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Zhiyong Sun

Publications and source records attributed to Zhiyong Sun.

At least 55 records · Page 3Linked to original sources
arXiv2023

A time-varying matrix solution to the Brockett decentralized stabilization problem

This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product $CB$ is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix $K(t)$ such that the closed-loop minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix $K(t)$) and a comparison study are also provided.

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arXiv2023

Characterizing bearing equivalence in directed graphs

In this paper, we study bearing equivalence in directed graphs. We first give a strengthened definition of bearing equivalence based on the \textit{kernel equivalence} relationship between bearing rigidity matrix and bearing Laplacian matrix. We then present several conditions to characterize bearing equivalence for both directed acyclic and cyclic graphs. These conditions involve the spectrum and null space of the associated bearing Laplacian matrix for a directed bearing formation. For directed acyclic graphs, all eigenvalues of the associated bearing Laplacian are real and nonnegative, while for directed graphs containing cycles, the bearing Laplacian can have eigenvalues with negative real parts. Several examples of bearing equivalent and bearing non-equivalent formations are given to illustrate these conditions.

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arXiv2023

Modelling and Kron reduction of power flow networks in directed graphs

Electrical grids are large-sized complex systems that require strong computing power for monitoring and analysis. Kron reduction is a general reduction method in graph theory and is often used for electrical circuit simplification. In this paper, we propose a novel formulation of the weighted Laplacian matrix for directed graphs. The proposed matrix is proved to be strictly equivalent to the conventionally formulated Laplacian matrix and is verified to well model a lossless DC power flow network in directed graphs. We as well present significant properties of the proposed weighted Laplacian and conditions of Kron reduction in directed graphs and in lossless DC power flow networks. The reduction method is verified via simulation models of IEEE-3, IEEE-5, IEEE-9, IEEE-14, and IEEE RTS-96 test systems.

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arXiv2022

Optimal control of nonlinear systems with unsymmetrical input constraints and its applications to the UAV circumnavigation problem

In this paper, a novel design scheme is introduced to solve the optimal control problem for nonlinear systems with unsymmetrical and state-dependent input constraints. By introducing an initial stabilizing control policy as the baseline of the constructed optimal control policy, we remove the assumption in the current study for the adaptive optimal control, that is, the internal dynamics should hold zero when the state of the system is in the origin. Particularly, nonlinear control systems with partially-unknown dynamics are investigated and the procedure to acquire the corresponding optimal control policy is presented. The stability for the closed-loop dynamics and the optimality of the obtained control policy are both proved. Besides, we apply the proposed control design framework to solve the optimal circumnavigation problem based on the accumulative Fisher information for a fixed-wing unmanned aerial vehicle (UAV). The control performance of our algorithm is compared with that of the existing circumnavigation control policy in a numerical simulation.

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arXiv2022

Leveraging second-order information for tuning of inverse optimal controllers

We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov function of the closed-loop dynamics. This draws a link between second-order methods known for their high speed of convergence and the tuning of inverse optimal stabilizing controllers to achieve a fast decay of the closed-loop trajectories towards a steady state. In particular, we ensure quadratic convergence, a feat that is otherwise not achieved with a constant input penalty matrix. To balance trade-offs, we suggest a practical implementation of the Hessian and validate this numerically on a network of phase-coupled oscillators that represent voltage source controlled power inverters.

