About Us
[Advanced Control Systems Group] [Autonomous Mobile Robotics Group]

Optimal Control

Optimal control

In many problem instances we want to control the system in an optimal way. An objective can be to minimize energy consumption, maximize profit, minimize tracking error, minimize settling time, etc. This natural desire in achieving the best possible system performance is usually formulated as an optimization problem, i.e. as a mathematical program.

Model predictive control

The modelled system dynamics can be used to predict the future system evolution based on the current system state. Control formulations where model-based predictions are used fall in the category of the model predictive control (MPC). The MPC objective is formulated as a function of the system states and control actions over a pre-specified horizon. The control sequence that minimizes the objective subject to the state+input constraints is then found.

In accordance to the receding horizon principle, the first element of the optimal sequence is applied to the system, and the whole procedure is repeated at the next time instance over a shifted horizon.

Thanks to the variety of model types that can be used for the prediction in the MPC framework, and due to the natural incorporation of the system constraints, the MPC quickly became a very popular control strategy in the process industries. However, one should point out the the real problem is not solved simply by using the MPC strategy - it is just ''moved'' to the underlying optimization problem. Precisely for that reason the MPC was applied mostly to the relatively slow processes for which one could afford (time- and money-wise) the usage of a significant computational power.

Luckily the things have changed in the last decade. We are now equipped with the techniques - the so-called multi-parametric mathematical programming - that allow the off-line pre-computation of the optimal control law. In this way, instead of solving a difficult optimization problem on-line, all we need to do is evaluate a look-up table like function.


Hybrid Systems

Recent technological advances have caused a considerable interest in the study of dynamical processes of a mixed continuous and discrete nature, denoted as hybrid systems. We focus on the class of discrete-time piecewise affine (PWA) systems that are defined by the partition of the extended state-input space into polyhedral regions and a set of different affine state update equations associated with those regions. A simple example of a hybrid system would be a car. The dynamics of the car switch when a gear shift occurs, either because the driver moves the stick shift (input event) or because the state variable "speed" exceeds a specified threshold (state event) in the case of an automatic transmission.

Different methods for the analysis and design of controllers for hybrid systems have emerged over the last few years. Among them, the class of optimal controllers is one of the most studied. The optimal control problem for a PWA model of the system can, in general, be restated as a mixed-integer program -- a non-convex mathematical problem that would be hard to solve in real-time. However, by using multi-parametric mathematical programming, the closed-form of the optimal control law can be computed off-line for the whole admissible range of the system states.

An important element in the industrial implementation of optimal controller strategies for hybrid systems is existence of a systematic system identification procedure of a PWA model of the system. Furthermore, to ensure a robust performance of the controlled system one needs to take into account the mismatch (i.e. uncertainty) between the model and the real system. This is the subject of our current research.


Sliding Mode Control

Sliding Mode Control (SMC) is an effective robust control approach for uncertain systems. SMC algorithm consists of the following steps. 1) Choosing a sliding surface in the state space that has a desired characteristics. 2) By the appropriate control law we first make the system states reach the surface (reaching phase), and then we keep them on the surface. Control signal from then on is a sum of two signals: a continuous one and the discontinuous one with a high switching frequency. Once the states have reached the sliding surface, the closed-loop system is insensitive to the variations in the system parameters and external disturbances.


Intelligent Control

In control of complex systems achieving and maintaining high performance under adverse conditions often cannot be ensured by conventional approaches to control. In such cases a common practice is to use highly sophisticated control approaches which are referred to as intelligent control. Intelligent control comprises a number of diverse research areas ranging from control systems and computer science to the operational research. It (usually) covers the following research topics: expert systems, neural networks, fuzzy systems, machine learning, multi-sensor integration, etc. Intelligent control systems are typically able to perform some of the following functions: planning future actions, emulate human expert behavior, learning from past experiences, integrating sensor information, identifying changes that could degrade system performance and reacting appropriately. Our group is primarily focused on research and development of advanced control algorithms based on neural networks and fuzzy logic.

Estimation Theory

Mobile Robot Localization

PROBLEM: Mobile robot localization problem is usually defined as a problem of estimating robot pose relative to the map of its environment. Depending on the prior knowledge we differentiate two cases: 1. the pose tracking problem (initial position of a mobile robot is known), and 2. the global localization problem (robot position has to be estimated from scratch). The pose tracking problem can be effectively solved with the classical Kalman filtering approach, because normal distribution accurately approximates the probability distribution around the true robot position. However, in the case of an unknown initial robot position (global localization problem), assumption about the normal probability distribution of the robot pose is violated and therefore more sophisticated algorithms have to be used.

