Lijun Zhu

Lijun Zhu, David J. Hill

The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized Lyapunov function to solve the problems. Also, a new synchronization definition is introduced and characterized by frequency boundedness and angle cohesiveness, the latter of which requires angles of any two connected nodes rather than any two arbitrary nodes to stay cohesive. It allows to take power fluctuations into explicit account as disturbances and can lead to less conservative stability condition. Applying the analysis framework, we derive two algebraic stability conditions for power systems that relate the underlying network topology and system parameters to the stability. Finally, to authors' best knowledge, we first explicitly give the estimation of region of attraction for power systems. The analysis is verified via numerical simulation showing that two stability conditions can complement each other for predicting the stability.

Lijun Zhu, Zhiyong Chen, David J. Hill et al.

The paper proposes a novel event-triggered control scheme for nonlinear systems based on the input-delay method. Specifically, the closed-loop system is associated with a pair of auxiliary input and output. The auxiliary output is defined as the derivative of the continuous-time input function, while the auxiliary input is defined as the input disturbance caused by the sampling or equivalently the integral of the auxiliary output over the sampling period. As a result, a cyclic mapping forms from the input to the output via the system dynamics and back from the output to the input via the integral. The event-triggering law is constructed to make the mapping contractive such that the stabilization is achieved and an easy-to-check Zeno-free condition is provided. With this idea, we develop a theorem for the event-triggered control of interconnected nonlinear systems which is employed to solve the event-triggered control for lower-triangular systems with dynamic uncertainties.

Lijun Zhu, Zhiyong Chen, Xi Chen et al.

This paper studies a stabilization problem for linear MIMO systems subject to external perturbation that further requires the closed-loop system render a specified gain from the external perturbation to the output. The problem arises from control of networked systems, in particular, robust output synchronization of heterogeneous linear MIMO multi-agent systems via output feedback/communication. We propose a new approach that converts a class of MIMO systems into a normal form via repeated singular value decomposition and prove that a stabilization controller with a specified external gain can be explicitly constructed for the normal form.Two scenarios with static state feedback and dynamic output feedback are investigated. By integrating the reference model and internal model techniques, the robust output synchronization problem for MIMO multi-agent systems is converted into a stabilization problem with a specified externalgain and solved by the developed approach.

Kaige Liu, Yang Li, Lijun Zhu et al.

Living organisms exhibit persistent autonomy through internally generated goals and self-sustaining behavioral organization, yet current embodied agents remain driven by externally scripted objectives. This dependence on predefined task specifications limits their capacity for long-term deployment in dynamic, unstructured environments where continuous human intervention is impractical. We propose that personality traits provide an intrinsic organizational principle for achieving persistent autonomy. Analogous to genotypic biases shaping biological behavioral tendencies, personalities enable agents to autonomously generate goals and sustain behavioral evolution without external supervision. To realize this, we develop PEPA, a three-layer cognitive architecture that operates through three interacting systems: Sys3 autonomously synthesizes personality-aligned goals and refines them via episodic memory and daily self-reflection; Sys2 performs deliberative reasoning to translate goals into executable action plans; Sys1 grounds the agent in sensorimotor interaction, executing actions and recording experiences. We validate the framework through real-world deployment on a quadruped robot in a multi-floor office building. Operating without reliance on fixed task specifications, the robot autonomously arbitrates between user requests and personality-driven motivations, navigating elevators and exploring environments accordingly. Quantitative analysis across five distinct personality prototypes demonstrates stable, trait-aligned behaviors. The results confirm that personality-driven cognitive architectures enable sustained autonomous operation characteristic of persistent embodied systems. Code and demo videos are available at https://sites.google.com/view/pepa-persistent/.

Mengmou Li, Lijun Zhu, Masaaki Nagahara

We show that a common Lyapunov matrix exists for the convex combination of two Hurwitz matrices if and only if the intersection of the set of strict Lyapunov matrices for one matrix and the set of non-strict Lyapunov matrices for the other is nonempty. This simple relaxation is useful for the convergence analysis of the augmented primal-dual gradient flow for constrained optimization problems with affine inequality constraints, which can be viewed as a polytopic linear parameter-varying (LPV) system driven by the active-constraint selector. Under a relaxed strong convexity condition, exponential convergence is proved for the LPV system. The analysis can further be extended to the integral quadratic constraints (IQCs) framework for LPV systems to facilitate numerical search of the convergence rate.

