arXiv subjects

Zhaobo Liu

Publications and source records attributed to Zhaobo Liu.

10 recordsLinked to original sources

arXiv2026

Strong Consistency and Optimal Tracking of the {\AA}str\"om-Wittenmark Self-Tuning Regulator with Unknown Input Gain

We study strong consistency and optimal tracking of the {\AA}str\"om-Wittenmark self-tuning regulator with unknown input gain. Existing results establish stability, optimal tracking and parameter consistency for the unmodified recursion under growth conditions on reference information. Other approaches obtain performance guarantees by adjusting the estimates used in feedback or adding decaying probing signals. For a class of minimum-phase linear systems with martingale difference noise, we establish joint guarantees for ordinary least squares with certainty-equivalent control without reference excitation, gain adjustment or added probing. For each bounded reference, average input and output energy are almost surely bounded, average squared tracking error converges almost surely to the noise variance, and all parameter estimates are strongly consistent whenever at least two parameters are estimated. For the consistency result, the key is a logarithmic lower bound on the cumulative squared difference between an auxiliary least-squares prediction of the noise and the reference. If the gain error persisted, this noise information and the actual least-squares recursion would give incompatible lower and upper bounds on the same weighted squared sum. This contradiction establishes gain convergence before stability and full parameter consistency.

math.OC↗

arXiv2026

Fundamental Limits of Adaptive Stabilization with an Unknown Growth Exponent

A basic question in adaptive control is how rapidly a discrete-time nonlinear plant with unknown parameters may grow while remaining stabilizable. When the nonlinear growth exponent is known and only a scalar coefficient is unknown, existing theory identifies 4 as the exact critical exponent for stabilizability. We determine how this critical exponent changes when the growth exponent is also unknown. For any positive disturbance bound, one feedback law stabilizes all plants in some neighborhood of a nominal parameter pair if and only if the nominal exponent is below $3\sqrt{3}/2$. At equality, every compact parameter set whose exponents do not exceed this value remains stabilizable. If the exponent belongs to a known finite set, the critical exponent remains 4 for every nondegenerate compact coefficient interval. Hence finite exponent sets and arbitrarily short exponent intervals can have different critical exponents. Uncertainty in the growth rate therefore changes the range of growth that feedback can stabilize, not merely the size of the uncertainty set. The critical exponent remains $3\sqrt{3}/2$ under a known positive state-dependent multiplier bounded above and away from zero. For a system whose coefficient and exponent are known functions of an unknown parameter, a compact parameter family is stabilizable when its exponents do not exceed this value. At an interior parameter point where the Jacobian of these functions has rank two and the exponent is at least this value, no compact neighborhood is stabilizable.

math.OC↗

arXiv2026

A Game-Theoretic Characterization of Feedback Capability for Fully Coupled Vector-Valued Nonparametric Systems

We study feedback stabilization for the discrete-time system $x_{t+1}=f(x_t)+u_t+w_{t+1}$ in $\mathbb{R}^d$ with unknown $f$ and arbitrary bounded disturbances. For scalar plants, the sharp feedback capability threshold under generalized Lipschitz uncertainty is $3/2+\sqrt{2}$. We treat fully coupled vector-valued systems, where scalar order and interval recursion are unavailable and coupling precludes a coordinatewise reduction. We introduce a response-history escape game in which the adversary seeks a finite envelope and an unbounded state radius. Borel determinacy ensures that exactly one player has a winning strategy at each slope. We prove that the same player wins from every finite response history, and slope monotonicity gives an independently defined game value $Γ_d$. We prove that $Γ_d$ is finite and is the strict feedback capability threshold for the plant problem. If $L<Γ_d$, one causal feedback law stabilizes every plant in the uncertainty class against every bounded disturbance sequence. If $L>Γ_d$, for every causal feedback law there exist a plant in the same class and a bounded disturbance sequence such that the closed-loop state sequence is unbounded. The proof uses one controller for all subcritical slopes and a realization in a Hilbert space based on the Kirszbraun--Valentine extension theorem. An explicit nearest-neighbor law gives a lower bound above one in every finite dimension, including $Γ_2\ge 2/\sqrt{3}$. Dimension monotonicity gives $Γ_d\leΓ_1$, and comparison with the scalar theory yields $Γ_1=3/2+\sqrt{2}$.

math.OC↗

arXiv2026

Genie Sim 3.0 : A High-Fidelity Comprehensive Simulation Platform for Humanoid Robot

