Research in Control

Research in the area of Control Theory, including the activities of the Control Systems Group (which includes the Information Control Engineering Group), ranges from theoretical issues such as robustness, aggregation, and adaptive control, to the construction of a computer-aided design environment for control systems, the use of neural networks for approximating optimal controller designs and system identification, the design of controllers for large space structures, and the control of hybrid systems. Multivariable and Robust Control The systematic design of multiple-input, multiple-output systems, using a unified time-domain and frequency-domain framework to meet accurate performance in the presence of plant and input uncertainty, is an extremely active research area in LIDS. Various theoretical and applied studies are being carried out by Professors Munther Dahleh, Eric Feron (chair of the IEEE Technical Committee on Robust Control), Steve Massaquoi, Alexandre Megretski, and their students. Theoretical research deals with issues of robustness, aggregation, and adaptive control. The aim of the research is to derive a computer-aided design environment for the design of control systems, which can address general performance objectives for various classes of uncertainty. Furthermore, new results on the robustness of nonlinear feedback systems, using feedback linearization, have been obtained for unstructured uncertainty model errors. Recent application-oriented studies include the control of large space structures, helicopters, and submarine control systems; issues of integrated flight control; control of chemical processes and distillation columns; automotive control systems; and the modeling and analysis of biological control systems. New applications for robust and programmed (finite state-based) control theory are now emerging at LIDS, including the real-time, agile guidance of single and multiple unmanned aerial vehicles, as well as vehicle anti-collision problems arising in air traffic control. Some of these concepts are implemented and tested on small helicopter systems. Professors Feron and Massaquoi are involved in a collaboration regarding the internal mechanisms that underlie the brain's ability to acquire programs that manage external dynamics and communication. Evolutionary Control Another new thrust regards the general question of how control systems might evolve over time to manage complex control problems. Professors Mitter, Dahleh, Massaquoi, and Berwick and postdoctoral associates Reuben Rabi and Fadi Nabib Karameh conduct this work. The hope is to understand principles common to self-optimizing control systems across multiple scales of time and space. Biology is used as the guiding example, with analysis of systems ranging from molecular biological control of metabolism to organ system interaction to ecological regulation. Feedback Control using Approximate Dynamic Programming Feedback controllers for nonlinear systems are often driven by potential (Lyapunov) functions, whereby the controller at each step steers the system in a direction of decrease of the potential function. The optimal cost-to-go function that results from dynamic programming formulations of control problems is a suitable such Lyapunov function, except that it may be difficult to compute. This research investigates whether recent approximate dynamic programming methods, that rely extensively on simulation and neural network training, can lead to a viable methodology for designing Lyapunov functions and controllers for nonlinear feedback systems. This research is carried out by Prof. Dahleh and his students. Identification and Adaptive Control Determining the fundamental limitations and capabilities of identification and adaptive control is an active area of research carried out by Prof. Dahleh and his students. This research program draws upon areas such as information-based complexity theory and computational learning theory, as well as upon the theory of robust control. One aim of this research is to develop a theory that combines both system identification and robust control within the same framework, in which a controller that meets given performance specifications can be designed based on finite noisy data. Issues studied include the representation of uncertainty in both noise and model, design of experiments, sample and computational complexity, and implementation of optimal algorithms. Computational Complexity Problems in systems and control theory are of varying degrees of difficulty, ranging from polynomial-time solvable to undecidable. Prof. John Tsitsiklis and coworkers have been using tools from theoretical computer science (theory of computation) to characterize the intrinsic difficulty of problems in stochastic optimal control, as well as various stability problems for hybrid systems, saturated linear systems, and linear time-varying systems. Control in Presence of Communications Constraints Prof. Mitter and colleagues Prof. Nicola Elia of Iowa State University, Prof. Sekhar Tatikonda of Yale University, plus several graduate students have been working on fundamental issues of control in the presence of communication constraints. The goal of this research is to understand the interaction between information and control in the presence of uncertainty. Development of real-time information theory forms an essential part of this research topic. Unmanned Air Vehicles Professors Dahleh and Feron and their students have been working on developing control architectures for unmanned vehicles. They have