arXiv subjects

Changrui Liu

Publications and source records attributed to Changrui Liu.

11 recordsLinked to original sources

arXiv2026

Asynchronous Model Predictive Control Under Model Mismatch: Stability and Performance Guarantees

Certainty-equivalence model predictive control (CE-MPC) is widely used for its simplicity and efficiency, but theoretical guarantees under asynchronous feedback remain limited. This paper establishes stability and performance guarantees for asynchronous CE-MPC of input-constrained nonlinear systems. We first derive a nominal stability condition and competitive-ratio bound that explicitly account for inter-execution intervals without prescribing a feedback mechanism. A value-function perturbation analysis for quadratic stage costs then accommodates additive, potentially non-smooth model mismatch without constraint qualification conditions. Combining these results yields stability criteria and competitive-ratio bounds for CE-MPC under general asynchronous feedback, including event/self-triggered and multi-step MPC. The guarantees explicitly relate prediction horizon, inter-execution time, and uncertainty magnitude, quantifying performance degradation relative to an ideal infinite-horizon controller. These results clarify tradeoffs between feedback frequency, model accuracy, and horizon length, guiding asynchronous MPC design using approximate or learned models.

eess.SY↗

arXiv2026

Photonic timing-engineered solitons for dual-microcomb metrology

Dissipative microcavity solitons offer a route to integrate comb-based metrology systems on photonic chips. However, integrated solitons generally lack agile control of comb parameters, particularly pulse timing control, hindering their application in quantum-limited metrology. Here we introduce dynamical soliton trapping to enable optically timing-engineered microcombs (OTEM). By injecting an auxiliary laser to anchor one of the microcomb lines, we create a potential well to trap and steer the soliton. Thus, soliton timing can be engineered by phase modulating the injected laser. Theory and measurement reveal the fast response bandwidth of the OTEM, which enabled a soliton slew rate of 31.3 ps/$\mu$s, surpassing existing time-programmable fiber laser combs by more than two orders of magnitude. Leveraging the timing scan, we used a single OTEM for single-pixel and parallel ranging by retrieving the phase of the multi-heterodyne beat spectrum. Picometer-scale ranging precision was achieved, establishing new record for optical absolute ranging. Our work can transform timing-engineering of microcavity solitons and endow integrated dual-microcomb metrology systems with enhanced precision.

physics.optics↗

arXiv2025

Approximate Model Predictive Control for Microgrid Energy Management via Imitation Learning

Efficient energy management is essential for reliable and sustainable microgrid operation amid increasing renewable integration. In this paper, an imitation learning-based framework to approximate mixed-integer Economic Model Predictive Control (EMPC) is proposed for microgrid energy management, considering fuel generators, renewable energy resources, a unified energy storage unit, and curtailable loads. Within the proposed framework, a neural network is trained to imitate expert EMPC control actions from offline trajectories, thereby enabling fast real-time decision making without solving online mixed-integer optimization problems, which often exhibit highly variable solution times across instances and do not scale well to large problem sizes; in particular, worst-case solve times can be excessively large and therefore unsuitable for real-time deployment. In contrast, the learned policy provides predictable and consistently low computation times. To enhance robustness and generalization, the learning process incorporates noise injection during training to mitigate distribution shift and explicitly accounts for forecast uncertainty in renewable generation and demand. Furthermore, a constraint-tightening approach combined with a projection layer is proposed to ensure recursive feasibility and constraint satisfaction of the learned controller. Simulation results demonstrate that the learned policy achieves economic performance comparable to EMPC, while reducing computation time by approximately one order of magnitude relative to the optimization-based EMPC.

eess.SY↗

arXiv2025

Robust Adaptive Discrete-Time Control Barrier Certificate

This work develops a robust adaptive control strategy for discrete-time systems using Control Barrier Functions (CBFs) to ensure safety under parametric model uncertainty and disturbances. A key contribution of this work is establishing a barrier function certificate in discrete time for general online parameter estimation algorithms. This barrier function certificate guarantees positive invariance of the safe set despite disturbances and parametric uncertainty without access to the true system parameters. In addition, real-time implementation and inherent robustness guarantees are provided. The proposed robust adaptive safe control framework demonstrates that the parameter estimation module can be designed separately from the CBF-based safety filter, simplifying the development of safe adaptive controllers for discrete-time systems. The resulting safe control approach guarantees that the system remains within the safe set while the controller adapts to model uncertainties, making it a promising strategy for discrete-time safety-critical systems.

eess.SY↗

arXiv2024

Certainty-Equivalence Model Predictive Control: Stability, Performance, and Beyond

Handling model mismatch is a common challenge in model predictive control (MPC). While robust MPC is effective, its conservatism often makes it less desirable. Certainty-equivalence MPC (CE-MPC), which uses a nominal model, offers an appealing alternative due to its design simplicity and low computational costs. This paper investigates CE-MPC for uncertain nonlinear systems with multiplicative parametric uncertainty and input constraints that are inactive at the steady state. The primary contributions are two-fold. First, a novel perturbation analysis of the MPC value function is provided, without assuming the Lipschitz continuity of the stage cost, better tailoring the widely used quadratic cost and having broader applicability in value function approximation, learning-based MPC, and performance-driven MPC design. Second, the stability and performance analysis of CE-MPC are provided, quantifying the suboptimality of CE-MPC compared to the infinite-horizon optimal controller with perfect model knowledge. The results provide insights in how the prediction horizon and model mismatch jointly affect stability and the worst-case performance. Furthermore, the general results are specialized to linear quadratic control, and a competitive ratio bound is derived, serving as the first competitive-ratio bound for MPC of uncertain linear systems with input constraints and multiplicative uncertainty.

