Course objectives

The course is structured into two modules: Industrial Automation and Nonlinear Systems. The goal of the Industrial Automation module is to let students familiarize with basic techniques for process planning and management. In particular, methods and algorithms of management science for modelling and solving complex decision problems will be presented. The goal of the Nonlinear Systems module is to discuss methods for the analysis of nonlinear systems using tools from system and control theory. Theory will be illustrated by means of examples from, e.g., mechanical engineering, electrical engineering and aeronautics. In addition, techniques for the synthesis of feedback regulators for nonlinear systems will be introduced.

Course program and content

Optimization module 

AUTOMATION OF PRODUCTION PROCESSES. Modelling of production processes. Flexible production systems. Management science. Operations research for decision problems.

MATHEMATICAL PROGRAMMING FOR DECISION PROBLEMS. Modelling of decision problems: variables, cost and constraints. Basics of convex programming. Examples of decision problems including product mix, resource allocation, transport and portfolio selection problems.

LINEAR PROGRAMMING (LP) PROBLEMS. Geometry of LP. Fundamental theorem of LP. Algorithms for LP problems.

Dual Programming.

Multi-parametric Programming.

The simplex method: phase 1 and 2. Tableau form of the simplex method.
Interior Point method.

Sensitivity analysis.

MIXED-INTEGER LINEAR PROGRAMMING (MILP). The use of binary variables in optimization programs. Branch and bound algorithm.
Extension also to the case of integer variables (and not only binary)

OPTIMIZATION PROBLEMS ON GRAPHS. Basics of computational complexity theory. Shortest spanning tree problem: Kruskal's algorithm. Shortest path problem: Dijkstra's and Floyd-Warshall algorithms. Flow networks: maximum flow problems and Ford-Fulkerson algorithm.

Dynamic programming: Bellman principle, cost-to-go and Bellman iterations. Application of dynamic programming to optimal control of finite state machines and shortest path problems.

Dynamic programming applied to mobile robotics.


Nonlinear Systems module

INTRODUCTION TO NONLINEAR PHENOMENA. Multiple equilibria, limit cycles, complex dynamics and chaos. Existence and uniqueness of state trajectories.

ANALYSIS OF SECOND-ORDER SYSTEMS. The phase plane: classification of equilibria. Lymit cycles and Poincaré-Bendixon theorem.

STABILITY THEORY. Lyapunov functions: theorems for checking stability and instability of equilibria. Global stability analysis. LaSalle theorems. Stability for time-varying systems.

NONLINEAR CONTROL. Methods based on Lyapunov functions. Backstepping techniques. Sliding Mode Control.

Teaching material

The material of the course will be available at

http://sisdin.unipv.it/labsisdin/teaching/courses/ails/files/ails.php

The lectures will be held in streaming. I will try to upload the registrations online afterwards.

Recommended textbooks (optimization part)

- W. L. Winston, M. Venkataramanan. Introduction to Mathematical Programming: Applications and Algorithm. 4th ed., Duxbury Press, 2002. 
- S Boyd L Vandenberghe , Convex Optimization, Cambridge University Press, 2004
- C. Vercellis. Ottimizzazione: Teoria, metodi, applicazioni. McGraw-Hill, 2008. (in Italian).