The development of robust and generalizable robot learning models is critically contingent upon the availability of large-scale, diverse training data and reliable evaluation benchmarks. Collecting data in the physical world poses prohibitive costs and scalability challenges, and prevailing simulation benchmarks frequently suffer from fragmentation, narrow scope, or insufficient fidelity to enable effective sim-to-real transfer. To address these challenges, we introduce Genie Sim 3.0, a unified simulation platform for robotic manipulation. We present Genie Sim Generator, a large language model (LLM)-powered tool that constructs high-fidelity scenes from natural language instructions. Its principal strength resides in rapid and multi-dimensional generalization, facilitating the synthesis of diverse environments to support scalable data collection and robust policy evaluation. We introduce the first benchmark that pioneers the application of LLM for automated evaluation. It leverages LLM to mass-generate evaluation scenarios and employs Vision-Language Model (VLM) to establish an automated assessment pipeline. We also release an open-source dataset comprising more than 10,000 hours of synthetic data across over 200 tasks. Through systematic experimentation, we validate the robust zero-shot sim-to-real transfer capability of our open-source dataset, demonstrating that synthetic data can server as an effective substitute for real-world data under controlled conditions for scalable policy training. For code and dataset details, please refer to: https://github.com/AgibotTech/genie_sim.

cs.RO↗

arXiv2026

Stability of MIMO PID With Backward Differences Under Fast Sampling: An Exact Spectral Criterion

Backward differences are a standard digital realization of derivative action in proportional-integral-derivative control. This note proves that, for multivariable state-space plants, this implementation can be unstable no matter how small the sampling period is. The exact lifted model reveals fast eigenvalues created by the stored previous output sample. Away from boundary spectra, stability is equivalent to ideal loop stability plus Schur stability of the product of the output, input, and derivative gain matrices.

math.OC↗

arXiv2020

Stabilizability Theorems on Discrete-time Nonlinear Uncertain Systems

This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule. Later, we find that a stabilizable multi-parameter system in discrete time is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed in this paper.

math.OC↗

arXiv2019

Inverse Eigenvalue Problem For Mass-Spring-Inerter Systems

This paper has solved the inverse eigenvalue problem for "fixed-free" mass-chain systems with inerters. It is well known that for a spring-mass system wherein the adjacent masses are linked through a spring, the natural frequency assignment can be achieved by choosing appropriate masses and spring stiffnesses if and only if the given positive eigenvalues are distinct. However, when we involve inerters, multiple eigenvalues in the assignment are allowed. In fact, arbitrarily given a set of positive real numbers, we derive a necessary and sufficient condition on the multiplicities of these numbers, which are assigned as the natural frequencies of the concerned mass-spring-inerter system.

math.OC↗

arXiv2019

Asymptotic Behavior of Least Squares Estimator for Nonlinear Autoregressive Models

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been established under mild conditions. These properties suggest the strong consistency of the least squares estimates in nonlinear autoregressive models which are not divergent.

math.PR↗

arXiv2018

Is It Possible to Stabilize Disrete-time Parameterized Uncertain Systems Growing Exponentially Fast?

This paper derives a somewhat surprising but interesting enough result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to an intuition, it shows that the growth rate of a discrete-time stabilizable system with linear parameterization is not necessarily to be small all the time. More specifically, to achieve the stabilizability, the system function $f(x)=O(|x|^b)$ with $b<4$ is only required for a very tiny fraction of $x$ in $\mathbb{R}$, even if it grows exponentially fast for the other $x$. The proportion of the mentioned set in $\mathbb{R}$, where the system fulfills the growth rate $ O(|x|^b)$ has also been computed, for both the stabilizable and unstabilizable cases. This proportion, as indicated herein, could be arbitrarily small, while the corresponding system is stabilizable.

math.OC↗

arXiv2018

When Adaptive Diffusion Algorithm Converges to True Parameter?

We attempt to answer the question what data brings adaptive diffusion algorithms converging to true parameters. The discussion begins with the diffusion recursive least squares (RLS). When unknown parameters are scalar, the necessary and sufficient condition of the convergence for the diffusion RLS is established, in terms of the strong consistency and mean-square convergence both. However, for the general high dimensional parameter case, our results suggest that the diffusion RLS in a connected network might cause a diverging error, even if local data at every node could guarantee the individual RLS tending to true parameters. Due to the possible failure of the diffusion RLS, we prove that the diffusion Robbins-Monro (RM) algorithm could achieve the strong consistency and mean-square convergence simultaneously, under some cooperative information conditions. The convergence rates of the diffusion RM are derived explicitly.

math.OC↗