arXiv subjects

Tong Heng Lee

Publications and source records attributed to Tong Heng Lee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Second-Order Non-Convex Optimization for Constrained Fixed-Structure Static Output Feedback Controller Synthesis

For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly garners much attention and interest. As is well-known, standard numerical tools in linear algebra are readily available which enable the determination of the optimal static LQR feedback gain matrix when all the system state variables are measurable. However, in various certain scenarios where some of the system state variables are not measurable, and consequent prescribed structural constraints on the controller structure arise, the optimization problem can become intractable due to the non-convexity characteristics that can then be present. In such cases, there have been some first-order methods proposed to cater to these problems, but all of these first-order optimization methods, if at all successful, are limited to only linear convergence. To speed up the convergence, a second-order approach in the matrix space is essential, with appropriate methodology to solve the linear equality constrained static output feedback (SOF) problem with a suitably defined linear quadratic cost function. Thus along this line, in this work, an efficient method is proposed in the matrix space to calculate the Hessian matrix by solving several Lyapunov equations. Then a new optimization technique is applied to deal with the indefiniteness of the Hessian matrix. Subsequently, through Newton's method with linear equality constraints, a second-order optimization algorithm is developed to effectively solve the constrained SOF LQR problem. Finally, two numerical examples are described which demonstrate the applicability and effectiveness of the proposed method.

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arXiv2022

Incremental Few-Shot Object Detection for Robotics

Incremental few-shot learning is highly expected for practical robotics applications. On one hand, robot is desired to learn new tasks quickly and flexibly using only few annotated training samples; on the other hand, such new additional tasks should be learned in a continuous and incremental manner without forgetting the previous learned knowledge dramatically. In this work, we propose a novel Class-Incremental Few-Shot Object Detection (CI-FSOD) framework that enables deep object detection network to perform effective continual learning from just few-shot samples without re-accessing the previous training data. We achieve this by equipping the widely-used Faster-RCNN detector with three elegant components. Firstly, to best preserve performance on the pre-trained base classes, we propose a novel Dual-Embedding-Space (DES) architecture which decouples the representation learning of base and novel categories into different spaces. Secondly, to mitigate the catastrophic forgetting on the accumulated novel classes, we propose a Sequential Model Fusion (SMF) method, which is able to achieve long-term memory without additional storage cost. Thirdly, to promote inter-task class separation in feature space, we propose a novel regularization technique that extends the classification boundary further away from the previous classes to avoid misclassification. Overall, our framework is simple yet effective and outperforms the previous SOTA with a significant margin of 2.4 points in AP performance.

cs.CV↗

arXiv2022

Velocity Obstacle Based Risk-Bounded Motion Planning for Stochastic Multi-Agent Systems

In this paper, we present an innovative risk-bounded motion planning methodology for stochastic multi-agent systems. For this methodology, the disturbance, noise, and model uncertainty are considered; and a velocity obstacle method is utilized to formulate the collision-avoidance constraints in the velocity space. With the exploitation of geometric information of static obstacles and velocity obstacles, a distributed optimization problem with probabilistic chance constraints is formulated for the stochastic multi-agent system. Consequently, collision-free trajectories are generated under a prescribed collision risk bound. Due to the existence of probabilistic and disjunctive constraints, the distributed chance-constrained optimization problem is reformulated as a mixed-integer program by introducing the binary variable to improve computational efficiency. This approach thus renders it possible to execute the motion planning task in the velocity space instead of the position space, which leads to smoother collision-free trajectories for multi-agent systems and higher computational efficiency. Moreover, the risk of potential collisions is bounded with this robust motion planning methodology. To validate the effectiveness of the methodology, different scenarios for multiple agents are investigated, and the simulation results clearly show that the proposed approach can generate high-quality trajectories under a predefined collision risk bound and avoid potential collisions effectively in the velocity space.

