1,277 research outputs found
On the Stability of Gated Graph Neural Networks
In this paper, we aim to find the conditions for input-state stability (ISS)
and incremental input-state stability (ISS) of Gated Graph Neural
Networks (GGNNs). We show that this recurrent version of Graph Neural Networks
(GNNs) can be expressed as a dynamical distributed system and, as a
consequence, can be analysed using model-based techniques to assess its
stability and robustness properties. Then, the stability criteria found can be
exploited as constraints during the training process to enforce the internal
stability of the neural network. Two distributed control examples, flocking and
multi-robot motion control, show that using these conditions increases the
performance and robustness of the gated GNNs
Distributed Flocking Control of Aerial Vehicles Based on a Markov Random Field
The distributed flocking control of collective aerial vehicles has
extraordinary advantages in scalability and reliability, \emph{etc.} However,
it is still challenging to design a reliable, efficient, and responsive
flocking algorithm. In this paper, a distributed predictive flocking framework
is presented based on a Markov random field (MRF). The MRF is used to
characterize the optimization problem that is eventually resolved by
discretizing the input space. Potential functions are employed to describe the
interactions between aerial vehicles and as indicators of flight performance.
The dynamic constraints are taken into account in the candidate feasible
trajectories which correspond to random variables. Numerical simulation shows
that compared with some existing latest methods, the proposed algorithm has
better-flocking cohesion and control efficiency performances. Experiments are
also conducted to demonstrate the feasibility of the proposed algorithm.Comment: 6 Page
Learning and Control of Dynamical Systems
Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise.
In this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems.
We deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.</p
Gaussian Control Barrier Functions : A Gaussian Process based Approach to Safety for Robots
In recent years, the need for safety of autonomous and intelligent robots has increased. Today, as robots are being increasingly deployed in closer proximity to humans, there is an exigency for safety since human lives may be at risk, e.g., self-driving vehicles or surgical robots. The objective of this thesis is to present a safety framework for dynamical systems that leverages tools from control theory and machine learning. More formally, the thesis presents a data-driven framework for designing safety function candidates which ensure properties of forward invariance. The potential benefits of the results presented in this thesis are expected to help applications such as safe exploration, collision avoidance problems, manipulation tasks, and planning, to name some.
We utilize Gaussian processes (GP) to place a prior on the desired safety function candidate, which is to be utilized as a control barrier function (CBF). The resultant formulation is called Gaussian CBFs and they reside in a reproducing kernel Hilbert space. A key concept behind Gaussian CBFs is the incorporation of both safety belief as well as safety uncertainty, which former barrier function formulations did not consider. This is achieved by using robust posterior estimates from a GP where the posterior mean and variance serve as surrogates for the safety belief and uncertainty respectively. We synthesize safe controllers by framing a convex optimization problem where the kernel-based representation of GPs allows computing the derivatives in closed-form analytically.
Finally, in addition to the theoretical and algorithmic frameworks in this thesis, we rigorously test our methods in hardware on a quadrotor platform. The platform used is a Crazyflie 2.1 which is a versatile palm-sized quadrotor. We provide our insights and detailed discussions on the hardware implementations which will be useful for large-scale deployment of the techniques presented in this dissertation.Ph.D
State-Dependent Dynamic Tube MPC: A Novel Tube MPC Method with a Fuzzy Model of Disturbances
Most real-world systems are affected by external disturbances, which may be
impossible or costly to measure. For instance, when autonomous robots move in
dusty environments, the perception of their sensors is disturbed. Moreover,
uneven terrains can cause ground robots to deviate from their planned
trajectories. Thus, learning the external disturbances and incorporating this
knowledge into the future predictions in decision-making can significantly
contribute to improved performance. Our core idea is to learn the external
disturbances that vary with the states of the system, and to incorporate this
knowledge into a novel formulation for robust tube model predictive control
(TMPC). Robust TMPC provides robustness to bounded disturbances considering the
known (fixed) upper bound of the disturbances, but it does not consider the
dynamics of the disturbances. This can lead to highly conservative solutions.
We propose a new dynamic version of robust TMPC (with proven robust stability),
called state-dependent dynamic TMPC (SDD-TMPC), which incorporates the dynamics
of the disturbances into the decision-making of TMPC. In order to learn the
dynamics of the disturbances as a function of the system states, a fuzzy model
is proposed. We compare the performance of SDD-TMPC, MPC, and TMPC via
simulations, in designed search-and-rescue scenarios. The results show that,
while remaining robust to bounded external disturbances, SDD-TMPC generates
less conservative solutions and remains feasible in more cases, compared to
TMPC.Comment: 39 pages, 16 figures, 4 tables, 2 appendices, to be submitted to
"international journal of robust and nonlinear control", [40] from paper
cites our code to be submitted
Concurrent Product and Supply Chain Architecture Design Considering Modularity and Sustainability
Since sustainability is a growing concern, businesses aim to integrate sustainability principles and practices into product and supply chain (SC) architecture (SCA) design. Modular product architecture (MPA) is essential for meeting sustainability demands, as it defines detachable modules by selecting appropriate components from various potential combinations. However, the prevailing practice of MPA emphasizes architectural aspects over interface complexity and design production processes for the structural dimension, potentially impending manufacturing, assembly/disassembly, and recovery efficiency. Most MPA has been developed assuming equal and/or fixed relations among modules rather than configuring for SC effectiveness. Therefore, such methods cannot offer guidance on modular granularity and its impact on product and SCA sustainability. Additionally, there is no comparative assessment of MPA to determine whether the components within the configured modules could share multiple facilities to achieve economic benefits and be effective for modular manufacture and upgrade. Therefore, existing modular configuration fails to link modularization drivers and metrics with SCA, hampering economic design, modular recycling, and efficient assembly/disassembly for enhancing sustainability.
This study focuses on the study of design fundamentals and implementation of sustainable modular drivers in coordination with SCA by developing a mathematical model. Here, the architectural and interface relations between components are quantified and captured in a decision structure matrix which acts as the foundation of modular clustering for MPA. Again, unlike previous design approaches focused only on cost, the proposed work considers facility sharing through a competitive analysis of commonality and cost. It also evaluates MPA's ease of disassembly and upgradeability by a comparative assessment of different MPA to enhance SCA sustainability. The primary focus is concurrently managing the interdependency between MPA and SCA by developing mathematical models. Consistent with the mathematical model, this thesis also proposes better solution approaches.
In summary, the proposed methods provide a foundation for modeling the link between product design and SC to 1) demonstrate how sustainable modular drivers affect the sustainability performance, 2) evaluate the contribution of modularity to the reduction of assembly/disassembly complexity and cost, 3) develop MPA in coordination with SC modularity by trading off modular granularity, commonality, and cost, and 4) identify a sustainable product family for combined modularity considering the similarity of operations, ease of disassembly and upgradability in SCA.
Using metaheuristic algorithms, case studies on refrigerators showed that MPA and its methodology profoundly impact SCA sustainability. It reveals that interactions between components with levels based on sustainable modular drivers should be linked with modular granularity for SCA sustainability. Another key takeaway is that instead of solely focusing on cost, facility sharing and ensuring ease of disassembly and upgradeability can help to reap sustainability benefits
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