[MUSIC] In this video we're going to simulate an estimator that receives information from a network that takes values of the output of a physical component, a physical plant. And we've already seen in previous video a piece of these, in particular physical component, and also the physical component with a network. I already prepared a simulating file for this. And it is here. What we see here is a plant with a state that is being a push on field. The output is being measured by a network. The network transmit information over a window using a non-deterministic choice of time instances. And those will be such that the next event doesn't occur sooner than T in min but it doesn't occur also later than T in max. Once the information arrives into the system, the estimator going to use that impossibly to reconstruct the state of the system exponentially fast. So the immunization file will do for us the selection of not only the simulation horizon but also the constants that corresponds to the maximum time until the next event and the minimum time until the next event correspondent to transmission of information. And the times in which those occur are chosen randomly at the initialization time. And then we have the inital conditions for the plant, the physical component which is a four dimensional system, and then the initial condition for the network. Now the estimator might have also some initial values which are similarly not supposed to be similar in any means by those of the plan of the physical system to estimate. And the system are having constants are linear. It then flows and it's given by this constants given here, a then the system matrix b, the input matrix which is equal to 0, and then the entity is the output matrix. Now the estimator is designed using methods that we're not explaining in this video but adx tab will assign again that will inject the information that arise at the event in an impulsive manner in order to create improvement in the estimator we have of the actual state. I noticed that all we'll receive for this system is one state rather than four components which is the dimension of the state. And the variables elimination are set to be similar as before in previous simulations. So let's run this initialization file and let's make sure that this has created the right values. So 10.2 for the window, and 50 seconds for the simulation, this sounds what we want, perfect. Now we can run the simulation. For which we'll have to compile and then it's going to start running, As expected The output of estimator we call it z hat which is an estimate of z which is a state of a physical component. And what we expect is that the z hat components, the four components of z hertz converge to the four components of z. Okay, we finished the simulation. And now we burn prep. Okay, so what we see here are, in each plot, the state of the system and also the estimate that is being provided at the output of the estimator. As you see in the first plot the initial conditions are off, and similarly trajectories that we obtain from the system and from the estimator is different. But after some events what you see is that estimates get close to the actual true system state. And after some jumps, one, two, three, and four, that are pretty close and remain pretty close. In theory they converge in the limit exponentially. And the same happens for variables as well. The estimator implements hybrid algorithm that is triggered whenever has a jump, whenever information arrives. And for that the implementation of a simulation needs to take care of the mechanism carefully. One can look into this just by going under the hood of the estimator block. Now the estimator block is no more than a general hybrid system. So we actually picked that from the, not necessarily from this higher physical system block but from the higher equation block which is this one, right here which is an optimize block. All right, so that's the simulation of a estimation problem where we have a series interconnection of three blocks. It is three blocks used, how it models. And the plant is not necessarily have this purely continuous time. And as you saw the [INAUDIBLE] is nondeterministic and the estimator is actually higher. [MUSIC]