Gewei Zuo, Lijun Zhu

The event-triggered control with intermittent output can reduce the communication burden between the controller and plant side over the network. It has been exploited for adaptive output feedback control of uncertain nonlinear systems in the literature, however the controller must partially reside at the plant side where the computation capacity is required. In this paper, all controller components are moved to the controller side and their dynamics use sampled states rather than continuous one with the benefit of directly estimating next triggering instance of some conditions and avoiding constantly checking event condition at the controller side. However, these bring two major challenges. First, the virtual input designed in the dynamic filtering technique for the stabilization is no longer differentiable. Second, the plant output is sampled to transmit at plant side and sampled again at controller side to construct the controller, and the two asynchronous samplings make the analysis more involving. This paper solves these two issues by introducing a new state observer to simplify the adaptive law, a set of continuous companion variables for stability analysis and a new lemma quantifying the error bound between actual output signal and sampled transmitted output. It is theoretically guaranteed that all internal signals in the closed-loop system are semiglobally bounded and the output is practically stabilized to the origin. Finally, the numerical simulation illustrates the effectiveness of proposed scheme.

Gewei Zuo, Lijun Zhu, Yujuan Wang et al.

A finite-time protocol for a multi-agent systems (MASs) can guarantee the convergence of every agent in a finite time interval in contrast to the asymptotic convergence, but the settling time depends on the initial condition and design parameters and is inconsistent across the agents. In this paper, we study the prescribed-time cooperative output regulation (PTCOR) problem for a class of linear heterogeneous MASs under a directed communication graph, where the settling time of every agent can be specified a priori and thus consistent. As a special case of PTCOR, the necessary and sufficient condition for prescribed-time output regulation of an individual system is first discussed. Then, the PTCOR problem is converted into two cascaded subsystem, where the first one composed of distributed estimate errors and local estimate errors and the second one is for local tracking errors. The criterion for prescribed-time stabilization of the cascaded system is proposed and is found to be different from that of traditional asymptotic stabilization of a cascaded system. Under the criterion and sufficient condition, the general PTCOR problem is studied in two scenarios including state feedback control and measurement output feedback control. In particular, a distributed prescribed-time observer for each subsystem is explicitly constructed to estimate the exosystem's state. Based on the observer, a distributed controller is proposed to achieve convergence of the regulated output to zero within a prescribed-time.

Gewei Zuo, Lijun Zhu, Yujuan Wang et al.

In this paper, we address the distributed prescribed-time convex optimization (DPTCO) problem for a class of nonlinear multi-agent systems (MASs) under undirected connected graph. A cascade design framework is proposed such that the DPTCO implementation is divided into two parts: distributed optimal trajectory generator design and local reference trajectory tracking controller design. The DPTCO problem is then transformed into the prescribed-time stabilization problem of a cascaded system. Changing Lyapunov function method and time-varying state transformation method together with the sufficient conditions are proposed to prove the prescribed-time stabilization of the cascaded system as well as the uniform boundedness of internal signals in the closed-loop systems. The proposed framework is then utilized to solve robust DPTCO problem for a class of chain-integrator MASs with external disturbances by constructing a novel variables and exploiting the property of time-varying gains. The proposed framework is further utilized to solve the adaptive DPTCO problem for a class of strict-feedback MASs with parameter uncertainty, in which backstepping method with prescribed-time dynamic filter is adopted. The descending power state transformation is introduced to compensate the growth of increasing rate induced by the derivative of time-varying gains in recursive steps and the high-order derivative of local reference trajectory is not required. Finally, theoretical results are verified by two numerical examples.

Gewei Zuo, Mengmou Li, Lijun Zhu

In this paper, we address the distributed prescribed-time convex optimization (DPTCO) for a class of networked Euler-Lagrange systems under undirected connected graphs. By utilizing position-dependent measured gradient value of local objective function and local information interactions among neighboring agents, a set of auxiliary systems is constructed to cooperatively seek the optimal solution. The DPTCO problem is then converted to the prescribed-time stabilization problem of an interconnected error system. A prescribed-time small-gain criterion is proposed to characterize prescribed-time stabilization of the system, offering a novel approach that enhances the effectiveness beyond existing asymptotic or finite-time stabilization of an interconnected system. Under the criterion and auxiliary systems, innovative adaptive prescribed-time local tracking controllers are designed for subsystems. The prescribed-time convergence lies in the introduction of time-varying gains which increase to infinity as time tends to the prescribed time. Lyapunov function together with prescribed-time mapping are used to prove the prescribed-time stability of closed-loop system as well as the boundedness of internal signals. Finally, theoretical results are verified by one numerical example.

Yuquan Li, Lianjie Ma, Han Ding et al.

