Real-time Predictive, Multivariable and Model-Based Control

Background

In Predictive Control a model of the plant is used to predict the future evolution of the system. Based on this prediction, at each time step t a performance index is optimized under operating constraints with respect to a sequence of future input moves in order to best follow a given trajectory. The first of such optimal moves is the control action applied to the plant at time t At time t+1 a new optimization is solved over a shifted prediction horizon.

Hybrid systems are heterogeneous systems that exhibit both continuous and discrete dynamics. A typical example would be a continuous system interacting with a controller that involves some logic components. Hybrid systems are ubiquitous in industry. Usually controllers for hybrid systems are designed heuristically: the most common approach resorts to using tools developed for linear systems, patched with a collection of heuristic rules. A lengthy and expensive trial and error procedure is required in order to achieve satisfactory performance characteristics.

Brief description

This research area considers the problem of computing the state feedback solution to predictive control problems for multivariable linear and hybrid systems and implementing it in real-time.

We focus on the solution to finite time, infinite time and min-max optimal control problems with cost functions based on 2, 1 and ∞ norms. We have demonstrated that the solution to all these optimal control problems can be expressed as a piecewise affine state feedback law. Along with the analysis of the solution properties we have developed algorithms that efficiently compute the sate feedback optimal controllers.

The results form a natural extension of the theory of the Linear Quadratic Regulator to constrained linear and hybrid systems. They also have important consequences for the implementation of predictive control laws. Precomputing offline the explicit piecewise affine feedback policy reduces the on-line computation for the predictive control law to a function evaluation, therefore avoiding the on-line solution of a mathematical program as is done in Model Predictive Control. Thus, this new technique has enlarged the scope of applicability of MPC to small-size/fast-sampling applications.

Current research

Developing further the theory by focusing on robustness, estimation, tracking and min-max control.

Computing low complexity stabilizing controllers for constrained linear and hybrid systems and trading off optimality for complexity in a systematic manner.

Studying new methods for efficient on-line evaluation of the piecewise affine state feedback optimal control law.

Selected Applications

Traction Control (in collaboration with Ford Research Labs)

Robotic Chameleons Visual Scanning(in collaboration with the Israeli Institute of Technology)

Diesel Engine Control (In Collaboration with Honeywell Research Labs)

Selected Publications (Go to Publication List for Download)

F. Borrelli. 'Constrained Optimal Control of Linear and Hybrid Systems', Lecture Notes in Control and Information Sciences, Springer-Verlag. Vol 290. 2003.

F. Borrelli, M. Baotic, A. Bemporad, M.Morari. 'Dynamic Programming for Constrained Optimal Control of Discrete-Time Hybrid Systems'. Automatica, vol. 41, no. 12, January 2005, p. 1709-1721.

P. Grieder, F. Borrelli, F.D. Torrisi, M. Morari. 'Computation of the constrained infinite time linear quadratic regulator', Automatica, vol. 40, no. 4, April 2004, p. 701-708.

A. Bemporad, F. Borrelli, M. Morari. 'Min-max Control of Constrained Uncertain Discrete-Time Linear Systems', IEEE Transaction on Automatic Control, Vol. 48, No. 9, September 2003, p. 1600-1606.

Software

MPT Multiparametric Toolbox download here

Linear Time Varying MPC Toolbox (package under preparation, please send an email if need urgently)

Large Scale Hybrid Distributed Control

Background

We focus on distributed control problems for large scale dynamical systems composed of loosely coupled subsystems. A set of unmanned vehicles moving in formation, cross-directional weight control in paper machines, the coordination of cameras in a monitoring network, and the coordination of wireless sensing/control devices for microclimate control in large buildings are all problems belonging to this class.

Brief description

In the control problem the subsystems are dynamically decoupled or loosely coupled. Nevertheless, their dynamical behavior is coupled through a performance index and the interconnection constraints. Such coupling is described through a graph where each system is a node and the control action at each node is based only on local and neighboring state information. We study the analysis and the synthesis of distributed controllers depending on the structural properties of the interconnection graph topology.

We have introduced a novel methodology for the synthesis of distributed controllers which takes explicitly into account the interconnection constraints and uses the model of the neighbors to predict their behavior. Stability conditions have been derived. Such conditions (i) highlight the role of prediction errors between neighbors in the stability of the aggregate system, (ii) are local to each node and depend only on neighboring nodes that can be reached trough at most two edges, thus leading to a complexity reduction for interconnection graphs of large diameter, and (iii) help understand the importance of information exchange between neighbors and its role in stabilizing the entire system.

Current research

The proposed distributed framework provides an attractive and simple way for synthesizing distributed controllers. We are currently studying

the analysis and the synthesis of coordination rules for improving the feasibility domain of the distributed control law.

the interplay between graph topology, stability, performance and robustness to disturbance propagations.

Selected Applications

Distributed Control of Organic Air Vehicles formations (in collaboration with Honeywell Research Labs)

Real-Time Scheduling, Resource Allocation and Trajectory Planning of Unmanned Vehicles (in collaboration with Honeywell Research Labs)

Production Scheduling in a FIAT-GM Engine Company

Selected Publications (Go to Publication List for Download)

F. Borrelli, T. Keviczky. 'Distributed LQR Design for Identical Dynamically Decoupled Systems'. IEEE Transaction on Automatic Control. 2008, In press.

F. Borrelli, T. Keviczky, G. Balas, G. Stewart, K. Fregene, D. Godbole. 'Hybrid Decentralized Control of Large Scale Systems'. Proceedings of Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, vol. 3414, Springer-Verlag GmbH . March 2005. p. 168-183.

