István Selek, PhD Post. Doctoral Researcher Systems Engineering Research Group University of Oulu, Oulu, Finland.

Slides:

Advertisements

Similar presentations

David Rosen Goals  Overview of some of the big ideas in autonomous systems  Theme: Dynamical and stochastic systems lie at the intersection of mathematics.

Advertisements

Lect.3 Modeling in The Time Domain Basil Hamed

Robotics Research Laboratory 1 Chapter 6 Design Using State-Space Methods.

S ystems Analysis Laboratory Helsinki University of Technology Near-Optimal Missile Avoidance Trajectories via Receding Horizon Control Janne Karelahti,

Computational Stochastic Optimization:

Modeling and simulation of systems Slovak University of Technology Faculty of Material Science and Technology in Trnava.

IAAC International Symposium in Systems & Control, 7-8 October 2013, Technion, Haifa, Israel P-O Gutman: Constrained control of uncertain linear time-invariant.

Water Resources Systems Modeling for Planning and Management An Introduction to the Development and Application of Optimization and Simulation Models for.

Decision Making: An Introduction 1. 2 Decision Making Decision Making is a process of choosing among two or more alternative courses of action for the.

PROCESS INTEGRATED DESIGN WITHIN A MODEL PREDICTIVE CONTROL FRAMEWORK Mario Francisco, Pastora Vega, Omar Pérez University of Salamanca – Spain University.

SPREADSHEETS IN EDUCATION OF LOGISTICS MANAGERS AT FACULTY OF ORGANIZATIONAL SCIENCES: AN EXAMPLE OF INVENTORY DYNAMICS SIMULATION L. Djordjevic, D. Vasiljevic.

INTEGRATED DESIGN OF WASTEWATER TREATMENT PROCESSES USING MODEL PREDICTIVE CONTROL Mario Francisco, Pastora Vega University of Salamanca – Spain European.

NORM BASED APPROACHES FOR AUTOMATIC TUNING OF MODEL BASED PREDICTIVE CONTROL Pastora Vega, Mario Francisco, Eladio Sanz University of Salamanca – Spain.

Problem statement; Solution structure and defining elements; Solution properties in a neighborhood of regular point; Solution properties in a neighborhood.

A Finite Sample Upper Bound on the Generalization Error for Q-Learning S.A. Murphy Univ. of Michigan CALD: February, 2005.

Chess Review May 11, 2005 Berkeley, CA Closing the loop around Sensor Networks Bruno Sinopoli Shankar Sastry Dept of Electrical Engineering, UC Berkeley.

Lecture outline Support vector machines. Support Vector Machines Find a linear hyperplane (decision boundary) that will separate the data.

Planning operation start times for the manufacture of capital products with uncertain processing times and resource constraints D.P. Song, Dr. C.Hicks.

PRODUCTION PLANNING ELİF ERSOY Production Planning2 WHAT IS PRODUCTION PLANNING?  Production planning is a process used by manufacturing.

Dynamic Optimization Dr

Overall Objectives of Model Predictive Control

Hydraulic Modeling of Water Distribution Systems

Overview of Model Predictive Control in Buildings

Industrial Process Modelling and Control Ton Backx Emeritaatsviering Joos Vandewalle.

MAKING COMPLEX DEClSlONS

Distributed control and Smart Grids

AUTOMATIC CONTROL THEORY II Slovak University of Technology Faculty of Material Science and Technology in Trnava.

Classifying optimization problems By the independent variables: –Integer optimization --- integer variables –Continuous optimization – real variables By.

ECES 741: Stochastic Decision & Control Processes – Chapter 1: The DP Algorithm 1 Chapter 1: The DP Algorithm To do:  sequential decision-making  state.

Bert Pluymers Johan Suykens, Bart De Moor Department of Electrotechnical Engineering (ESAT) Research Group SCD-SISTA Katholieke Universiteit Leuven, Belgium.

Introduction A GENERAL MODEL OF SYSTEM OPTIMIZATION.

Voltage Control in Power Systems: Preliminary Results T. Geyer, G. Ferrari-Trecate, T. Geyer, G. Ferrari-Trecate, M. Morari Automatic Control Laboratory.

ECES 741: Stochastic Decision & Control Processes – Chapter 1: The DP Algorithm 31 Alternative System Description If all w k are given initially as Then,

Quadruped Robot Modeling and Numerical Generation of the Open-Loop Trajectory Introduction We model a symmetric quadruped gait for a planar robot with.

PENN S TATE Department of Industrial Engineering 1 Revenue Management in the Context of Dynamic Oligopolistic Competition Terry L. Friesz Reetabrata Mookherjee.

Network Appurtenances Major operations within a water transport and distribution systems are: 1. Transmission. 2. Storage. 3. Pumping.

Approximate Dynamic Programming Methods for Resource Constrained Sensor Management John W. Fisher III, Jason L. Williams and Alan S. Willsky MIT CSAIL.