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arXiv2021

Convex Parameterization and Optimization for Robust Tracking of a Magnetically Levitated Planar Positioning System

Magnetic levitation positioning technology has attracted considerable research efforts and dedicated attention due to its extremely attractive features. The technology offers high-precision, contactless, dust/lubricant-free, multi-axis, and large-stroke positioning. In this work, we focus on the accurate and smooth tracking problem of a multi-axis magnetically levitated (maglev) planar positioning system for a specific S-curve reference trajectory. The floating characteristics and the multi-axis coupling make accurate identification of the system dynamics difficult, which lead to a challenge to design a high performance control system. Here, the tracking task is achieved by a 2-Degree of Freedom (DoF) controller consisting of a feedforward controller and a robust stabilizing feedback controller with a prescribed sparsity pattern. The approach proposed in this paper utilizes the basis of an H-infinity controller formulation and a suitably established convex inner approximation. Particularly, a subset of robust stabilizable controllers with prescribed structural constraints is characterized in the parameter space, and so thus the re-formulated convex optimization problem can be easily solved by several powerful numerical algorithms and solvers. With this approach, the robust stability of the overall system is ensured with a satisfactory system performance despite the presence of parametric uncertainties. Furthermore, experimental results clearly demonstrate the effectiveness of the proposed approach.

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arXiv2021

Towards Generalized and Incremental Few-Shot Object Detection

Real-world object detection is highly desired to be equipped with the learning expandability that can enlarge its detection classes incrementally. Moreover, such learning from only few annotated training samples further adds the flexibility for the object detector, which is highly expected in many applications such as autonomous driving, robotics, etc. However, such sequential learning scenario with few-shot training samples generally causes catastrophic forgetting and dramatic overfitting. In this paper, to address the above incremental few-shot learning issues, a novel Incremental Few-Shot Object Detection (iFSOD) method is proposed to enable the effective continual learning from few-shot samples. Specifically, a Double-Branch Framework (DBF) is proposed to decouple the feature representation of base and novel (few-shot) class, which facilitates both the old-knowledge retention and new-class adaption simultaneously. Furthermore, a progressive model updating rule is carried out to preserve the long-term memory on old classes effectively when adapt to sequential new classes. Moreover, an inter-task class separation loss is proposed to extend the decision region of new-coming classes for better feature discrimination. We conduct experiments on both Pascal VOC and MS-COCO, which demonstrate that our method can effectively solve the problem of incremental few-shot detection and significantly improve the detection accuracy on both base and novel classes.

cs.CV↗

arXiv2021

Improved Hierarchical ADMM for Nonconvex Cooperative Distributed Model Predictive Control

Distributed optimization is often widely attempted and innovated as an attractive and preferred methodology to solve large-scale problems effectively in a localized and coordinated manner. Thus, it is noteworthy that the methodology of distributed model predictive control (DMPC) has become a promising approach to achieve effective outcomes, e.g., in decision-making tasks for multi-agent systems. However, the typical deployment of such distributed MPC frameworks would lead to the involvement of nonlinear processes with a large number of nonconvex constraints. To address this important problem, the development and innovation of a hierarchical three-block alternating direction method of multipliers (ADMM) approach is presented in this work to solve this nonconvex cooperative DMPC problem in multi-agent systems. Here firstly, an additional slack variable is introduced to transform the original large-scale nonconvex optimization problem. Then, a hierarchical ADMM approach, which contains outer loop iteration by the augmented Lagrangian method (ALM) and inner loop iteration by three-block semi-proximal ADMM, is utilized to solve the resulting transformed nonconvex optimization problem. Additionally, it is analytically shown and established that the requisite desired stationary point exists for convergence in the algorithm. Finally, an approximate optimization stage with a barrier method is then applied to further significantly improve the computational efficiency, yielding the final improved hierarchical ADMM. The effectiveness of the proposed method in terms of attained performance and computational efficiency is demonstrated on a cooperative DMPC problem of decision-making process for multiple unmanned aerial vehicles (UAVs).

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arXiv2021

Global Iterative Sliding Mode Control of an Industrial Biaxial Gantry System for Contouring Motion Tasks

This paper proposes a global iterative sliding mode control approach for high-precision contouring tasks of a flexure-linked biaxial gantry system. For such high-precision contouring tasks, it is the typical situation that the involved multi-axis cooperation is one of the most challenging problems. As also would be inevitably encountered, various factors render the multi-axis cooperation rather difficult; such as the strong coupling (which naturally brings nonlinearity) between different axes due to its mechanical structure, the backlash and deadzone caused by the friction, and the difficulties in system identification, etc. To overcome the above-mentioned issues, this work investigates an intelligent model-free contouring control method for such a multi-axis motion stage. Essentially in the methodology developed here, it is firstly ensured that all the coupling, friction, nonlinearity, and disturbance (regarded as uncertain dynamics in each axis) are suitably posed as `uncertainties'. Then, a varying-gain sliding mode control method is proposed to adaptively compensate for the matched unknown dynamics in the time domain, while an iterative learning law is applied to suppress the undesirable effects (arising from the repetitive matched and unmatched uncertainties in the iteration domain). With this approach, the chattering that typically results from the overestimated control gains in the sliding mode control is thus suppressed during the iterations. To analyze the contouring performance and show the improved outcomes, rigorous proof is furnished on both the stability in the time domain and the convergence in the iteration domain; and the real-time experiments also illustrate that the requirements of precision motion control towards high-speed and complex-curvature references can be satisfied using the proposed method, without prior knowledge of the boundary to the unknown dynamics.