Vision-Language-Action (VLA) models enable generalist robotic manipulation but suffer from high inference latency. This bottleneck stems from the massive number of visual tokens processed by large language backbones. Existing methods either prune or merge tokens uniformly, degrading the spatial reasoning essential for robotic control. We present DepthCache, a training-free framework that leverages depth as a structural prior for visual token compression. It partitions observations into depth-based regions and applies spatially differentiated merge ratios, preserving the near-field workspace while compressing the distant background. To exploit temporal redundancy, DepthCache distributes the merging process across consecutive frames, ensuring consistent representations while reducing per-step computation. A motion-adaptive pipeline further optimizes auxiliary view compression based on end-effector dynamics. The framework requires no model modification, generalizing across diverse VLA architectures. On the LIBERO benchmark, DepthCache achieves up to 1.28x inference speedup with less than 1% average success rate degradation across three VLA models (pi_0.5, OpenVLA, GR00T), whereas pruning and merging baselines incur 4--24% degradation at comparable compression. Real-world experiments on a physical manipulator demonstrate that DepthCache enables faster task throughput and more responsive closed-loop control in latency-sensitive scenarios.

Lianjie Ma, Yuquan Li, Bingzheng Jiang et al.

Foundation-model-based monocular depth estimation offers a viable alternative to active sensors for robot perception, yet its computational cost often prohibits deployment on edge platforms. Existing methods perform independent per-frame inference, wasting the substantial computational redundancy between adjacent viewpoints in continuous robot operation. This paper presents AsyncMDE, an asynchronous depth perception system consisting of a foundation model and a lightweight model that amortizes the foundation model's computational cost over time. The foundation model produces high-quality spatial features in the background, while the lightweight model runs asynchronously in the foreground, fusing cached memory with current observations through complementary fusion, outputting depth estimates, and autoregressively updating the memory. This enables cross-frame feature reuse with bounded accuracy degradation. At a mere 3.83M parameters, it operates at 237 FPS on an RTX 4090, recovering 77% of the accuracy gap to the foundation model while achieving a 25X parameter reduction. Validated across indoor static, dynamic, and synthetic extreme-motion benchmarks, AsyncMDE degrades gracefully between refreshes and achieves 161FPS on a Jetson AGX Orin with TensorRT, clearly demonstrating its feasibility for real-time edge deployment.

Yaohang Xu, Lianjie Ma, Gewei Zuo et al.

Reinforcement Learning (RL) and Imitation Learning (IL) are the standard frameworks for policy acquisition in manipulation. While IL offers efficient policy derivation, it suffers from compounding errors and distribution shift. Conversely, RL facilitates autonomous exploration but is frequently hindered by low sample efficiency and the high cost of trial and error. Since existing hybrid methods often struggle with complex tasks, we introduce Mixture of RL and IL Experts (MoRI). This system dynamically switches between IL and RL experts based on the variance of expert actions to handle coarse movements and fine-grained manipulations. MoRI employs an offline pre-training stage followed by online fine-tuning to accelerate convergence. To maintain exploration safety and minimize human intervention, the system applies IL-based regularization to the RL component. Evaluation across four complex real-world tasks shows that MoRI achieves an average success rate of 97.5% within 2 to 5 hours of fine-tuning. Compared to baseline RL algorithms, MoRI reduces human intervention by 85.8% and shortens convergence time by 21%, demonstrating its capability in robotic manipulation.

Yuzhi Jiang, Yujun Liang, Junhao Li et al.

Humanoid robots, characterized by numerous degrees of freedom and a high center of gravity, are inherently unstable. Safe omnidirectional locomotion on stairs requires both omnidirectional terrain perception and reliable foothold selection. Existing methods often rely on forward-facing depth cameras, which create blind zones that restrict omnidirectional mobility. Furthermore, sparse post-contact unsafe stepping penalties lead to low learning efficiency and suboptimal strategies. To realize safe stair-traversal gaits, this paper introduces a single-stage training framework incorporating a dense unsafe stepping penalty that provides continuous feedback as the foot approaches a hazardous placement. To obtain stable and reliable elevation maps, we build a rolling point-cloud mapping system with spatiotemporal confidence decay and a self-protection zone mechanism, producing temporally consistent local maps. These maps are further refined by an Edge-Guided Asymmetric U-Net (EGAU), which mitigates reconstruction distortion caused by sparse LiDAR returns on stair risers. Simulation and real-robot experiments show that the proposed method achieves a near-100\% safe stepping rate on stair terrains in simulation, while maintaining a remarkably high safe stepping rate in real-world deployments. Furthermore, it completes a continuous long-distance walking test on complex outdoor terrains, demonstrating reliable sim-to-real transfer and long-term stability.

