Adaptif model öngörülü kontrolör ile konsensus kontrolü
Consensus control with adaptive model predictive control
Yazar: ANIL YILMAZ
Danışman: DOÇ. DR. YAPRAK YALÇIN
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2021
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control

Özet:
Sanayi devriminden günümüze kadar teknolojinin imkanlarıyla bir çok alanda ürünler üretilmektedir. Geçtiğimiz son kırk yılda ise bu ürünlerin beraber kullanılması problemi üzerinde durulmaktadır ve son yıllarda da bu beraber işleyişin otonom olması üzerinde çalışılmaktadır. Literatürde bu yaklaşıma konsensus (sürü) kontrolü denilmektedir. 
Konsensus probleminin çözümü için birçok kontrol yöntemi bulunmaktadır. Bu kontrol yöntemleri içerisinde sistem modelinden yararlanılarak gelecek sistem durumlarının öngörüsünü yapıp gelecekteki davranışı da kontrol kuralı işareti üretiminde göz önünde bulunduran, sistem ajanlarının davranışına kısıt ekleme olanağı da sağlayan Model Öngörülü Kontrol (MPC) bu çalışmada kullanılmıştır. 
Merkezi yönetim birimlerinin olmadığı kolonilerinin sürü çalısmalarında her ajanın, sürüdeki diğer ajanların tümü ya da bir kısmının verilerine (konum, hız) erişebildigi varsayımı yapılmaktadır. Diğer yandan, literatürde MPC ile konsensus kontrolü genellikle hedef formasyonun, matematiksel olarak ifade edilebilen geometrik şekiller olduğu durumlar için yapılmaktadır. Bununla birlikte literatürde konsensus kontrolü için, adaptif model öngürülü kontrol yapısı konusu yeterli olarak ele alınmamaktadır. Bu çalışma ile adaptif model öngürülü kontrol yapısı formasyon kontrolü sağlanarak literatüre katkıda bulunmak hedeflenmiştir. 
Diğer yandan bu çalışmada, aynı dinamiklere sahip formasyon üyeleri kullanarak adaptif model öngürülü formasyon kontrolü problemini merkezi karar verici birimin olmadığı, ilgili ajanların kendi başına karar alabildiği bir yapı olarak ele aldık. Bu çalışma kapsamında ele alınan probleme göre kolonilerdeki tüm ajanlar haberleşme topolojisine göre komşu ajanın bilgilerine ulaşabilmektedir. Bu çalışmada ajan dinamiklerinde bulunan bilinmeyen parametreler çevrimiçi olarak daldırma ve değişmezlik yöntemi ile kestirilmiş ve kestirilen bu parametreler MPC kontrolde kullanılmıştır. Çalısma kapsamında ajan dinamikleri, parametre kestiricisi, MPC kontrolörü MATLAB&SIMULUNK ortamında gerçeklenerek, önerilen yöntemin başarısı test edilmiştir.

Abstract:
From the industrial revolution to the present, products are produced in many areas within the possibilities of technology. In the last thirty years, the problem of using machines altogether has been focused on, and in recent years, autonomous cooperation has been researched. In the literature, this approach is called consensus control. 
In consensus studies of colonies without central control units, it is assumed that each agent can access the data (location, speed) of all or some of the other agents in the group. On the other hand, in the literature, consensus control with MPC is usually done for cases where target formation is geometric shapes that can be expressed mathematically. The adaptive model predictive control structure is not adequately addressed for consensus control in the literature. Within the scope of this study, it is aimed to contribute to the literature by providing the adaptive model predictive control structure for formation control. Moreover, in the literature, formation control is generally done for known fixed shapes that can be defined mathematically.
There are many control methods to solve the consensus problem. Among these control methods, Model Predictive Control (MPC), which predicts future system states by using the system model and produces control signals by taking into account the predicted state and/or output information. MPC also provides the opportunity to add constraints to the behavior of system agents.
