arXiv subjects

Kanghong Shi

Publications and source records attributed to Kanghong Shi.

At least 19 recordsLinked to original sources

arXiv2026

Absolute Stability of Nonlinear Negative Imaginary Systems with Application to Potential Energy Shaping

This paper establishes absolute stability conditions for nonlinear negative imaginary (NI) systems interconnected with static nonlinear feedback. We first show that the NI property is preserved when the feedback nonlinearity can be expressed as the gradient of a continuously differentiable function, and the composite storage of the resulting system remains positive definite. This condition provides a direct connection between nonlinear static feedback and storage-function shaping along the measured output channels. Building on this result, conditions are derived for absolute stability of the closed-loop system under mild assumptions. The linear specialization of the results strictly generalizes prior absolute stability results for linear NI systems, allowing coupled nonlinearities not covered by existing slope-restricted or sector-bounded frameworks. Finally, the proposed theory is illustrated through a linear example highlighting this generalization and a nonlinear example that shows the utility of the proposed results in potential energy shaping.

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arXiv2026

Digital Control of Negative Imaginary Systems Using Discrete-Time Multi-HIGS: Application to a Dual-Stage MEMS Force Sensor

In this paper, we propose a digital control approach for multi-input multi-output negative imaginary (NI) systems using discrete-time hybrid integrator-gain systems (HIGS) controllers. We show the NI property of the bimodal and trimodal discrete-time HIGS, as well as the parallel combinations of them, which are referred to as the multi-HIGS. Also, we demonstrate that linear NI systems can be asymptotically stabilized using discrete-time HIGS in digital control. We apply discrete-time bimodal and trimodal multi-HIGS controllers to a two-input two-output dual-stage force sensor with lightly damped resonant modes. To validate the theoretical findings, the closed-loop performance is evaluated in both time and frequency domains. Experimental results show that the discrete-time multi-HIGS effectively suppresses resonances while preserving favorable phase characteristics, which highlights its potential as a robust nonlinear NI controller for the digital control of NI systems.

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arXiv2025

Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees

We propose a neural control method to provide guaranteed stabilization for mechanical systems using a novel negative imaginary neural ordinary differential equation (NINODE) controller. Specifically, we employ neural networks with desired properties as state-space function matrices within a Hamiltonian framework to ensure the system possesses the NI property. This NINODE system can serve as a controller that asymptotically stabilizes an NI plant under certain conditions. For mechanical plants with colocated force actuators and position sensors, we demonstrate that all the conditions required for stability can be translated into regularity constraints on the neural networks used in the controller. We illustrate the utility, effectiveness, and stability guarantees of the NINODE controller through an example involving a nonlinear mass-spring system.

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arXiv2024

Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems

We introduce a hybrid control system called a hybrid integrator-gain system (HIGS) based integral resonant controller (IRC) to stabilize negative imaginary (NI) systems. A HIGS-based IRC has a similar structure to an IRC, with the integrator replaced by a HIGS. We show that a HIGS-based IRC is an NI system. Also, for a SISO NI system with a minimal realization, we show there exists a HIGS-based IRC such that their closed-loop interconnection is asymptotically stable. Also, we propose a proportional-integral-double-integral resonant controller and a HIGS-based proportional-integral-double-integral resonant controller, and we show that both of them can be applied to asymptotically stabilize an NI system. An example is provided to illustrate the proposed results.

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arXiv2024

On the Stability of Networked Nonlinear Negative Imaginary Systems with Applications to Electrical Power Systems

In the transition to achieving net zero emissions, it has been suggested that a substantial expansion of electric power grids will be necessary to support emerging renewable energy zones. In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Luré-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time.

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arXiv2024

Discrete-time Integral Resonant Control of Negative Imaginary Systems: Application to a High-speed Nanopositioner

We propose a discrete-time integral resonant control (IRC) approach for negative imaginary (NI) systems, which overcomes several limitations of continuous-time IRC. We show that a discrete-time IRC has a step-advanced negative imaginary property. A zero-order hold-sampled NI system can be asymptotically stabilized using a discrete-time IRC with suitable parameters. A hardware experiment is conducted where a high-speed flexure-guided nanopositioner is efficiently damped using the proposed discrete-time IRC with the discrete-time controller being implemented in FPGA hardware at the sampling rate of 1.25 MHz.