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arXiv2021

Receding Horizon Motion Planning for Multi-Agent Systems: A Velocity Obstacle Based Probabilistic Method

In this paper, a novel and innovative methodology for feasible motion planning in the multi-agent system is developed. On the basis of velocity obstacles characteristics, the chance constraints are formulated in the receding horizon control (RHC) problem, and geometric information of collision cones is used to generate the feasible regions of velocities for the host agent. By this approach, the motion planning is conducted at the velocity level instead of the position level. Thus, it guarantees a safer collision-free trajectory for the multi-agent system, especially for the systems with high-speed moving agents. Moreover, a probability threshold of potential collisions can be satisfied during the motion planning process. In order to validate the effectiveness of the methodology, different scenarios for multiple agents are investigated, and the simulation results clearly show that the proposed approach can effectively avoid potential collisions with a collision probability less than a specific threshold.

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arXiv2021

Generalized Iterative Super-Twisting Sliding Mode Control: A Case Study on Flexure-Joint Dual-Drive H-Gantry Stage

Mechatronic systems are commonly used in the industry, where fast and accurate motion performance is always required to guarantee manufacturing precision and efficiency. Nevertheless, the system model and parameters are difficult to be obtained accurately. Moreover, the high-order modes, strong coupling in the multi-axis systems, or unmodeled frictions will bring uncertain dynamics to the system. To overcome the above-mentioned issues and enhance the motion performance, this paper introduces a novel intelligent and totally model-free control method for mechatronic systems with unknown dynamics. In detail, a 2-degree-of-freedom (DOF) architecture is designed, which organically merges a generalized super-twisting algorithm with a unique iterative learning law. The controller solely utilizes the input-output data collected in iterations such that it works without any knowledge of the system parameters. The rigorous proof of convergence ability is given and a case study on flexture-joint dual-drive H-gantry stage is shown to validate the effectiveness of the proposed method.

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arXiv2021

Optimal Decentralized Control for Uncertain Systems by Symmetric Gauss-Seidel Semi-Proximal ALM

The H2 guaranteed cost decentralized control problem is investigated in this work. More specifically, on the basis of an appropriate H2 re-formulation that we put in place, the optimal control problem in the presence of parameter uncertainties is then suitably characterized by convex restriction and solved in parameter space. It is shown that a set of stabilizing decentralized controller gains for the uncertain system is parameterized in a convex set through appropriate convex restriction, and then an approximated conic optimization problem is constructed. This facilitates the use of the symmetric Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which attains high computational effectiveness. A comprehensive analysis is given on the application of the approach in solving the optimal decentralized control problem; and subsequently, the preserved decentralized structure, robust stability, and robust performance are all suitably guaranteed with the proposed methodology. Furthermore, an illustrative example is presented to demonstrate the effectiveness of the proposed optimization approach.

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arXiv2021

Semi-Definite Relaxation Based ADMM for Cooperative Planning and Control of Connected Autonomous Vehicles

This paper investigates the cooperative planning and control problem for multiple connected autonomous vehicles (CAVs) in different scenarios. In the existing literature, most of the methods suffer from significant problems in computational efficiency. Besides, as the optimization problem is nonlinear and nonconvex, it typically poses great difficultly in determining the optimal solution. To address this issue, this work proposes a novel and completely parallel computation framework by leveraging the alternating direction method of multipliers (ADMM). The nonlinear and nonconvex optimization problem in the autonomous driving problem can be divided into two manageable subproblems; and the resulting subproblems can be solved by using effective optimization methods in a parallel framework. Here, the differential dynamic programming (DDP) algorithm is capable of addressing the nonlinearity of the system dynamics rather effectively; and the nonconvex coupling constraints with small dimensions can be approximated by invoking the notion of semi-definite relaxation (SDR), which can also be solved in a very short time. Due to the parallel computation and efficient relaxation of nonconvex constraints, our proposed approach effectively realizes real-time implementation and thus also extra assurance of driving safety is provided. In addition, two transportation scenarios for multiple CAVs are used to illustrate the effectiveness and efficiency of the proposed method.