Groundwater pumping to remediate groundwater pollution March 5, 2002.

Chapter 20 1 Overall Objectives of Model Predictive Control 1.Prevent violations of input and output constraints. 2.Drive some output variables to their.

CSE4334/5334 DATA MINING CSE4334/5334 Data Mining, Fall 2014 Department of Computer Science and Engineering, University of Texas at Arlington Chengkai.

CONTROL OF MULTIVARIABLE SYSTEM BY MULTIRATE FAST OUTPUT SAMPLING TECHNIQUE B. Bandyopadhyay and Jignesh Solanki Indian Institute of Technology Mumbai,

Networks in Engineering A network consists of a set of interconnected components that deliver a predictable output to a given set of inputs. Function InputOutput.

CDAE Class 3 Sept. 4 Last class: 1. Introduction Today: 1. Introduction 2. Preferences and choice Next class: 2. Preferences and choice Important.

© 2011 Autodesk Freely licensed for use by educational institutions. Reuse and changes require a note indicating that content has been modified from the.

Water Resources System Modeling

Stochastic Optimization

D Nagesh Kumar, IIScOptimization Methods: M5L1 1 Dynamic Programming Introduction.

Conference on PDE Methods in Applied Mathematics and Image Processing, Sunny Beach, Bulgaria, 2004 NUMERICAL APPROACH IN SOLVING THE PDE FOR PARTICULAR.

Chapter 20 Model Predictive Control

دانشگاه صنعتي اميركبير دانشكده مهندسي پزشكي استاد درس دكتر فرزاد توحيدخواه بهمن 1389 کنترل پيش بين-دکتر توحيدخواه MPC Stability-2.

Optimization of Nonlinear Singularly Perturbed Systems with Hypersphere Control Restriction A.I. Kalinin and J.O. Grudo Belarusian State University, Minsk,

Chapter 4 The Maximum Principle: General Inequality Constraints.

Components of Water Networks Eng. Mona Al-Gharbawi Eng. Ayman Al-Afifi

Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Pipe Networks 

Water Resources Planning and Management Daene C. McKinney System Performance Indicators.

Linear Programming and Applications

1 Introduction Optimization: Produce best quality of life with the available resources Engineering design optimization: Find the best system that satisfies.

Introduction and Preliminaries D Nagesh Kumar, IISc Water Resources Planning and Management: M4L1 Dynamic Programming and Applications.

Chapter 20 Model Predictive Control (MPC) from Seborg, Edgar, Mellichamp, Process Dynamics and Control, 2nd Ed 1 rev. 2.1 of May 4, 2016.

Modeling and Simulation Dr. Mohammad Kilani

Water Resources Planning and Management Daene McKinney

Systems of Equations and Inequalities

CHAPTER 8 Operations Scheduling

Overall Objectives of Model Predictive Control

سمینار درس کنترل پیش بین

Christopher Crawford PHY

Solve the differential equation. {image}

Distributed Stochastic Model Predictive Control

دانشگاه صنعتي اميركبير

Presentation transcript:

István Selek, PhD Post. Doctoral Researcher Systems Engineering Research Group University of Oulu, Oulu, Finland

Model Structure Conservation law (with respect to reservoirs) (Distrurbance) Prediction sub-model Auxiliary Component (required by the cost function) Hydrodynamic network model

Given a dynamic model of a water distribution system of the form Where, subject to

Find a policy

Solution proposal, 3 level hierarchial approach: 1.Optimal control decision u(k) is calculated 2.Optimal time distribution of flows for all actuators is calculated 3.Calculate actuator opreational rules using flow distribution

1.Are there robust solutions ? 2.Is it possible to design a WDS which fulfills robust operational requirements ? 3.What are the necesary and sufficient conditions for the existence of robust solutions ?

The existence of effective target tube is a necessary and sufficient condition for robustness !

Constraints Putting these together

The calculation proceeds in two steps. Step 1

Find a policy which maintains the state trajectory within at time instant k, and minimizes

Receding Horizon Principle: each time instant k an open loop (closed loop) optimization problem is defined and solved on a finite time horizon [k, k+N] using a small number of lookahead steps. Findwhich minimizes Open Loop Feedback Control Findwhich minimizes Closed Loop Feedback Control The lookahead optimization will result in a sequence: Apply the first element of the sequence

Permutational Invariance: invariance of the state subject to control sequence permutations The control sequence The system’s dynamics Integrator form The distrurbance (demand) sequence

Permutational Invariance: invariance of the state subject to control sequence permutations

Tank dynamics Can be written as

Must be transformed at each time instant Control constraints Effective target tube (state space) Control Constraints Effective target tube Putting these together The a vector is calculated For which the following equation is satisfied for all admissible realizations of the disturbance

Cost (objective) function is not defined yet !

8 direct (discrete) pumping stations 3 continuous pumping stations 8 tanks 6 (stochastic) consumption zones Water demand model Cost function (pumping costs)