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arXiv2024

Discrete-time Negative Imaginary Systems from ZOH Sampling

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case.

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arXiv2024

Unified Control of Voltage, Frequency and Angle in Electrical Power Systems: A Passivity and Negative-Imaginary based Approach

This paper proposes a unified methodology for voltage regulation, frequency synchronization, and rotor angle control in power transmission systems considering a one-axis generator model with time-varying voltages. First, we formulate an output consensus problem with a passivity and negative-imaginary (NI) based control framework. We establish output consensus results for both networked passive systems and networked NI systems. Next, we apply the output consensus problem by controlling large-scale batteries co-located with synchronous generators -- using real-time voltage phasor measurements. By controlling the battery storage systems so as to dispatch real and reactive power, we enable simultaneous control of voltage, frequency, and power angle differences across a transmission network. Validation through numerical simulations on a four-area transmission network confirms the robustness of our unified control framework.

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arXiv2024

Digital control of negative imaginary systems: a discrete-time hybrid integrator-gain system approach

A hybrid integrator-gain system (HIGS) is a control element that switches between an integrator and a gain, which overcomes some inherent limitations of linear controllers. In this paper, we consider using discrete-time HIGS controllers for the digital control of negative imaginary (NI) systems. We show that the discrete-time HIGS themselves are step-advanced negative imaginary systems. For a minimal linear NI system, there always exists a HIGS controller that can asymptotically stablize it. An illustrative example is provided, where we use the proposed HIGS control method to stabilize a discrete-time mass-spring system.

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arXiv2023

A Nonlinear Negative Imaginary Systems Framework with Actuator Saturation for Control of Electrical Power Systems

In the transition to net zero, it has been suggested that a massive expansion of the electric power grid will be required to support emerging renewable energy zones. In this paper, we propose the use of battery-based feedback control and nonlinear negative imaginary systems theory to reduce the need for such an expansion by enabling the more complete utilization of existing grid infrastructure. By constructing a novel Lur'e-Postnikov-like Lyapunov function, a stability result is developed for the feedback interconnection of a nonlinear negative imaginary system and a nonlinear negative imaginary controller. Additionally, a new class of nonlinear negative imaginary controllers is proposed to deal with actuator saturation. We show that in this control framework, the controller eventually leaves the saturation boundary, and the feedback system is locally stable in the sense of Lyapunov. This provides theoretical support for the application of battery-based control in electrical power systems. Validation through simulation results for single-machine-infinite-bus power systems supports our results. Our approach has the potential to enable a transmission line to operate at its maximum power capacity, as stability robustness is ensured by the use of a feedback controller.

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arXiv2023

Negative Imaginary Control Using Hybrid Integrator-Gain Systems: Application to MEMS Nanopositioner

In this paper, we propose a new approach to address the control problem for negative imaginary (NI) systems by using hybrid integrator-gain systems (HIGS). We investigate the single HIGS of its original form and its two variations, including a multi-HIGS and the serial cascade of two HIGS. A single HIGS is shown to be a nonlinear negative imaginary system, and so is the multi-HIGS and the cascade of two HIGS. We show that these three types of HIGS can be used as controllers to asymptotically stabilize linear NI systems. The results of this paper are then illustrated in a real-world experiment where a 2-DOF microelectromechanical system nanopositioner is stabilized by a multi-HIGS.

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arXiv2023

Nonlinear Negative Imaginary Systems with Switching

In this paper, we extend nonlinear negative imaginary (NI) systems theory to switched systems. Switched nonlinear NI systems and switched nonlinear output strictly negative imaginary (OSNI) systems are defined. We show that the interconnection of two switched nonlinear NI systems is still switched nonlinear NI. The interconnection of a switched nonlinear NI system and a switched nonlinear OSNI system is asymptotically stable under some assumptions. This stability result is then illustrated using a numerical example.

