Jean-Jacques E. Slotine - US grants

This research aims at developing a design methodology for sliding mode observers for a class of nonlinear systems. The dual problem, that of sliding mode control presents some very interesting features in that in principle it possesses ideal robustness properties in the face of parametric uncertainty and disturbances. In practice, however, control chattering has severely limited the method's applicability. Observer design deals with the problem of reconstructing the state vector from measurements of the system output. For nonlinear systems, observers are currently designed using linearized techniques, particularly extended Kalman filtering. It would be highly desirable to design observers that directly account for the full nonlinear dynamics of the plant, as do sliding mode controllers. This award will allow the exploration of the ideas described above. In developing the theory and considering a simple practical example it should be possible to determine if the appplication of sliding mode observers is truly practical, or contains hidden difficulties.

There is a strong current research interest in adaptive control of robots, that is, control strategies which would allow a robot manipulator to automatically adapt to changes in its environment, loads, or to exceptional disturbances in order to successfully complete manipulation or assembly tasks. Some controller designs rely on approximations of system dynamics while others require measurements of joint accelerations and inversion of inertia matrices. This project further develops a new method which utilizes system kinetic energy rather than the fully expanded system dynamics. The method's strengths include guaranteed global convergence of the tracking, and computational simplicity. The project's focus is external control of unknown dynamic parameters, the problem of controlling the end effector of a passive mechanism along a desired trajectory using an active robot. This problem represents a large class of important practical applications involving motion control of complex mechanisms or mobile environments. Opening a door, turning a crank, as well as more complex problems in industrial settings belong to this class. The controlled mechanism has its own nonlinear dynamics which are generally unknown. The research will concentrate on transient performance of the control algorithms, and on trade-offs between joint space and Cartesian space formulations.

Humans and other animals are capable of remarkable range of intricate motor behaviors. Although the brain systems involved in motor control are mostly known, the way in which these systems function interactivley in motor control are mostly known, the way in which these systems function interactivley in motor control is still only partially understood. The investigators on this project have recetly developed a model of cerebellar control in which they propose that the cerebellum implements servo (feedback based) control of limb movements through the processing of "wave variables" (Massaquoi & Slotine, 1996). Wave variables are special linear combinations of command and senory signals that ensure stability of servo systems despite delays in signal transmission. The previously developed simple wave-variable-based cerebellar control model displays single-joint movement control of two-joint horizontal planar arm movement and also produces several realistic internal signals. The model includes the roles of the intermediate and lateral cerebellum and parts of the cerebrum, spinal cord, peripheral nerve and muscles. The current project is designed to verify and futher develop the cerebellar model by attempting to correlate signals observed in active experimental primates with those predicted by the model, and to account for motor behavior of healthy human subjects and humans suffering from cerebellar dysfunction. The performance of the model will be analyzed from the perspective of robot balance and leg control during ambulation. The investigating team seeks to develop a mdoel of human (primate) cerebellar system function which is physiologically, neurroanatomically and quantitatively accurate, and also fully comprehensible in engineering terms. It is anticipated that this will contribute significantly to the understanding of the mechanisms, capacities and limitations of human and animal motor control in health and disease. The project should also provide nsights into design principles for intelligent executive systems in general, both natural (brain-based) and artificial (robotic). Anticipated applications of this line of investigation include more precise and specific interpretation of functional neuroimaging data, improved rational design of neuroprosthetic devices and neurosurgical interventions, and the design of more behaviorally adaptable, well-coordinated and agile robots.

Networked microgrids (NMG, e.g., interconnections of house or district level microgrids powered by a solar panel or wind turbine) are increasingly utilized for sharing resources among microgrids, which can offer significant economic benefits. However, there is a poorly understood trade-off between robustness and fragility in this network setting. On one hand, the interconnection of multiple individual microgrids can improve the robustness of the microgrid network since the increased aggregate inertia will allow for better rejection of relatively small disturbances like load and renewable generation changes or minor load/generator outages. On the other hand, the interconnection will also extend the electrical and operational couplings between individual microgrids and lead to more routes of cascading failures (for example, a local failure of any microgrid can propagate throughout the network and threaten the whole network fragility). The project will make contributions in: (i) development of high-fidelity models of networked microgrids, bringing a new application domain to dynamics analysis and controls; (ii) development of computationally tractable optimization algorithms to solve the stability constrained optimal power flow problems involved in the analysis of the control actions; (iii) introduction of innovative network reconfiguration and intentional islanding algorithms to enhance networked microgrids resilience, which can inform innovations in risk mitigation of other complex networks. In the broader contexts, this project can help protecting critical infrastructures, e.g., airports, hospitals, buildings, during prolonged power outages due to natural disasters or cyberphysical attacks.

Aiming to fill the knowledge gap, this project will investigate intricate aspects of the robustness-fragility trade-off in networked microgrids. This knowledge then allows for the synthesis and validation of integrated preventive-corrective operational strategies that achieve the optimal compromise between overall robustness and fragility. Technically, we will analyze independently two complementary preventive-corrective strategies for ensuring the security of the NMG system with respect to the most common faults. Analyzing the cost-risk tradeoff of these two control actions will then lead to an optimal integration of preventive and corrective strategies into NMG operations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.