MPC can be formulated in many dynamic system presentations. These are the step response model, Impulse response model, Transfer function model, Linear model in state space, Nonlinear model in state space respectively.
All MPC algorithms consist of 3 basic elements. Different approaches can be taken by using these basic elements. These three basic elements are model, objective function and control law respectively.
The model of the system is one of the most important issues for MPC. In a good design, the system model should be well modeled to create the best check mark. This model must be incomplete enough to fully capture system dynamics and allow theoretical analysis. The process model is used to calculate estimates of future exits. Various models are used to represent the relationship between outcomes against different use cases of MPC. A model can be a linear or a nonlinear system. Generally, dynamic models are represented by state-space systems. In this study, in MPC design linear state space model of the agents is used.
Different objective functions can be used in various MPC algorithms. The purpose of this function is to ensure that the system output y (t) follows a specified reference w(t) throughout the prediction horizon. It also punishes the control signal in doing so.
To find the control input u(t+k |t) for the system, it is necessary to minimize the cost function created for the system. To obtain this, it is necessary to establish the state and output prediction equations interms of known and measurable values and future control signals.  After prediction equations are found these are substititued in objective function and the future control signals that minimizes objective function is found. If the system is linear and there are no constraints, the control sign can be found analytically by minimizing the objective function. In other cases, it is necessary to make iterative solutions.
Three mini autonomous land vehicles following the leader in a triangle formation is the subject of this study. To achieve this, an adaptive model predictive control structure is created. It is assumed that these three mini autonomous land vehicles (agents) and the leader have similar dynamics.
In the first chapter, the aim of the thesis is discussed and literature research is done. In literature, formation control, MPC and the use of immersion and invariance methodology in industry are mentioned.
At the end of the first chapter, brief information about the immersion and invariance (I&I) is given. After the general information, the mathematical expression of the parameter estimator is written. These immersion and invariance equations are applied on the nonlinear vehicle model 
In the following chapter, multi-degree of freedom nonlinear vehicle dynamic equations and coefficients required to control vehicles are explained. The linearization and discretization of the created vehicle dynamics are explained.
A good system modeling is required to create a good control structure and apply it as desired in real systems. This model should show the physical maneuverability of the vehicle and reflect the real system as much as possible. In this study a cascade control with an inner loop and outer loop is established. In the outer loop we construct a nonlinear controller and we use the nonlinear system model. However, for the inner loop we designed a linear model predictive controller. Since a linear controller is used in the inner loop, nonlinear system equations is linearized and system matrices in linear state space is obtained. 
With a simple physical model of a wheeled vehicle, the effects affecting vehicle dynamics should be demonstrated. There is a lot of information about vehicle dynamics and modeling in the literature. Our main goal here is to make our model as simple and applicable as possible. Depending on the purpose, many vehicle dynamics can be created. Since we want to control the position, it is thought that the x and y position values, speed and head angle of our vehicle will be sufficient for us. In this context, a 4-state vehicle dynamics equation is created. In order to find the vehicle dynamics equations, the vehicle model reduced to one wheel can be used to find the force and moment magnitudes acting on the vehicle.
In the fourth chapter, Immersion and Invariance parameter estimator and MPC based formation controller design is performed.
We discussed the adaptive model predictive formation control problem as a structure in which there is no central control unit and each agent can make decisions on their own. According to the problem dealt with in this study, all agents in the colonies can access the information of the neighboring agent according to the communication topology. In this study, the unknown parameters in agent dynamics are estimated online by Immersion and Invariance method and these estimated parameters are used in MPC control. Within the scope of our study, agent dynamics, Immersion and Invariance (I&I) parameter estimator, MPC controller are implemented in MATLAB & SIMULUNK environment, and the success of the proposed method is tested.
In the last section, the results obtained are summarized and the results are shown in graphics. The contributions of this study are emphasized. 
Overall, it has been shown that the MPC successfully generates the desired controller performance criteria for a consensus problem. It has been observed that the use of parameter estimation obtained by the Immersion and Invariance method in the consensus MPC structure gives a successful adaptive performance.