Arthur J. Redfern, Lijun Zhu, Molly K. Newquist

This paper describes a CNN where all CNN style 2D convolution operations that lower to matrix matrix multiplication are fully binary. The network is derived from a common building block structure that is consistent with a constructive proof outline showing that binary neural networks are universal function approximators. 71.24% top 1 accuracy on the 2012 ImageNet validation set was achieved with a 2 step training procedure and implementation strategies optimized for binary operands are provided.

Imil Hamda Imran, Zhiyong Chen, Lijun Zhu et al.

In traditional adaptive control, the certainty equivalence principle suggests a two-step design scheme. A controller is first designed for the ideal situation assuming the uncertain parameter was known and it renders a Lyapunov function. Then, the uncertain parameter in the controller is replaced by its estimation that is updated by an adaptive law along the gradient of Lyapunov function. This principle does not generally work for a multi-agent system as an adaptive law based on the gradient of (centrally constructed) Lyapunov function cannot be implemented in a distributed fashion, except for limited situations. In this paper, we propose a novel distributed adaptive scheme, not relying on gradient of Lyapunov function, for general multi-agent systems. In this scheme, asymptotic consensus of a second-order uncertain multi-agent system is achieved in a network of directed graph.

Lijun Zhu, Zhigang Peng, James McClellan et al.

The increasing volume of seismic data from long-term continuous monitoring motivates the development of algorithms based on convolutional neural network (CNN) for faster and more reliable phase detection and picking. However, many less studied regions lack a significant amount of labeled events needed for traditional CNN approaches. In this paper, we present a CNN-based Phase- Identification Classifier (CPIC) designed for phase detection and picking on small to medium sized training datasets. When trained on 30,146 labeled phases and applied to one-month of continuous recordings during the aftershock sequences of the 2008 MW 7.9 Wenchuan Earthquake in Sichuan, China, CPIC detects 97.5% of the manually picked phases in the standard catalog and predicts their arrival times with a five-times improvement over the ObsPy AR picker. In addition, unlike other CNN-based approaches that require millions of training samples, when the off-line training set size of CPIC is reduced to only a few thousand training samples the accuracy stays above 95%. The online implementation of CPIC takes less than 12 hours to pick arrivals in 31-day recordings on 14 stations. In addition to the catalog phases manually picked by analysts, CPIC finds more phases for existing events and new events missed in the catalog. Among those additional detections, some are confirmed by a matched filter method while others require further investigation. Finally, when tested on a small dataset from a different region (Oklahoma, US), CPIC achieves 97% accuracy after fine tuning only the fully connected layer of the model. This result suggests that the CPIC developed in this study can be used to identify and pick P/S arrivals in other regions with no or minimum labeled phases.

Lijun Zhu, Lindsay Chuang, James H. McClellan et al.

In the presence of background noise, arrival times picked from a surface microseismic data set usually include a number of false picks that can lead to uncertainty in location estimation. To eliminate false picks and improve the accuracy of location estimates, we develop an association algorithm termed RANSAC-based Arrival Time Event Clustering (RATEC) that clusters picked arrival times into event groups based on random sampling and fitting moveout curves that approximate hyperbolas. Arrival times far from the fitted hyperbolas are classified as false picks and removed from the data set prior to location estimation. Simulations of synthetic data for a 1-D linear array show that RATEC is robust under different noise conditions and generally applicable to various types of subsurface structures. By generalizing the underlying moveout model, RATEC is extended to the case of a 2-D surface monitoring array. The effectiveness of event location for the 2-D case is demonstrated using a data set collected by the 5200-element dense Long Beach array. The obtained results suggest that RATEC is effective in removing false picks and hence can be used for phase association before location estimates.

Entao Liu, Lijun Zhu, Anupama Govinda Raj et al.

Passive microseismic data are commonly buried in noise, which presents a significant challenge for signal detection and recovery. For recordings from a surface sensor array where each trace contains a time-delayed arrival from the event, we propose an autocorrelation-based stacking method that designs a denoising filter from all the traces, as well as a multi-channel detection scheme. This approach circumvents the issue of time aligning the traces prior to stacking because every trace's autocorrelation is centered at zero in the lag domain. The effect of white noise is concentrated near zero lag, so the filter design requires a predictable adjustment of the zero-lag value. Truncation of the autocorrelation is employed to smooth the impulse response of the denoising filter. In order to extend the applicability of the algorithm, we also propose a noise prewhitening scheme that addresses cases with colored noise. The simplicity and robustness of this method are validated with synthetic and real seismic traces.