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The general problem of determining optimal process control can be summarized as follows: Given a process defined by its model, find among the admissible commands the one that allows both : verify given initial and final conditions; to satisfy various constraints; to optimize a chosen criterion. This definition calls for a few comments: Any search for control, and a fortiori for optimal control, requires the manipulation of mathematical expressions, in particular those characterizing the evolution of the process, i.e. its model. The choice of model is therefore of prime importance.
Nowadays, testing complex systems is not easy and the time allocated to validation teams is often considered too short. This article explains how to properly define, plan, track, and optimize the testing of complex systems. It falls within a systems engineering context. It describes the processes associated with the test and gives best practices. It proposes a test typology that facilitates the development of the test strategy. It addresses the issue of documentation and test management. It presents various optimization criteria to minimize test costs and risks during and at the end of the test.
In the aeronautics sector, and especially since the development of the fly-by-wire technology (FBW), the theory of modal control has been successfully applied to the tuning of flight control laws. The civil aircraft autopilot still remains the leading application in order to illustrate such techniques. An application of the modal control is presented in this article: the autopilot in the landing phase. The sensitivity of command laws to external perturbances and model variations are also dealt with.
Evolutionary Algorithms (EA), including the most famous ones, Genetic Algorithms (GA), are based on Darwin’s theory. These problem-solving or stochastic optimization methods mimic in a very simplified manner the capabilities of populations of living organisms to adapt to their environments thanks to selection and genetic inheritance mechanisms. This paper provides a brief panorama of artificial Darwinism and its varied and numerous applications.
This article presents the formal and applicative aspects of Petri nets (RdP). This is a tool for modeling and analyzing systems in the formof states, transitions and tokens, in which control evolves asynchronously and concurrently. The concept of token is used to represent capacity. Various extensions to RdP are discussed, offering greater functional expressiveness and more compact modeling. Another type of extension involves the incorporation of time. These extensions make it possible to introduce the notions of urgency, watchdog and duration. Finally, a set of application tools is presented for modeling, simulation and code generation.
Delays are common in science and engineering, arising from transmission, propagation, and memory pheno- mena. In control theory, delays can cause instability, oscillations, and bandwidth limitations, requiring careful consideration.This article introduces delay systems using functional differential equations, generalizing ordinary differential equations. It covers stability analysis methods for such systems in frequency and time domains, focusing on computationally verifiable conditions. It also addresses control design challenges, emphasizing computational methods. Examples, code snippets, and references are provided for illustration and further study.
This tutorial presents an introduction to the analysis and design of systems with finite/fixed-time convergence. The main attention is paid to finite-time and fixed-time convergent dynamics. Two large groups of approaches to the analysis/synthesis of this type of convergence are described: based on Lyapunov functions and the theory of homogeneous systems. Some popular control and estimation algorithms, which have accelerated convergence rates, are reviewed. The discretization problems of finite/fixed time convergent systems are discussed. All given results are illustrated by simple examples (scalar or planar).
on the identification of parameters of a system of equations that describes the behavior of a physical phenomenon. The methods called "Physics-Informed Neural Network" and "Physics Constrained Learning" with respective acronyms PINN and PCL, based on the so-called physics-driven neural networks, are firstly presented in a general context and secondly explained and tested in the case of a first-order ordinary differential equation governing for instance the charging of a capacitor. The physicalparameter considered, representing the capacitance, is assumed to be constant or time-varying.
This article deals with controller synthesis for nonlinear systems subject to constraints on states and control, as well as bounded disturbances, and for specifications such as safety, reachability, or more complex properties formulated using automata or temporal logics. In this context, symbolic approaches, based on the abstraction of the system through a symbolic model (with a finite number of states and controls), enable the automatic synthesis of controllers certified as “correct by construction.” This article presents in a didactic manner the key elements of these approaches (abstraction, synthesis, and concretization of controllers) and provides an overview of advanced themes in this dynamically evolving research field.
Whether creating a new product or improving an existing one, the engineer in charge of creating a piloted system generally follows a two-phase approach: A first step is to study the passive (uncontrolled) behavior of the system; the second stage essentially concerns the definition of specifications for the determination and implementation of control laws to drive the active system.
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