T. Keviczky, F. Borrelli, G. Balas. 'Decentralized Receding Horizon Control for Large Scale Dynamically Decoupled Systems'. Automatica, vol. 42, no. 12, December 2006, p. 2105-2116.

Advanced Vehicle Dynamic Control

Background

Trends in the automotive industry point in the direction of increased employment of electronics, computers, and controls with emphasis on the improved functionality and overall system robustness. While this affects all vehicle areas, there is a particular interest in active safety, which effectively complements the passive safety counterpart. Passive safety is primarily focused on the structural integrity of the vehicle. Active safety on the other hand is primarily used to avoid accidents and at the same time facilitate better vehicle controllability and stability especially in emergency situations, such as what may occur when suddenly encountering slippery parts of the road.

In our research we expect that future control systems will be facilitated by additional actuator types such as active steering, active suspensions, or active differentials, and by additional sensor information, such as onboard cameras, infrared cameras and radars. All these will be further complemented by GPS information. In this context, it is possible to imagine that future vehicles would be able to identify obstacles on the road such as an animal, a rock, or a fallen tree/branch, and assist the driver by following the best possible path and at the same time keeping the vehicle on the road at a safe distance from incoming traffic. Additional information about the environment could come from surrounding vehicles and provide a significant amount of preview to the controller. This is particularly useful if one travels on snow or ice covered surfaces. In this case, it is very easy to reach the limit of vehicle handling capabilities.

Brief description

With the described trend in sensors and actuators infrastructure, it comes natural to ask what is the optimum way for controlling the vehicle maneuver in a given obstacle avoidance situation. Our research focuses on formal methods for designing advanced autonomous guidance system. In particular, together with the Ford Research Laboratories in Dearborn, USA, we are applying the Explicit MPC algorithms and Nonlinear Constrained Optimal Control theory to several advanced vehicle dynamics control problems.

We have successfully applied Explicit MPC strategies to a traction control design problem. Road tests on a Ford Focus have shown that explicit MPC can be implemented in real time and can systematically handle the challenges arising from nonlinear tire dynamics. The journal 'USA Today' on the 28-10-2005 wrote about the Ford Traction Contoller: '..Traction control on the V-6 test car was just right -- perhaps unique in all the industry. It allowed tire spin when starting forcefully on slick roads and gradually eased the spinning without trying to stop it'

We have successfully applied MPC strategies for the development of active steering controllers. Road tests on a Jaguar vehicle have shown that MPC keeps the vehicle on the desired track despite slippery road conditions and high vehicle speeds. It has been shown that MPC can stabilize the vehicle travelling at high speeds on icy roads. Under the same conditions, any controller designed with traditional methods does not succeed in stabilizing the vehicle. To the best of our knowledge, for the first time a nonlinear MPC scheme has been implemented on a dSPACE rapid prototyping system to control the vehicle dynamics of an autonomous passenger car with a sampling frequency of 20 Hz.

Current research

We are working on implementing a complex predictive control scheme for controlling the logitudinal and lateral motion of the vehicle by using active differentials, steering, brakes and throttle.

Selected Publications (Go to Publication List for Download)

Francesco Borrelli, Alberto Bemporad, Mike Fodor, Davor Hrovat. An MPC/Hybrid System Approach to Traction Control. IEEE Transaction on Control System Technology, vol. 14, no. 3, May 2006, p. 541-552.

Francesco Borrelli, Paolo Falcone, Tamas Keviczky, Jahan Asgari, Davor Hrovat. MPC-based approach to active steering for autonomous vehicle systems. International Journal on Vehicle Autonomous Systems, vol. 3, no. 2/3/4, November 2005, p. 265-291.

P. Falcone, F. Borrelli, J. Asgari, H. E. Tseng, D. Hrovat. 'Predictive Active Steering Control for Autonomous Vehicle Systems". IEEE Transaction on Control System Technology, vol. 15, no. 3, May 2007, p. 566-580

Multi-parametric Programming and Control Theory

Backgorund

The operations research community has addressed parameter variations in mathematical programs at two levels: sensitivity analysis, which characterizes the change of the solution with respect to small perturbations of the parameters, and parametric programming, where the characterization of the solution for a full range of parameter values is sought. Our interest in multiparametric programming arises from the field of system theory and optimal control. For discrete time dynamical systems finite time constrained optimal control problems can be formulated as mathematical programs where the cost function and the constraints are functions of the initial state of the dynamical system. By using multiparametric programming we can characterize and compute the solution of the optimal control problem explicitly as a function of the initial state.

Brief description

Our research focuses on design and implementation of algorithms for solving multi-parametric linear programs, multi-parametric quadratic programs, multi-parametric mixed-integer linear and quadratic programs.

We have developed novel algorithms for solving the aforementioned parametric optimization problems. The main idea of the multiparametric algorithms is to construct a critical region in a neighborhood of a given parameter, by using necessary and sufficient conditions for optimality, and then to recursively explore the parameter space outside such a region. For this reason the methods are classified as 'geometric'. They constitute the basic tools for computing the state feedback optimal control laws for constrained systems in the same way as algorithms for solving the Riccati equation are the main tools for computing optimal controllers for linear systems.

Current Research

We are continuously improving the efficiency of the proposed algorithms and developing novel algorithms for broader classes of parametric optimization problems.

Selected Publications (Go to Publication List for Download)

F. Borrelli, A. Bemporad, M. Morari. 'A Geometric Algorithm for Multi-Parametric Linear Programming', Journal of Optimization Theory and Applications, Vol. 110, No. 3, September 2003, p. 515-540.

F. Borrelli. 'Constrained Optimal Control of Linear and Hybrid Systems', Lecture Notes in Control and Information Sciences, Springer-Verlag. Vol 290. 2003.