Dynamical System Design

Dynamical System Design is an universitary course held for the master's student of management engineering of LIUC University on how to use formal models for decision-making in complex contexts. It combines intuitive system thinking, basic mathematics, and simulation practice with an ad hoc software simulator to turn qualitative reasoning into operational decisions.

The course perspective is practical: models are not built for elegance alone, but to support decision-making, clarify assumptions, and run what-if and scenario analyses in uncertain dynamics environments.

Course Principles

Purpose-driven modeling
Progressive refinement
Prediction for decision
Framework linking world, system, modeler, and model
The modeler defines a system boundary, builds a model, and interprets behavior to support action.

From Craft To Engineering

A central principle is moving from ad-hoc decision habits to explicit and repeatable engineering logic. The course contrasts "the craftsman" approach with a structured modeling approach that can be discussed, transferred, and improved collaboratively.

Complexity Is Managed, Not Removed

The course distinguishes complication from complexity: complication can be reduced by better representation, while complexity is a real property of systems. The task of the modeler is to choose the right abstraction level.

Qualitative First, Quantitative Next

Modeling starts with variables and dependencies, then evolves toward equations and simulation. This phased method makes assumptions explicit before numerical formalization.

Validation And Sensitivity

A model is useful only if it behaves coherently under alternative scenarios. The course emphasizes validation, what-if analysis, and sensitivity analysis as core quality criteria.

Craftsman and engineer metaphor
The course repeatedly frames decision-making as an engineering discipline, not only a personal craft.

Topics Covered

Qualitative dependency scheme example
Example of signed qualitative dependencies used to reason about feedback and control.
8-tuple representation of a dynamic system
Formal system specification with time, inputs, states, transition function, and outputs.

Examples Discussed During The Course

Direct And Inverse Problems

Beer-keg and inventory-style exercises are used to show the difference between estimating outputs and searching for input conditions that achieve a target outcome.

Forecasting Under Partial Observability

Cases like penalty-kick prediction illustrate how behavior can be inferred from output histories, with probabilistic reasoning and black-box thinking.

Socio-Technical Decision Cases

Urban dynamics, epidemiological reasoning, queueing in emergency contexts, and competitive market analogies show how models inform policy and managerial trade-offs.

Inclined plane theory case example
A playful but formal case translates a narrative into dynamic equations for prediction.
Risk and uncertainty topics image
Risk, uncertainty, stochasticity, and path dependency as recurring decision lenses.