Cyber Physical Systems - Lecture 4

Cyber Physical Systems (CPS) - Lecture 4

• CPS is an abbreviation for Cyber Physical Systems
• Lecture 4 covers Discrete Dynamics & State Machines
• Discrete systems operate in a sequence of distinct steps or have signals taking discrete values. Discrete systems have discrete dynamics
• Today's lecture will cover models (i.e., programs) of discrete systems, types and interfaces including states, transitions, guards, and determinism/receptiveness.

Discrete Systems - Example Design Problem

• Count the number of cars in a parking garage by sensing cars entering and leaving.
• Display the count.
• Arrival detection triggers "up" signal
• Departure detection triggers "down" signal

Discrete Systems - Example Diagram

• Diagram shows Arrival Detector, Departure Detector, Counter display with a sum.
• 'up' signal increases counter, 'down' signal decreases counter.
• Pure signal: up/down → {absent, present}
• Discrete Actor: Counter: (R → {absent, present}) → (R → {absent} ∪ N).

Discrete Systems - Finite State Machine (FSM)

• A state machine that models a system with discrete dynamics.
• At each reaction, maps inputs to outputs.
• The map depends on the current state.
• An FSM where the set of States is finite
  • Example: States = {State1, State2, State3}

FSM Notation

• Diagrammatic representation of FSMs
• States are shown as circles
• Transitions are shown as arrows between states
• Associated with each transition are the transition's guard (condition that enables it), and an action/description.

Examples of Guards

• true: Transition always enabled.
• p1: Transition enabled if p1 is present.
• ¬p1: Transition enabled if p1 is absent.
• p1 ∧ p2: Transition enabled if both p1 and p2 are present.
• p1 ∨ p2: Transition enabled if either p1 or p2 is present.

Examples of Guards with numerical values

• p3: Transition enabled if p3 is present.
• p3 = 1: Transition is enabled if p3 has value 1.
• p3 > 5: Transition is enabled if p3's value is above 5.

Garage Counter FSM

• Shows a FSM for a parking garage counter.
• States represent the number of cars in the garage – Example: state 0, 1, ..., M (M maximum capacity)

Garage Counter Mathematical Model

• Formally defines the update function, initial conditions, the states.
• Function calculates the next state of the system based on current input and state.
• Example, UpdateFunction (s(n), x(n)).

Example of Thermostat

• A simple thermostat FSM. The thermostat has different states to heat or cool depending in temperature.
• States: heating, cooling
• Transitions occur based on current temperature

This quiz focuses on Lecture 4 of Cyber Physical Systems, covering Discrete Dynamics & State Machines. You'll explore the operation of discrete systems, state transitions, and the design problem of counting cars in a parking garage through discrete signals. Test your understanding of models, types, and interfaces in CPS.