cs.MA↗

arXiv2020

On Robust Stability and Performance with a Fixed-Order Controller Design for Uncertain Systems

Typically, it is desirable to design a control system that is not only robustly stable in the presence of parametric uncertainties but also guarantees an adequate level of system performance. However, most of the existing methods need to take all extreme models over an uncertain domain into consideration, which then results in costly computation. Also, since these approaches attempt (rather unrealistically) to guarantee the system performance over a full frequency range, a conservative design is always admitted. Here, taking a specific viewpoint of robust stability and performance under a stated restricted frequency range (which is applicable in rather many real-world situations), this paper provides an essential basis for the design of a fixed-order controller for a system with bounded parametric uncertainties. A Hurwitz polynomial is used in the design and the robust stability is characterized by the notion of positive realness, such that the required robust stability condition is then suitably successfully constructed. Also, the robust performance criteria in terms of sensitivity shaping under different frequency ranges are constructed based on an approach of bounded realness analysis. Necessary and sufficient conditions are provided for both the robust stability and robust performance criteria. Furthermore, these conditions are expressed in the framework of linear matrix inequality (LMI) constraints, and thus can be efficiently solved. Comparative simulations are provided to illustrate the effectiveness and efficiency of the proposed approach.

math.OC↗

arXiv2020

Trajectory Generation by Chance Constrained Nonlinear MPC with Probabilistic Prediction

Continued great efforts have been dedicated towards high-quality trajectory generation based on optimization methods, however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly, the future position of these moving obstacles in the presence of uncertainty within some possible prescribed prediction horizon. To cater to this rather major shortcoming, this work shows how a variational Bayesian Gaussian mixture model (vBGMM) framework can be employed to predict the future trajectory of moving obstacles; and then with this methodology, a trajectory generation framework is proposed which will efficiently and effectively address trajectory generation in the presence of moving obstacles, and also incorporating presence of uncertainty within a prediction horizon. In this work, the full predictive conditional probability density function (PDF) with mean and covariance is obtained, and thus a future trajectory with uncertainty is formulated as a collision region represented by a confidence ellipsoid. To avoid the collision region, chance constraints are imposed to restrict the collision probability, and subsequently a nonlinear MPC problem is constructed with these chance constraints. It is shown that the proposed approach is able to predict the future position of the moving obstacles effectively; and thus based on the environmental information of the probabilistic prediction, it is also shown that the timing of collision avoidance can be earlier than the method without prediction. The tracking error and distance to obstacles of the trajectory with prediction are smaller compared with the method without prediction.

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arXiv2020

Infinite-Horizon Optimal Control of Switched Boolean Control Networks with Average Cost: An Efficient Graph-Theoretical Approach

This study investigates the infinite-horizon optimal control problem for switched Boolean control networks with an average-cost criterion. A primary challenge of this problem is the prohibitively high computational cost when dealing with large-scale networks. We attempt to develop a more efficient and scalable approach from a graph-theoretical perspective. First, a weighted directed graph structure called the $\textit{optimal state transition graph}$ (OSTG) is established, whose edges encode the optimal action for each one-step transition between states reachable from a given initial state subject to various constraints. Then, we reduce the infinite-horizon optimal control problem into a minimum mean cycle (MMC) problem in the OSTG. Finally, we develop a novel algorithm that can quickly find a particular MMC by resorting to Karp's algorithm in graph theory and construct afterward an optimal switching and control law based on state feedback. Time complexity analysis shows that our algorithm can outperform all existing methods in terms of time efficiency. A 16-node signaling network in leukemia is used as a benchmark to test its effectiveness. Results show that the proposed graph-theoretical approach is much more computationally efficient: it runs hundreds or even thousands of times faster than existing methods.

