A Finite State Machine Modeling a Chess Game

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Из курса от партнера University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 оценки

University of California, Santa Cruz

Cyber-Physical Systems: Modeling and Simulation

6 оценки

Cyber-physical systems (CPS for short) combine digital and analog devices, interfaces, networks, computer systems, and the like, with the natural and man-made physical world. The inherent interconnected and heterogeneous combination of behaviors in these systems makes their analysis and design an exciting and challenging task. CPS: Modeling and Simulation provides you with an introduction to modeling and simulation of cyber-physical systems. The main focus is on models of physical process, finite state machines, computation, converters between physical and cyber variables, and digital networks. The instructor of this course is Ricardo Sanfelice (https://hybrid.soe.ucsc.edu), Associate Professor in the Department of Computer Engineering at the University of California Santa Cruz.

Из урока

Modeling Cyber Components: Finite State Machines, Computations, Algorithms, and a First CPS Model

Finite-State Machines (Part 1)5:44

Finite-State Machines (Part 2)3:04

Finite-State Machines (Part 3)5:41

Simulation of a Finite State Machine6:37

A Finite-State Machine for Controlling the Temperature in a Room5:31

Simulation of a Finite State Machine to Control the Temperature of a Room7:19

A Finite State Machine Modeling a Chess Game7:13

A Cyber-Physical System Model of a Thermostat (Part 1)6:28

A Cyber-Physical System Model of a Thermostat (Part 2)4:53

Simulation of a Cyber-Physical System Model of a Thermostat7:50

Models of Computations6:28

A General Discrete-Time Model of a Linear Time-Invariant Algorithm4:55

Познакомьтесь с преподавателями

Ricardo Sanfelice
Associate Professor
Department of Computer Engineering

[MUSIC]

With the addition of the gar function, now the finite state machine can

make transitions when certain conditions are true, and

those conditions might involve the input, the state, and the output.

One other feature that sometimes is needed is to be able to have

multiple possible states at the transition time.

Let's consider the following, Chessboard game.

It's a simplified version of the real game.

So we're going to do a grid of nine cells.

Each cell will have a number.

And according to the choice of the player, which for

us will be the input, we will characterize where the state of the system,

which corresponds to which cell one currently is at, would be.

So let's label these ones as red.

And this one as green.

The idea is as follows.

Suppose that one is the start.

And that if v is equal to red,

then new state.

Is any of the cells that is adjacent to one and red.

Well, if v is equal to green,

Then the new state could be any.

State that is adjacent to current state.

With green.

What does it mean?

Logically, he says

that if q = 1 and

v = red, then from

this plot q plus can be

either 1 again or 5.

If q = 1 and v = green,

Then the new value could be 2 or 4.

And we can continue this.

Now we can go to the next state, which will be q = 2.

Consider first v = red,

The new value of this state could be

any value among 1, 3, and 5.

And then similarly if q = 2 and v = green,

Then the new value from 2,

could be 2 itself, 4, or 6.

And we can continue these for all possible values of q and

all corresponding values of 3.

The point here is as you see here,

this is telling us that

the new state is not unique.

So such simple problems lead to finite state machines,

with set-valued, Transition function.

The way we are going to write that down is as we did before.

The new value of the state q is given by the transition function.

But now, because this might be a set that is more than a point,

we might have an E symbol right there.

And this delta is now not necessarily a function but

a set value map for which we will use the double-arrow symbol,

the symbol denoting that you might be mapping

points into sets that are more than a point.

So these are type of machines, and one can add an output and

one can add a gar function as we did before, but these are the type of

machines that have nondetermination into the cyber-physical model.

[MUSIC]

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