A Matlab Toolbox For Hybrid Systems

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2008Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2008Hibrit sistemler hem analog hem de lojik dinamikler içerir. Ayrık olay sistemleri sınıfı, sınırlı sayıda kaynak içeren sistemleri içerir. Bu kaynaklar çeşitli kullanıcılar arasında paylaşılır. Bu kullanıcılar çeşitli ortak hedeflerin sağlanması için çalışır. Tezin ilk bölümünde Max-Plus cebri ve Max-Plus-Lineer (MPL) sistemler incelenmiştir. Tezin ikinci bölümünde hibrit sistemlerin çeşitli alt sınıflarını ve bu alt sınıfların birbirleri ile ilişkileri incelenmiştir. Bu alt sınıflar sırası ile Piecewise Affine (parçalı ilgin, PWA) sistemler, Mixed Logical Dynamical ( karısık lojik dinamik, MLD) sistemler, Linear Complementarity (lineer tümlemeli, LC) sistemler, Extended Linear Complementarity ( genisletilmis lineer tümlemeli) sistemler ve Max-Min-Plus-Scaling (MMPS) sistemlerdir. Hem Max-Plus-Linear (MPL) sistemler hem de yukarıda belirtilen hibrit sistem alt sınıfları için model öngörmeli kontrolörün uygulamaları incelenmiştir. En son ana bölümde geliştirilmiş fonksiyonlar örneklerle açıklanmaktadır. Bu fonksiyonlar üç ana grup altında toplanabilir. İlk grup hibrit sistem alt sınıflarını birbirlerine çeviren fonksiyonları içermektedir. İkinci grup ise daha önceden olusturulmus fonksiyonların araç kutusuna eklemlenmesini sağlar. Son gruptaki fonksiyonlar ise giriş işaretleri üstünde sınırlamalar içeren Max-Min-Plus-Scaling (MMPS) sistemler için genel bir model öngörücülü kontrolör algoritması geliştirilmesini amaçlar.Hybrid systems contain both analog and logical dynamics. The class of discrete event systems essentially consists of systems that contain a finite number of resources that are shared by several users all of which contribute to the achievement of some common goal. In the first main chapter, we will introduce the Max-Plus Algebra and Max-Plus-Linear(MPL) systems. In the third chapter, we will consider some subclasses of hybrid systems and their relations: Piecewise Affine systems (PWA) , Mixed Logical Dynamical (MLD) systems, Linear Complementarity (LC) systems, Extended Linear Complementarity (ELC) systems and Max-Min-Plus-Scaling (MMPS) systems. For both MPL systems and the mentioned subclasses of hybrid systems we will consider the implementation of the model predictive control scheme. In the last main chapter we will explain developed functions with examples. These functions can be grouped in three main groups. The first group consists of functions to convert hybrid system subclasses to each other. The second group of functions is used to implement previous built functions to our toolbox. The last group of functions aims to build an general model predictive controller algorithm for Max-Min-Plus-Scalar (MMPS) systems with limitations on input.Yüksek LisansM.Sc

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Strong Stationarity Conditions for Optimal Control of Hybrid Systems

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine system can be written as the optimizer of a mathematical program which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.Comment: 30 pages, 4 figure

Model Predictive Control for Signal Temporal Logic Specification

We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a receding horizon control framework. We prove correctness of our algorithms, and present experimental results for controller synthesis for building energy and climate control

Formal Synthesis of Control Strategies for Positive Monotone Systems

We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances. Such systems are widely used to model the dynamics of transportation and biological networks. The specifications are described using signal temporal logic (STL), which can express a broad range of temporal properties. We formulate the problem as a mixed-integer linear program (MILP) and show that under the assumptions made in this paper, which are not restrictive for traffic applications, the existence of open-loop control policies is sufficient and almost necessary to ensure the satisfaction of STL formulas. We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions. We also develop a robust model predictive framework to plan controls optimally while ensuring the satisfaction of the specification. Illustrative examples and a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16 pages, double colum

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

From Uncertainty Data to Robust Policies for Temporal Logic Planning

We consider the problem of synthesizing robust disturbance feedback policies for systems performing complex tasks. We formulate the tasks as linear temporal logic specifications and encode them into an optimization framework via mixed-integer constraints. Both the system dynamics and the specifications are known but affected by uncertainty. The distribution of the uncertainty is unknown, however realizations can be obtained. We introduce a data-driven approach where the constraints are fulfilled for a set of realizations and provide probabilistic generalization guarantees as a function of the number of considered realizations. We use separate chance constraints for the satisfaction of the specification and operational constraints. This allows us to quantify their violation probabilities independently. We compute disturbance feedback policies as solutions of mixed-integer linear or quadratic optimization problems. By using feedback we can exploit information of past realizations and provide feasibility for a wider range of situations compared to static input sequences. We demonstrate the proposed method on two robust motion-planning case studies for autonomous driving