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arXiv2022

Relay Hindsight Experience Replay: Self-Guided Continual Reinforcement Learning for Sequential Object Manipulation Tasks with Sparse Rewards

Exploration with sparse rewards remains a challenging research problem in reinforcement learning (RL). Especially for sequential object manipulation tasks, the RL agent always receives negative rewards until completing all sub-tasks, which results in low exploration efficiency. To solve these tasks efficiently, we propose a novel self-guided continual RL framework, RelayHER (RHER). RHER first decomposes a sequential task into new sub-tasks with increasing complexity and ensures that the simplest sub-task can be learned quickly by utilizing Hindsight Experience Replay (HER). Secondly, we design a multi-goal & multi-task network to learn these sub-tasks simultaneously. Finally, we propose a Self-Guided Exploration Strategy (SGES). With SGES, the learned sub-task policy will guide the agent to the states that are helpful to learn more complex sub-task with HER. By this self-guided exploration and relay policy learning, RHER can solve these sequential tasks efficiently stage by stage. The experimental results show that RHER significantly outperforms vanilla-HER in sample-efficiency on five singleobject and five complex multi-object manipulation tasks (e.g., Push, Insert, ObstaclePush, Stack, TStack, etc.). The proposed RHER has also been applied to learn a contact-rich push task on a physical robot from scratch, and the success rate reached 10/10 with only 250 episodes.

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arXiv2022

Guiding vector fields for the distributed motion coordination of mobile robots

We propose coordinating guiding vector fields to achieve two tasks simultaneously with a team of robots: first, the guidance and navigation of multiple robots to possibly different paths or surfaces typically embedded in 2D or 3D; second, their motion coordination while tracking their prescribed paths or surfaces. The motion coordination is defined by desired parametric displacements between robots on the path or surface. Such a desired displacement is achieved by controlling the virtual coordinates, which correspond to the path or surface's parameters, between guiding vector fields. Rigorous mathematical guarantees underpinned by dynamical systems theory and Lyapunov theory are provided for the effective distributed motion coordination and navigation of robots on paths or surfaces from all initial positions. As an example for practical robotic applications, we derive a control algorithm from the proposed coordinating guiding vector fields for a Dubins-car-like model with actuation saturation. Our proposed algorithm is distributed and scalable to an arbitrary number of robots. Furthermore, extensive illustrative simulations and fixed-wing aircraft outdoor experiments validate the effectiveness and robustness of our algorithm.

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arXiv2022

Cooperative constrained motion coordination of networked heterogeneous vehicles

We consider the problem of cooperative motion coordination for multiple heterogeneous mobile vehicles subject to various constraints. These include nonholonomic motion constraints, constant speed constraints, holonomic coordination constraints, and equality/inequality geometric constraints. We develop a general framework involving differential-algebraic equations and viability theory to determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination task constraints. If a coordinated motion solution exists for the derived differential-algebraic equations and/or inequalities, a constructive algorithm is proposed to derive an equivalent dynamical system that generates a set of feasible coordinated motions for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. The motion generation algorithm is well-backed by simulation data for a wide variety of coordination situations involving heterogeneous vehicles. We then extend the vehicle control framework to deal with the cooperative coordination problem with time-varying coordination tasks and leader-follower structure. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.

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arXiv2021

Quadrotor Control on $SU(2)\times R^3$ with SLAM Integration

We present a trajectory tracking controller for a quadrotor unmanned aerial vehicle (UAV) configured on $SU(2)\times R^3$, and relate this result to a family of geometric tracking controllers on $SO(3)\times R^3$. The theoretical results are complemented by simulation examples, and the controller is subsequently implemented in practice and integrated with a simultaneous localization and mapping (SLAM) system through an extended Kalman filter (EKF). This facilitates the operation of the UAV without external motion capture systems, and we demonstrate that the proposed control system can be used for inventorying tasks in a supermarket environment without external positioning systems.

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arXiv2021

Steady state characterization and frequency synchronization of a multi-converter power system on high-order manifolds

We investigate the stability properties of a multi-converter power system model, defined on a high-order manifold. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of AC signals. We characterize the steady state set, primarily determined by the steady state angles and DC power input. Based on eigenvalue conditions of its Jacobian matrix, we show asymptotic stability of the multi-converter system in a neighborhood of the synchronous steady state set by applying the center manifold theory. We guarantee the eigenvalue conditions via an explicit approach. Finally, we demonstrate our results based on a numerical example involving a network of identical DC/AC converter systems.