GOAL: Our research is focusing on the design of an efficient localization algorithms with emphasis on the global localization problem. Additional problem that may occur during localization is the so-called "kidnapped robot problem", where the mobile robot is being teleported to another location. In this case, it is apparent that the localization algorithm must effectively detect such a situation and estimate the new robot pose as fast as possible.

METHODOLOGY: The estimation strategy used in our research is based on the particle filter algorithms. In the context of global localization, compared to the classical approach based on Kalman filters, the main advantage of particle filters is their ability to approximate arbitrary probability distribution. However, since the particle filter based algorithms are, in general, computationally demanding we are also investigating how to reduce complexity of the the robot localization algorithms.

Tire/Road Friction estimation

PROBLEM: This topic plays important role in many vehicle control systems due to the fact that the vehicle behavior is primarily determined by the forces transferred between the wheels and the road. Therefore, many vehicle control systems like Anti-lock Brake System (ABS), Traction Control (TC) system, Electronic Stability Program (ESP) can be generally considered as control systems whose goal is efficient control of the amount of forces transferred from the vehicle tire and the road. Since the actual friction force cannot be easily measured, it has to be estimated on the basis of information collected from standard sensors (e.g. wheel speed encoders).

GOAL: Our research focuses on the design of the tire/road friction estimators that provide information about the tire/road friction, either by estimating the actual value of the friction force or by the road condition parameter. Additionally, a tire/road friction estimator should cope with the problem of signal and model uncertainties (measurement noise, modeling uncertainties, time variability of the process, etc.).

METHODOLOGY: Methodologies used here include optimal filtering such as Kalman filter (and its sub-variants), Artificial Neural Networks based methods and Nonlinear methods based on passivity.


Distributed Control

Distributed control systems for real-time applications depend heavily on the reliability of the communication. Buses like CAN are not reliable enough to be used in the "x-by-wire" systems (airplane, car, rail). It is hard to mathematically describe and verify event-triggered systems. That is why the time-triggered systems such as TTP/C and FlexRay are being developed and researched.

Because of the widespread use of CAN in the automobile and other industries, systems that emulate CAN or use CAN-like communications are being investigated too. These solutions balance between the development and implementation costs on one side and the control system requirements on the other side. One such communication protocol is a Time-Triggered CAN (TTCAN).

A goal of the project "Distributed control systems for rail vehicles" -- a joint project by the Faculty of Electrical Engineering and Computing and Končar - Electrical Engineering Institute -- is to develop new control systems based on the latest technologies to be implemented in the rail vehicles produced by Končar company.



Wind Turbines
Modern wind turbines in the MW class operate in a wide spectra of environmental conditions from calm to stormy winds. Wind turbine behavior changes drastically with the change of an operating point since the wind power increases with the third power of the wind speed.

Turbine operation can be divided in two very distinct regions:
1. Below Rated (wind speed bellow the nominal value) The wind power is lower than the nominal power output of the turbine. The control system has to assure maximal capture of the wind power through some optimal control strategy.

2. Above Rated (wind speed above the nominal value) The amount of wind power captured by the turbine has to be limited to protect it from overspeed as well as to protect the power generator from overload. We focus on the turbine control in the above rated region. In particular, we utilize the so-called pitch control, where, as the name suggests, the wind power capture is limited by pitching the blades of the turbine.
Although very efficient in limiting the wind power capture the pitch control is introducing additional structural loads. To minimize fatigue and avoid premature structural failure of the turbine these structural loads should be taken into account during the controller design. The change of the wind turbine characteristics with the increasing wind speed observes a nonlinear character. To ensure efficient limitation of the captured wind power through the entire operating range the control system has to be adaptive. Furthermore, since wind turbines operate without direct human supervision the control system has to encompass constant system monitoring and fault detection. In the case of unrecoverable system error it has to position (stop) the turbine to the safe state and alert the remote personnel. All tasks mentioned above make the wind turbine control system design a challenging task where advanced control strategies have to be explored to achieve the fine balance between the system robustness and performance.


Load Frequency Control
Load Frequency Control (LFC) is an essential service in power systems that maintains the system's integrity by matching generation and demand in real time. Its aim is to track the load demands in the power system together with prearranged power flows between different countries (or areas) while keeping the system frequency at a constant value (50 Hz in Europe). The signals sent by the LFC-controller via communication channels have variable time delays.

Time Delay Systems (TDS)

The presence of time delay can make many existing control systems inadequate and can even lead to instabillity. Some controllers for time-delay systems have delay dependent parameters, while others can stabilize systems with delays less than some maximal value. Delays can exist in the state variables, in the input signal, or in both. LFC is modeled as an input-delay uncertain system and we use sliding mode control to achieve the desired behavior.


Automotive Systems