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arXiv2020

Data-Driven Multi-Objective Controller Optimization for a Magnetically-Levitated Nanopositioning System

The performance achieved with traditional model-based control system design approaches typically relies heavily upon accurate modeling of the motion dynamics. However, modeling the true dynamics of present-day increasingly complex systems can be an extremely challenging task; and the usually necessary practical approximations often render the automation system to operate in a non-optimal condition. This problem can be greatly aggravated in the case of a multi-axis magnetically-levitated nanopositioning system where the fully floating behavior and multi-axis coupling make extremely accurate identification of the motion dynamics largely impossible. On the other hand, in many related industrial automation applications, e.g., the scanning process with the maglev system, repetitive motions are involved which could generate a large amount of motion data under non-optimal conditions. These motion data essentially contain rich information; therefore, the possibility exists to develop an intelligent automation system to learn from these motion data and to drive the system to operate towards optimality in a data-driven manner. Along this line then, this paper proposes a data-driven controller optimization approach that learns from the past non-optimal motion data to iteratively improve the motion control performance. Specifically, a novel data-driven multi-objective optimization approach is proposed that is able to automatically estimate the gradient and Hessian purely based on the measured motion data; the multi-objective cost function is suitably designed to take into account both smooth and accurate trajectory tracking. Experiments are then conducted on the maglev nanopositioning system to demonstrate the effectiveness of the proposed method, and the results show rather clearly the practical appeal of our methodology for related complex robotic systems with no accurate model available.

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arXiv2020

Optimal Control of Boolean Control Networks with Discounted Cost: An Efficient Approach based on Deterministic Markov Decision Process

This paper deals with the infinite-horizon optimal control problem for Boolean control networks (BCNs) with a discounted-cost criterion. This problem has been investigated in existing studies with algorithms characterized by high computational complexity. We thus attempt to develop more efficient approaches for this problem from a deterministic Markov decision process (DMDP) perspective. First, we show the eligibility of a DMDP to model the control process of a BCN and the existence of an optimal solution. Next, two approaches are developed to handle the optimal control problem in a DMDP. One approach adopts the well-known value iteration algorithm, and the other resorts to the Madani's algorithm specifically designed for DMDPs. The latter approach can find an exact optimal solution and outperform existing methods in terms of time efficiency, while the former value iteration based approach usually obtains a near-optimal solution much faster than all others. The 9-state-4-input \textit{ara} operon network of the bacteria \textit{E. coli} is used to verify the effectiveness and performance of our approaches. Results show that both approaches can reduce the running time dramatically by several orders of magnitude compared with existing work.

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arXiv2019

Finite-Horizon Optimal Control of Boolean Control Networks: A Unified Graph-Theoretical Approach

This paper investigates the finite-horizon optimal control (FHOC) problem of Boolean control networks (BCNs) from a graph theory perspective. We first formulate two general problems to unify various special cases studied in the literature: (i) the horizon length is $\textit{a priori}$ fixed; (ii) the horizon length is unspecified but finite for given destination states. Notably, both problems can incorporate time-variant costs, which are rarely considered in existing work, and a variety of constraints. The existence of an optimal control sequence is analyzed under mild assumptions. Motivated by BCNs' finite state space and control space, we approach the two general problems in an intuitive and efficient way under a graph-theoretical framework. A weighted state transition graph and its time-expanded variants are developed, and the equivalence between the FHOC problem and the shortest path problem in specific graphs is established rigorously. Two custom algorithms are developed to find the shortest path and construct the optimal control sequence with lower time complexity, though technically a classical shortest-path algorithm in graph theory is sufficient for all problems. Compared with existing algebraic methods, our graph-theoretical approach can achieve state-of-the-art time efficiency while targeting the most general problems. Furthermore, our approach is the first one capable of solving Problem (ii) with time-variant costs. Finally, the Ara operon genetic network in $\textit{E. coli}$ is used as a benchmark example to validate the effectiveness of our approach, and the results of two tasks show that our approach can dramatically reduce the running time.

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arXiv2019

Development of a General Momentum Exchange Devices Fault Model for Spacecraft Fault-Tolerant Control System Design

This paper investigates the mechanism of various faults of momentum exchange devices. These devices are modeled as a cascade electric motor EM - variable speed drive VSD system. Considering the mechanical part of the EM and the VSD system, the potential faults are reviewed and summarized. Thus with a clear understanding of these potential faults, a general fault model in a cascade multiplicative structure is established for momentum exchange devices. Based on this general model, various fault scenarios can be simulated, and the possible output can be appropriately visualized. In this paper, six types of working condition are identified and the corresponding fault models are constructed. Using this fault model, the control responses using reaction wheels and single gimbal control moment gyros under various fault conditions are demonstrated. The simulation results show the severities of the faults and demonstrate that the additive fault is more serious than the multiplicative fault from the viewpoint of control accuracy. Finally, existing fault-tolerant control strategies are brief summarized and potential approaches including both passive and active ones to accommodate gimbal fault of single gimbal control moment gyro is demonstrated.

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