output regulation problem can be converted into a robust non-adaptive stabilization problem for the augmented system with integral input-to-state stable (iISS) inverse dynamics. Moreover, a dynamic gain approach can adaptively raise the gain to a sufficiently large constant to achieve stabilization without requiring any a priori knowledge of the uncertainties appearing in the dynamics of the exosystem and the system. Furthermore, we apply the nonparametric learning framework to globally reconstruct and estimate multiple sinusoidal signals with unknown frequencies without the need for adaptive parametric techniques. An explicit nonlinear mapping can directly provide the estimated parameters, which will exponentially converge to the unknown frequencies. Finally, a feedforward control design is proposed to solve the linear output regulation problem using the nonparametric learning framework. Two simulation examples are provided to illustrate the effectiveness of the theoretical results.

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arXiv2024

Distributed State Estimation for Linear Time-invariant Systems with Aperiodic Sampled Measurement

This paper deals with the state estimation of linear time-invariant systems using distributed observers with local sampled-data measurement and aperiodic communication. Each observer agent perceives partial information of the system to be observed but does not satisfy the observability condition. Consequently, distributed observers are designed to exponentially estimate the state of the system to be observed by time-varying sampling and asynchronous communication. Additionally, explicit upper bounds on allowable sampling periods for convergent estimation errors are given. Finally, a numerical example is provided to demonstrate the validity of the theoretical results

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arXiv2024

Nonparametric Steady-State Learning for Nonlinear Output Feedback Regulation

This article addresses the nonparametric and robust output regulation problem of the general nonlinear output feedback system with error output. The global robust output regulation problem for a class of general output feedback nonlinear systems with an uncertain exosystem and high relative degree can be tackled by constructing a linear generic internal model, provided that a continuous nonlinear mapping exists. Leveraging the proposed nonadaptive framework facilitates the conversion of the nonlinear robust output regulation problem into a robust nonadaptive stabilization formulation for the augmented system endowed with Input-to-State Stable dynamics. This approach removes the need for constructing a specific Lyapunov function with positive semidefinite derivatives and avoids the common assumption of linear parameterization of the nonlinear system. The nonadaptive approach is extended by incorporating the nonparametric learning framework to ensure the feasibility of the nonlinear mapping, which can be tackled using a data-driven method. Moreover, the introduced nonparametric learning framework allows the controlled system to learn the dynamics of the steady-state input behavior from the signal generated from the internal model with the output error as the feedback. As a result, the nonparametric approach can be advantageous to guarantee the convergence of the estimation and tracking error even when the underlying controlled system dynamics are complex or poorly understood. The effectiveness of the theoretical results is illustrated for three practical examples: regulation of a magnetic levitation system, regulation of a virtual synchronous generator, and heading control of a surface vessel.

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arXiv2024

An Execution-time-certified Riccati-based IPM Algorithm for RTI-based Input-constrained NMPC

Establishing an execution time certificate in deploying model predictive control (MPC) is a pressing and challenging requirement. As nonlinear MPC (NMPC) results in nonlinear programs, differing from quadratic programs encountered in linear MPC, deriving an execution time certificate for NMPC seems an impossible task. Our prior work \cite{wu2023direct} introduced an input-constrained MPC algorithm with the exact and only \textit{dimension-dependent} (\textit{data-independent}) number of floating-point operations ([flops]). This paper extends it to input-constrained NMPC problems via the real-time iteration (RTI) scheme, which results in \textit{data-varying} (but \textit{dimension-invariant}) input-constrained MPC problems. Therefore, applying our previous algorithm can certify the execution time based on the assumption that processors perform fixed [flops] in constant time. As the RTI-based scheme generally results in MPC with a long prediction horizon, this paper employs the efficient factorized Riccati recursion, whose computational cost scales linearly with the prediction horizon, to solve the Newton system at each iteration. The execution-time certified capability of the algorithm is theoretically and numerically validated through a case study involving nonlinear control of the chaotic Lorenz system.

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arXiv2023

Distributed State Estimation for Jointly Observable Linear Systems over Time-varying Networks

This paper deals with a distributed state estimation problem for jointly observable multi-agent systems operated over various time-varying network topologies. The results apply when the system matrix of the system to be observed contains eigenvalues with positive real parts. They also can apply to situations where the communication networks are disconnected at every instant. We present sufficient conditions for the existence of distributed observers for general linear systems over periodic communication networks. Using an averaging approach, it is shown that the proposed distributed observer can provide exponentially converging state estimates of the state of the linear system when the network is uniformly connected on average. This average connectedness condition offers a more relaxed assumption that includes periodic switching, Markovian switching and Cox process switching as special cases. All the agents in the network share the estimated state with their neighbours through the network and cooperatively reconstruct the entire state locally. Furthermore, this study presents two exponential stability results for two classes of switched systems, providing valuable tools in related distributed state estimation approaches. A toy example and three practical applications are provided to illustrate the effectiveness of the theoretical results.

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arXiv2023

Nonlinear Bipartite Output Regulation with Application to Turing Pattern

In this paper, a bipartite output regulation problem is solved for a class of nonlinear multi-agent systems subject to static signed communication networks. A nonlinear distributed observer is proposed for a nonlinear exosystem with cooperation-competition interactions to address the problem. Sufficient conditions are provided to guarantee its existence and stability. The exponential stability of the observer is established. As a practical application, a leader-following bipartite consensus problem is solved for a class of nonlinear multi-agent systems based on the observer. Finally, a network of multiple pendulum systems is treated to support the feasibility of the proposed design. The possible application of the approach to generate specific Turing patterns is also presented.

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arXiv2023

Distributed Time- and Event-Triggered Observers for Linear Systems: Non-Pathological Sampling and Inter-Event Dynamics

For an autonomous linear time-invariant (LTI) system, a distributed observer with time-triggered periodic observations and event-triggered communication is proposed to estimate the state of the system. It is shown that the sampling period is critical for the existence of desirable observers. A necessary and sufficient condition is established to give all feasible sampling periods that lead to convergent error dynamics and characterize delicate relationships among sampling periods, topologies, and system matrices. An event-triggering mechanism based on locally sampled data is designed to regulate the communication among agents, and the convergence of the estimation errors under the mechanism holds for a class of positive and convergent triggering functions, which include the commonly used exponential function as a special case. The mixed time- and event-triggered architecture naturally excludes the existence of Zeno behavior as the system updates at discrete instants. When the triggering function is bounded by exponential functions, analytical characterization of the relationship among sampling, event triggering, and inter-event behaviour is established. Finally, several examples are provided to illustrate the effectiveness and merits of the theoretical results.

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