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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 217-219+223-232页

作者： Leine, Remco I. van, de Wouw, Nathan Department of Mechanical and Process Engineering Institute of Mechanical Systems ETH Zurich CH-8092 Zurich Switzerland Dynamics and Control Group Department of Mechanical Engineering Eindhoven University of Technology PO Box 513 5600 MB Eindhoven Netherlands

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ISBN: (纸本)9783540769743

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Intelligent control Based on Reinforcement Learning for Batch Thermal Sterilization of Canned Foods

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IFAC Proceedings Volumes 2008年第2期41卷 3568-3573页

作者： S. Syafiie Carlos Vilas Miriam R. Garcia Fernando Tadeo Antonio A. Alonso Ernesto Martinez Department of Systems Engineering and Automatic Control University of Valladolid 47011 Valladolid Spain { Process Engineering Group IIM-CSIC Vigo Spain National Research Council of Argentina Avellaneda 3657 3000-Santa Fe Argentina

A control technique based on Reinforcement Learning is proposed for controlling thermal sterilization of canned food. Without using an a-priori mathematical model of the process, the proposed Model-Free Learning controller (MFLC) aims to follow a temperature profile during two stages of the process: first heating by manipulating the saturated steam valve and then cooling by opening the water valve) by learning. From the defined state-action space, the MFLC agent learns the environment interacting with the process batch to batch and then using a tabular state-action mapping. The results show the advantages of the proposed technique for this kind of processes.

关键词： Reinforcement Learning Intelligent process control Sterilization process Batch process

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Measure and integration theory

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 43-57页

作者： Leine, Remco I. van de Wouw, Nathan Department of Mechanical and Process Engineering Institute of Mechanical Systems ETH Zurich CH-8092 Zurich Switzerland Dynamics and Control Group Department of Mechanical Engineering Eindhoven University of Technology PO Box 513 5600 MB Eindhoven Netherlands

ISBN: (纸本)9783540769743

The theory of measures forms the basis for the modern integration theory and both are quintessential for the understanding of measure differential inclusions which will be dealt with in Chapter 4. Moreau, who introduced the notion measure differential inclusions in [117-120, 122, 123], directly introduces the so-called *** measure. In Chapter 4, it will be explained in more detail that a measure *** inclusion actually describes how the *** measure of the state relates to the state and time in analogy with the fact that a (first-order) differential inclusion (or equation) describes how the time derivative of the state depends on the state and time. In this chapter we give a brief overview of measure and integration theory and relate the differential measure used by Moreau to real measures and (signed) measures. The theory presented in this chapter is based on standard textbooks about measure and integration theory [47,150], various publications of Moreau and others [63,116, 122,124] as well as the work of P. Ballard communicated through lecture notes of a summer course on Non-smooth Dynamical systems (2003, Praz-sur-Arly). This chapter may be very demanding and a reader on the verge of despair should keep the key result of this chapter in mind: every function of locally bounded variation can be decomposed in an absolutely continuous function, a step function and a singular function. As will appear in Chapter 4, solutions of measure differential inclusions are defined as functions of locally bounded variation. The latter fact clearly implies that the solutions of measure differential inclusions may include the contribution of step functions, which can account for jumps in the state evolution (such as e.g. velocity jumps in mechanical systems with impacts).

关键词： Dynamical systems

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Non-smooth dynamical systems

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 59-77页

ISBN: (纸本)9783540769743

A dynamical system is a system whose state evolves with time. The evolution is governed by a set of rules, and is usually put in the form of equations. Continuous-time systems are dynamical systems of which the state is allowed to change (continuously or discontinuously) at all times t. Continuous-time systems are usually described by ordinary differential equations. Discrete-time systems are dynamical systems of which the state can only change at discrete time-instances t1 2 3.... In this chapter we will consider continuoustime dynamical systems with a non-smooth (and possibly discontinuous) timeevolution of the state. After a brief introduction to diffrential quations, we will consider differential equations with a discontinuous right-hand side. The equirement for the existence of a solution leads to the need to fill in the graph of the discontinuous right-hand side (Filippov's convex method). The resulting set-valued right-hand side brings forth a differential inclusion, which will be discussed in detail in Section 4.2. Subsequently, the differential measure of the state, which classically contains a density with respect to the Lebesgue measure, is extended in Section 4.3 with an atomic part. This leads to a measure differential inclusion, being the mathematical framework used in this work to describe dynamical systems with state evolutions with discontinuities (state jumps). In Chapters 6 and 8, we will present stability and convergence results for measure differential inclusions.

