arXiv subjects

Zirui Niu

Publications and source records attributed to Zirui Niu.

5 recordsLinked to original sources

arXiv2026

On the Solvability of Quasi-Regulator Equations in Non-smooth Output Regulation

Motivated by the prevalence of non-smooth, possibly non-periodic signals in real-world applications, the output regulation of linear systems subject to non-smooth non-periodic exogenous signals has emerged as a challenging problem. A fundamental prerequisite for solving this problem is the existence of solutions to the so-called ``quasi-regulator equations''. In this paper, we investigate the solvability of these equations. To this end, we reformulate the quasi-regulator equations as differential-algebraic equations and highlight the critical role played by the system's relative degree. We finally propose a ``non-smooth non-resonance condition'' that, under specific relative degree requirements, provides a necessary and sufficient characterization of the solvability of the quasi-regulator equations.

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arXiv2026

Approximate Simulation-based Hierarchical Control of Nonlinear Systems

Controlling complex dynamical systems to satisfy sophisticated specifications remains a significant challenge in modern engineering. A promising approach to this problem is the approximate simulation-based hierarchical control (ASHC) technique. In this method, a simplified representation of the complex system, called the abstract system, is first designed and controlled. An interface function is then designed to translate the control law into the input of the complex system, thereby achieving approximate control synthesis. However, most existing results in ASHC are only for linear systems. This paper proposes a constructive method for solving the ASHC problem for nonlinear systems. To this end, we propose invariance equation-based methods to achieve the two classical requirements of the ASHC technique, namely the bounded output discrepancy and the $m$-relation. We then study the solvability conditions of the problem and summarise the overall design procedures. We illustrate the results with a practical example, providing step-by-step solutions to the ASHC problem of a DC-to-DC \'Cuk converter.

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arXiv2026

Interconnection-based Model Reduction for Linear Hybrid Systems

In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in the hybrid setting, and we present families of reduced-order models for each interconnection via a hybrid characterisation of the steady-state responses. By combining the results for each interconnection, the design of a reduced-order model that achieves moment matching simultaneously for both interconnections is studied. In addition, we show that the presented results have simplified counterparts when the jumps of the hybrid system are periodic. A numerical simulation is finally given to illustrate the results.

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arXiv2025

Bridging Abstraction-Based Hierarchical Control and Moment Matching: A Conceptual Unification

In this paper, we establish a relation between approximate-simulation-based hierarchical control (ASHC) and moment matching techniques, and build a conceptual bridge between these two frameworks. To this end, we study the two key requirements of the ASHC technique, namely the bounded output discrepancy and the $M$-relation, through the lens of moment matching. We show that, in the linear time-invariant case, both requirements can be interpreted in the moment matching perspective through certain system interconnection structures. Building this conceptual bridge provides a foundation for cross-pollination of ideas between these two frameworks.

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arXiv2025

Output Regulation of Linear Systems with Non-periodic Non-smooth Exogenous Signals

We address the output regulation problem of linear systems with non-smooth and non-periodic exogenous signals. Specifically, we first formulate and solve the full-information problem by designing a state-feedback controller. We study the solvability of the regulator equations, providing a new non-resonance condition. We then focus on the error-feedback problem, for which we design a (non-robust) internal model leveraging the concept of canonical realisation and applying a high-gain method for the stabilisation of the closed-loop system under the minimum-phase assumption. Finally, we study the regulation problem involving model parameter uncertainties. Drawing ideas from both hybrid and time-varying (smooth) output regulation, we propose two methods to establish an internal model that is robust to uncertainties. The first method is an extension of the hybrid internal model, while the second relies on a new concept of immersion. In this non-smooth case, the immersion is established based on integrals rather than derivatives. The effectiveness of the proposed solutions is illustrated by a circuit regulation example.

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