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arXiv2021

Distributed adaptive stabilization

In this paper we consider distributed adaptive stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that uncertain multivariable linear systems are stabilizable by diagonal matrix high gains if the system matrix is an H-matrix with positive diagonal entries. Based on matrix measure and stability theory for diagonally dominant systems, we consider two classes of uncertain linear systems, and derive a threshold condition to ensure their exponential stability by a monotonically increasing diagonal gain matrix. When each individual gain function in the matrix gain is updated by state-dependent functions using only local state information, the boundedness and convergence of both system states and adaptive matrix gains are guaranteed. We apply the adaptive distributed stabilization approach to adaptive synchronization control for large-scale complex networks consisting of nonlinear node dynamics and time-varying coupling weights. A unified framework for adaptive synchronization is proposed that includes several general design approaches for adaptive coupling weights to guarantee network synchronization.

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arXiv2021

Distributed coordinated path following using guiding vector fields

It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating their motions. The vector field uses a path parameter as a virtual coordinate that is communicated among neighboring robots. Then, the virtual coordinate is utilized to control the relative parametric displacement between robots along the paths. This enables us to design a saturated control algorithm for a Dubins-car-like model. The algorithm is distributed, scalable, and applicable for any smooth paths in an $n$-dimensional configuration space, and global convergence is guaranteed. Simulations with up to fifty robots and outdoor experiments with fixed-wing aircraft validate the theoretical results.

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arXiv2021

Distributed learning for optimal allocation of synchronous and converter-based generation

Motivated by the penetration of converter-based generation into the electrical grid, we revisit the classical log-linear learning algorithm for optimal allocation {of synchronous machines and converters} for mixed power generation. The objective is to assign to each generator unit a type (either synchronous machine or DC/AC converter in closed-loop with droop control), while minimizing the steady state angle deviation relative to an optimum induced by unknown optimal configuration of synchronous and DC/AC converter-based generation. Additionally, we study the robustness of the learning algorithm against a uniform drop in the line susceptances and with respect to a well-defined feasibility region describing admissible power deviations. We show guaranteed probabilistic convergence to maximizers of the perturbed potential function with feasible power flows and demonstrate our theoretical findings via simulative examples of power network with six generation units.

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arXiv2020

Grid-forming lambda-omega virtual oscillator control in converter-based power systems

Inspired by the kinetics of wave phenomena in reaction-diffusion models of biological systems, we propose a novel grid-forming control strategy for control of three-phase DC/AC converters in power systems. The ($λ-ω$) virtual oscillator control or (lambda-omega) VOC is a natural increment on ideas from virtual oscillator dynamics rotating at a fixed nominal frequency to adaptive, angle-based frequency function. We study a network of identical three-phase DC/AC converters interconnected via $Π$ transmission lines. For this, we prove almost global asymptotic stability for a reduced (time-scale separated) version of the model, associated to a well-defined set of controller gains and system parameters. Additionally, we link the (λ-ω) VOC to well-studied controllers in the literature, e.g. droop control. Finally, we validate our results on an example three DC/AC converter network.

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arXiv2020

Collaborative Target Tracking in Elliptic Coordinates: a Binocular Coordination Approach

This paper concentrates on the collaborative target tracking control of a pair of tracking vehicles with formation constraints. The proposed controller requires only distance measurements between tracking vehicles and the target. Its novelty lies in two aspects: 1) the elliptic coordinates are used to represent an arbitrary tracking formation without singularity, which can be deduced from inter-agent distances, and 2) the regulation of the tracking vehicle system obeys a binocular coordination principle, which simplifies the design of the control law by leveraging rich physical meanings of elliptic coordinates. The tracking system with the proposed controller is proven to be exponentially convergent when the target is stationary. When the target drifts with a small velocity, the desired tracking formation is achieved within a small margin proportional to the magnitude of the target's drift velocity. Simulation examples are provided to demonstrate the tracking performance of the proposed controller.

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