关键词： Dynamical systems

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Introduction

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 1-19页

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Convergence properties of monotone measure differential inclusions

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 191-215页

ISBN: (纸本)9783540769743

In this chapter, we present theorems which give sufficient conditions for the convergence of measure differential inclusions with certain maximal monotonicity properties. The framework of measure differential inclusions allows us to describe systems with state discontinuities, as has been shown in the previous chapters. The material presented in this chapter is based on the paper [104]. The chapter is organised as follows. First, we define the convergence property of dynamical systems in Section 8.1 and state the associated properties of convergent systems. Theorems are presented in Section 8.2 which give sufficient conditions for the convergence of measure differential inclusions with certain maximal monotonicity properties. Furthermore, we illustrate in Section 8.3 how these convergence results for measure differential inclusions can be exploited to solve tracking problems for certain classes of non-smooth mechanical systems with friction and one-way clutches. Illustrative examples of convergent mechanical systems are discussed in detail in Section 8.4. Finally, Section 8.5 presents concluding remarks.

关键词： Dynamical systems

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Non-smooth analysis

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 21-41页

ISBN: (纸本)9783540769743

This chapter presents some basic mathematical theory from non-smooth analysis [10,12,37,56,77,78,147,149]. The aim of this chapter is not to give a real introduction to non-smooth analysis as the above textbooks are much better suited for that task. Instead, the primary aim of the chapter is to make the reader is familiar with the terminology and notation used in this monograph. Moreover, it provides a compendium on non-smooth and convex analysis which is useful when reading the following chapters. The reader might want to look up how a mathematical term is exactly defined, making use of the index in combination with this chapter. We begin with a brief introduction to sets (Section 2.1). The notion of continuity of functions is relaxed in Section 2.2 to semi-continuity and the notion of the classical derivative of smooth functions is extended to generalised differentials for non-smooth functions in Section 2.3. Subsequently, we discuss set-valued functions in Section 2.4. Topics from convex analysis are reviewed in Section 2.5 and the subderivative is discussed in Section 2.6.

关键词： Computational mechanics

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Mechanical systems with set-valued force laws

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 79-107页

ISBN: (纸本)9783540769743

Some theoretical background on non-smooth systems has been discussed in the previous chapter. Mechanical multibody systems form a special and important class of non-smooth systems, because they can be cast in an elegant structured form. The special structure of mechanical systems is due to the fact that the dynamics is described by the Lagrangian formalism, which links dynamics to variational calculus. Moreover, contact forces are incorporated in the equation of motion by using the Lagrange multiplier theorem. But most importantly, contact forces are (mostly) derived from (pseudo-)potentials or dissipation functions. In this chapter we will discuss the mathematical formulation of Lagrangian mechanical systems with unilateral contact and friction modelled with setvalued force laws. It is important to note that (finite-dimensional) Lagrangian mechanical systems encompass rigid multibody systems as well as discretized continuous systems (e.g. through a Ritz approach or a nite-element discretization) with possible frictional unilateral contacts. First, we discuss how set-valued force laws can be derived from non-smooth potentials. Subsequently, we treat the contact laws for unilateral contact and various types of friction within the setting of non-smooth potential theory. This leads to a unified approach with which all set-valued forces can be formulated. Finally, we incorporate the set-valued forces as Lagrangian multipliers in the Newton-Euler equations. The notation in this chapter is kept as close as possible to the notation of Glocker [63].

关键词： Friction

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Lyapunov stability theory for measure differential inclusions

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 109-152页

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ISBN: (纸本)9783540769743

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Stability properties in mechanical systems

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Lecture Notes in Applied and Computational Mechanics 2008年 36卷 153-190页

ISBN: (纸本)9783540769743

In this chapter, we apply the stability results of Chapter 6 for measure differential inclusions to Lagrangian mechanical systems with set-valued force laws, which have been formulated in Chapter 5. The special structure of Lagrangian mechanical systems allows for a natural choice of the Lyapunov function, a systematic derivation of the proof for this large class of systems as well as a physical interpretation of the results. In the following, we study stability properties of equilibrium sets of the measure differential inclusion (5.96) M(q)du - h(q, u)dt = WN(q)dPN+WD(q) dPD ∀t, where dPN and dPd obey the set-valued constitutive laws (5.98). We assume existence of solutions of (5.96) for all admissible initial conditions. We denote an equilibrium position of (5.96) by q*. The generalised velocities u vanish at an equilibrium point as we assume all contacts to be scleronomic (i.e. the normal contact distances gN(q) as well as all relative velocities γD(q,u) do not explicitly depend on time). With Ε we denote an equilibrium set of the measure differential inclusion in first-order form, while Εq is reserved for the union of equilibrium positions q*, i.e. Ε = {(q,u) ∈ n × n q ∈ Εq, u = 0}.

关键词： System stability

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