derived an architecture for the autonomous controller that enables the vehicle to perform agile maneuvers. The basis for this architecture is the derivation of a robust hybrid automaton. This automaton describes a rich set of controlled trajectories that can be attained by the vehicle, as well as the control necessary to transition between these trajectories. The robustness analysis of this dynamical description gives rise to a new and exciting class of robustness analysis problems that has not been looked at in the literature. The researchers have developed a complete simulation/animation environment, and their software (based on the above architecture) is now in use at Draper Laboratory, Barron Associates, Inc. and the Air Force Research Laboratory. A recent development in this problem is deriving efficient algorithms for performing real-time motion planning (contrasted from path planning, where vehicle dynamics are not taken into account) in a cluttered environment. These algorithms are based on randomization techniques performed on the manifold on which the dynamics evolve. This research entails the development of a hierarchical control system that replaces the human pilot in order to perform agile maneuvers.   With sponsorship from Draper Laboratory, Prof. John Deyst and his students are developing new guidance and control methods for operation of intelligent unmanned air vehicles (UAVs). This work addresses the coordinated action of groups of UAVs that operate together to accomplish complex tasks. Such coordinated action is required to accomplish tasks that are impossible, or would take excessively long periods of time, for a single vehicle to complete. Significant issues being addressed are the safe and effective flight of UAVs near each other, including rendezvous and docking of one vehicle with another. This capability is of particular significance for resupply of one vehicle by another, so as to allow sustained operation near some desired location, which might be some distance from a user. Coordinated flight is also essential for integrating various kinds of information sensed by many vehicles simultaneously. The operational needs of this class of systems pose particularly stringent requirements on various aspects of vehicle guidance and control. Identification and Learning of Complex Systems Prof. Dahleh has led a research effort in developing a theoretical framework for learning and identification of complex systems. To accurately define such a problem, one needs to: make assumptions about the generation of data; choose a model class from which a model will be selected; and choose a metric that captures the distance between the model and the actual system. One can also choose multiple model classes and derive a metric to evaluate which model class to choose. Classical approaches suffer from many pitfalls. First, they assume that the system that generated the data belongs to the model class (or one of the model classes). Second, they assume that the data record is long enough that one can accurately estimate the actual system. In fact, model quality evaluation methods assume such asymptotic convergence in computing a metric evaluating different model classes. Prof. Dahleh and his students have developed a new theoretical framework in which undermodeling is explicit in the problem formulation. Equivalently, the process that generates the data is not a member of the model classes considered. This work began in Dr. Saligrama Venkatesh's thesis several years ago. Recently, Dr. Soosan Beheshti developed a new measure of model quality evaluation, Model Description Complexity (MDC), that is computed from finite data. MDC is the correct generalization of AIC and MDL methods used heavily for evaluating model sets. Identification of Jump Parameter Systems Many systems are best modeled as jump-systems - systems that switch between relatively simple systems. Switching is controlled by a Markovian system. A hurdle in identifying such systems is the estimation of the sequence of switching from the continuous observations at the output. Prof. Dahleh and his students have developed a new framework for analyzing such systems based on Shannon's channel coding theorem and distortion theory. This work is the topic of the PhD thesis of Nuno Martins. Control, Communication, Computation Communication channels impose constraints on feedback systems that limit the achievable closed-loop stability and performance. Control theory has focused on characterizing the fundamental limitations and capabilities of closed-loop systems in the presence of both plant and input uncertainty. Communication constraints introduce a new class of uncertainty (e.g., quantization, average bit rate, or capacity) that existing theory deals with only indirectly. Prof. Nicola Elia visited LIDS for a semester to help in this area. Prof. Dahleh and his students, in collaboration with Prof. Elia, have derived new results for computing stability limitations of feedback systems in the presence of various channels, using both deterministic and probabilistic models. Analysis and Synthesis of Hybrid Systems Many applications involve the interaction of both discrete (logic) and continuous systems. A feedback system with bit constraints is an example of such interaction. The motion planning problems of UAVs is another example. Prof. Dahleh and Prof. Megretski are leading an effort to derive a formal theory for modeling, analysis, and synthesis of pure discrete systems. This work is the first step towards the derivation of a complete formal theory for hybrid systems.