Differential flatness has demonstrated numerous advantages and diverse applications in motion planning and control and while traditionally associated with robotic and mechanical systems, its applicability extends beyond these domains. By employing a change in the coordinate system, differential flatness transforms complex, nonlinear system dynamics into a linear representation. In essence, it provides a model inversion strategy that proves particularly useful for solving problems related to optimal trajectory generation and tracking under various constraints.This work offers an overview of past and current advancements in optimization-based motion planning problems that employ differential flatness. To the best of our knowledge, no prior review has been conducted from this perspective. We begin with an in-depth analysis of the foundational principles of flatness, examining its key properties and its intrinsic connection to feedback linearization. Particular emphasis is placed on the available choices for flat parameterization, which facilitate the characterization of costs and constraints in optimization problems. Furthermore, we explore tools for curve parameterization, which are essential for addressing trajectory generation problems involving constraints such as saturation limits, collision avoidance or obstacle navigation. Our review is structured around the general framework of motion planning, which comprises three main components: guidance, control, and adaptation. For each of these components, we analyze and synthesize the use of differential flatness.Rather than aiming for an exhaustive catalog or focusing narrowly on specific applications, this review seeks to highlight the benefits of differential flatness and aims to inspire new research directions in motion planning and control.
Finite-time stability (FTS) is crucial for modern engineering systems with stringent real-time requirements. This paper investigates FTS for stochastic nonlinear systems driven by fractional Brownian motion (fBm), a process exhibiting long-range dependence. The non-semimartingale property of fBm presents analytical challenges. Utilizing fractional Wick–Itô–Skorohod integrals and the fractional multidimensional Itô formula, the finite-time dynamics are rigorously analyzed. Sufficient conditions for FTS are established, and an explicit estimate of the settling time is provided. Based on the above theory, the finite-time control for non-local diffusion systems is further discussed. By using a finite-dimensional modal approximation, a finite-time feedback law is constructed from a linear stabilizing component and a non-Lipschitz power-type term. Verifiable gain conditions are derived to compensate for the bounded linear perturbation, the nonlinear drift, and the Malliavin correction induced by the fBm. And an explicit settling-time bound is obtained for the controlled modal system. Numerical simulations validate the theoretical results.
The model-free control (MFC) theory, which employs an ultra-local model to replace the conventional model of a plant, has recently become a research trend in the field of power electronics and electrical drives. The idea is to control a system just by having the measured data without using the parameters of the plant in order to avoid disturbances and parameter mismatch effects. Therefore, the MFC considers the inner dynamics, disturbances, and unmodeled parts of the system as a lumped unknown term. Then, identifies it and rejects its effect in the control process. Due to its powerful performance and straightforward implementation routine, the MFC has been extensively applied to power converters and has also been integrated with other popular control methods in the field, such as model predictive control and sliding mode control. This article gives a comprehensive survey of the MFC methods applied to power converters. A classification is made for various types of MFC strategies, and their different applications are explored. Then, the design and implementation challenges are discussed. Finally, some notes are given about the future trends of this method.
Enterprises planning material requirements must account for multiple sources of uncertainty. Considering the impact of yield uncertainty is of prime importance to decision-makers. To mitigate the effects of random yield on the continuity of manufacturing operations, we propose establishing a reserve stock to prevent shortages due to defective items within safety stock levels. If no reserve stock is established, this implies that the safety stock is composed exclusively of perfect, defect-free units. In this paper, we propose an analytical approach to assessing the reserve stock level based on safety stock calculations under variable probability of non-defectiveness. By explicitly accounting for failures in both planned deliveries and safety stock, we propose a three-tier framework for the potential application of a combined safety and reserve stock policy. The paper formulates a multi-criteria approach to evaluating supply strategies. It develops a flowchart for selecting a supply strategy in material requirements planning, accounting for ordering costs and the holding costs of safety and reserve stocks under random yields. The proposed approach allows the consolidation of demands across multiple periods into a single delivery at minimum cost, incorporating a probabilistic assessment of safety and reserve stock levels to achieve the required shortage-free service level.
This survey provides a comprehensive overview of distributed estimation, filtering, and fault detection techniques in the context of cyber–physical systems (CPS). Distributed algorithms are crucial for large-scale system monitoring as they enable parallel data processing, local fault identification, and real-time analysis across multiple nodes.To establish a strong foundation, we first define essential aspects of linear dynamical systems and related graph theoretic concepts, emphasizing observability conditions that are key for local state estimation. We introduce the mathematical framework necessary to understand both the theoretical underpinnings and practical implementations of distributed algorithms in CPS environments.After discussing consensus algorithms, this survey highlights single-time and double-time-scale consensus-based estimation and filtering approaches. We provide a detailed comparative analysis of these methodologies, examining their computational requirements, communication overhead, and performance characteristics in resource-constrained environments. We further explore different diffusion-based estimation techniques and observationally redundant designs to enhance resilience and robustness against failures and adversarial attacks.In addition, we investigate distributed fault detection methods that enable local isolation of faults over large-scale CPS. We present both stateless and stateful detection mechanisms, along with threshold-based techniques that balance detection accuracy and false alarm rates. These approaches are essential for maintaining system integrity and preventing cascading failures in critical infrastructure.This survey concludes with an exploration of diverse real-world applications. We examine implementation challenges and algorithm adaptations in smart grid and power networks, social systems, target tracking and localization, and intelligent transportation systems. Each application domain demonstrates how theoretical advances translate into practical solutions for complex monitoring problems.By bridging theoretical insights with practical applications, this survey and tutorial provides valuable understanding and research directions in the field of distributed algorithm design for CPS, offering both newcomers and experienced researchers a comprehensive resource for addressing current challenges and future opportunities.