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arXiv2023

A negative imaginary approach to hybrid integrator-gain system control

In this paper, we show that a hybrid integrator-gain system (HIGS) is a nonlinear negative imaginary (NNI) system. We prove that the positive feedback interconnection of a linear negative imaginary (NI) system and a HIGS is asymptotically stable. We apply the HIGS to a MEMS nanopositioner, as an example of a linear NI system, in a single-input single-output framework. We analyze the stability and the performance of the closed-loop interconnection in both time and frequency domains through simulations and demonstrate the applicability of HIGS as an NNI controller to a linear NI system.

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arXiv2022

Making Nonlinear Systems Negative Imaginary via State Feedback

This paper provides a state feedback stabilization approach for nonlinear systems of relative degree less than or equal to two by rendering them nonlinear negative imaginary (NI) systems. Conditions are provided under which a nonlinear system can be made a nonlinear NI system or a nonlinear output strictly negative imaginary (OSNI) system. Roughly speaking, an affine nonlinear system that has a normal form with relative degree less than or equal to two, after possible output transformation, can be rendered nonlinear NI and nonlinear OSNI. In addition, if the internal dynamics of the normal form are input-to-state stable, then there exists a state feedback input that stabilizes the system. This stabilization result is then extended to achieve stability for systems with a nonlinear NI uncertainty.

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arXiv2022

Negative Imaginary State Feedback Equivalence for a Class of Nonlinear Systems

In this paper, we investigate the necessary and sufficient conditions under which a class of nonlinear systems are state feedback equivalent to nonlinear negative imaginary (NI) systems with positive definite storage functions. The nonlinear systems of interest have a normal form of relative degree less than or equal to two. The nonlinearity of the system is restricted with respect to a subset of the state variables, which are the state variables that have external dynamics. Under mild assumptions, such systems are state feedback equivalent to nonlinear NI systems and nonlinear output strictly negative imaginary (OSNI) systems if and only if they are weakly minimum phase. Such a state feedback control approach can also asymptotically stabilize the systems in question against nonlinear OSNI system uncertainties. A numerical example is provided to show the process of the state feedback equivalence control and stabilization of uncertain systems.

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arXiv2021

Negative Imaginary State Feedback Equivalence for Systems of Relative Degree One and Relative Degree Two

This paper presents necessary and sufficient conditions under which a linear system of relative degree either one or two is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show for a class of linear time-invariant strictly proper systems, that such a system can be rendered minimal and NI using full state feedback if and only if it is controllable and weakly minimum phase. A strongly strict negative imaginary state feedback equivalence result is also provided. The NI state feedback equivalence result is then applied in a robust stabilization problem for an uncertain system with a strictly negative imaginary uncertainty.

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arXiv2021

Necessary and Sufficient Conditions for State Feedback Equivalence to Negative Imaginary Systems

In this paper, we present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. We also considered the problems of state feedback equivalence to output strictly negative imaginary systems and strongly strict negative imaginary systems. Then we apply the NI state feedback equivalence result to robustly stabilize an uncertain system with strictly negative imaginary uncertainty. An example is provided to illustrate the proposed results, for the purpose of stabilizing an uncertain system.

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arXiv2021

Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems with Free Body Motion

This paper provides a protocol to address the robust output feedback consensus problem for networked heterogeneous nonlinear negative-imaginary (NI) systems with free body dynamics. We extend the definition of nonlinear NI systems to allow for systems with free body motion. A new stability result is developed for the interconnection of a nonlinear NI system and a nonlinear output strictly negative-imaginary (OSNI) system. Also, a class of networked nonlinear OSNI controllers is proposed to achieve output feedback consensus for heterogeneous networked nonlinear NI systems. We show that in this control framework, the system outputs converge to the same limit trajectory. This consensus protocol is illustrated by a numerical example.

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