math.OC↗

arXiv2024

Sensitivity Analysis for Piecewise-Affine Approximations of Nonlinear Programs with Polytopic Constraints

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results.

eess.SY↗

arXiv2024

Cooperative Relative Localization in MAV Swarms with Ultra-wideband Ranging

Relative localization (RL) is essential for the successful operation of micro air vehicle (MAV) swarms. Achieving accurate 3-D RL in infrastructure-free and GPS-denied environments with only distance information is a challenging problem that has not been satisfactorily solved. In this work, based on the range-based peer-to-peer RL using the ultra-wideband (UWB) ranging technique, we develop a novel UWB-based cooperative relative localization (CRL) solution that integrates the relative motion dynamics of each host-neighbor pair to build a unified dynamic model and takes the distances between the neighbors as \textit{bonus information}. Observability analysis using differential geometry shows that the proposed CRL scheme can expand the observable subspace compared to other alternatives using only direct distances between the host agent and its neighbors. In addition, we apply the kernel-induced extended Kalman filter (EKF) to the CRL state estimation problem with the novel-designed Logarithmic-Versoria (LV) kernel to tackle heavy-tailed UWB noise. Sufficient conditions for the convergence of the fixed-point iteration involved in the estimation algorithm are also derived. Comparative Monte Carlo simulations demonstrate that the proposed CRL scheme combined with the LV-kernel EKF significantly improves the estimation accuracy owing to its robustness against both measurement outliers and incorrect measurement covariance matrix initialization. Moreover, with the LV kernel, the estimation is still satisfactory when performing the fixed-point iteration only once for reduced computational complexity.

cs.RO↗

arXiv2024

Stability and Performance Analysis of Model Predictive Control of Uncertain Linear Systems

Model mismatch often poses challenges in model-based controller design. This paper investigates model predictive control (MPC) of uncertain linear systems with input constraints, focusing on stability and closed-loop infinite-horizon performance. The uncertainty arises from a parametric mismatch between the true and the estimated system under the matrix Frobenius norm. We examine a simple MPC controller that exclusively uses the estimated system model and establishes sufficient conditions under which the MPC controller can stabilize the true system. Moreover, we derive a theoretical performance bound based on relaxed dynamic programming, elucidating the impact of prediction horizon and modeling errors on the suboptimality gap between the MPC controller and the Oracle infinite-horizon optimal controller with knowledge of the true system. Simulations of a numerical example validate the theoretical results. Our theoretical analysis offers guidelines for obtaining the desired modeling accuracy and choosing a proper prediction horizon to develop certainty-equivalent MPC controllers for uncertain linear systems.

math.OC↗

arXiv2022

Wilcoxon-Mann-Whitney Effects for Clustered Data: Informative Cluster Size

In clustered data setting, informative cluster size has been a focus of recent research. In the nonparametric context, the problem has been considered mainly for testing equality of distribution functions. The aim in this paper is to develop inferential procedure for the Wilcoxon-Mann-Whintey effect (also known as the nonprametric relative effect). Unbiased estimator is provided and its asymptotic properties are investigated. The asymptotic theory is employed to develop inferential methods. While the proposed method takes information in the cluster sizes into consideration when constructing the estimator, it is equally applicable for ignorable cluster size situation. Simulation results show that our method appropriately accounts for informative cluster size and it generally outperforms existing methods, especially those designed under ignorable cluster sizes. The applications of the method is illustrated using data from a longitudinal study of alcohol use and a periodontal study.

stat.ME↗

arXiv2022

Mathematical Modeling of Drug Use: The Dynamics of Monosubstance Dependence for Two Addictive Drugs

Based on previous work done in this field, we build a dynamical system that describes changes in drug addiction in an isolated population when two addictive substances are available simultaneously. We then use our model to investigate whether the system captures the process of users switching drug habits. One of the motivations for this project is to mathematically check the conjecture that being addicted to a less-addictive substance will effectively lead individuals to become dependent on more addictive and potentially more dangerous drugs. We introduce additional assumptions, under which our model is reduced to a competitive Lotka-Volterra system. This dynamical system has three or four fixed points, stability of which then gives an implication about the outcomes of the competition between addictive substances and, therefore, the fate of individuals in the population. From the analysis of the reduced model, we determine that there actually exist parameter regimes that capture the following dynamics: depending on the initial distribution of the drug preference; either the use of both drugs will die out, the usage of one of the drugs will become prevalent, or addictions to both drugs will coexist.

math.DS↗

arXiv2020

Detection Defense Against Adversarial Attacks with Saliency Map

It is well established that neural networks are vulnerable to adversarial examples, which are almost imperceptible on human vision and can cause the deep models misbehave. Such phenomenon may lead to severely inestimable consequences in the safety and security critical applications. Existing defenses are trend to harden the robustness of models against adversarial attacks, e.g., adversarial training technology. However, these are usually intractable to implement due to the high cost of re-training and the cumbersome operations of altering the model architecture or parameters. In this paper, we discuss the saliency map method from the view of enhancing model interpretability, it is similar to introducing the mechanism of the attention to the model, so as to comprehend the progress of object identification by the deep networks. We then propose a novel method combined with additional noises and utilize the inconsistency strategy to detect adversarial examples. Our experimental results of some representative adversarial attacks on common datasets including ImageNet and popular models show that our method can detect all the attacks with high detection success rate effectively. We compare it with the existing state-of-the-art technique, and the experiments indicate that our method is more general.

cs.LG↗