Athanasios Sideris

Constrained H-infinity optimal control for robust control design

Constrained H-infinity optimal control provides a framework for robust control systems design with mixed time and frequency domain specifications. In constrained H-infinity optimal control the frequency domain specifications are formulated in terms of an H-infinity norm minimization problem and the time domain constraints as hard bounds on time responses of the closed-loop systems due to given test inputs e.g. step responses, etc. The latter are formulated as affine constraints to the H-infinity optimization problem and thus treated exactly, instead of approximately being translated to "equivalent" frequency domain specifications. This problem has been completely solved for general discrete time multivariable systems and its solution consists of solving a finite dimensional convex minimization problem (FDOP) and a standard H-infinity optimization problem.

Current research aims at extending constrained H-infinity optimization in many significant ways. A first objective is to develop the constrained H-infinity optimal control framework so that structured model uncertainty is handled with reduced conservatism and thus an even more complete set of specifications (time and frequency domain specifications, structured and parametric model uncertainty) can be addressed directly.

Another objective is to obtain low-order constrained H-infinity optimal controllers. Currently constrained H-infinity optimal controllers have a very large apparent order, but due to a great number of approximate pole-zero cancellations the effective order of these controllers seems to be at the same level with that of unconstrained H-infinity controllers.

Ongoing research in constrained H-infinity control includes extensions for continuous time and sampled data system. The basic work accomplished already in this direction promises an even more effective and efficient application of constrained H-infinity optimal control to practical control problems.

Finally, this project has an experimental component. A flexible beam experiment has been constructed under NSF funding and constrained H-infinity optimal control is currently applied and compared with weighted H-infinity optimization and "mu"-synthesis methods for the design of robust controllers.

Neural network control for robotic manipulators

In this research project the design of of controllers which include neural network components is being investigated for the purpose of controlling robotic manipulators. Control system configurations consisting of conventional PID controllers and neural networks connected in a feedforward or feedback fashion are being considered. The basic idea in such a scheme is to obtain improved control system performance in repetitive trajectory control tasks as the neural network is being trained. Important considerations include on-line training of the neural networks and their ability to generalize. A novel neural network structure resulting as a combination of Feedforward Neural network and the Cerebellar Model Articulation Controller (CMAC) network has been proposed and its properties are currently under investigation.

Robust control of vehicle motion

This project considers the control of combined longitudinal and lateral motion of individual vehicles with partial state measurements, which are longitudinal and lateral deviations, longitudinal velocity and yaw rate.

We have developed, an eighth order nonlinear state-space model to describe the combined lateral and longitudinal vehicle motion, where both coupling terms arising from the velocities and from the controls are included. Linearization around circular motion with arbitrary constant velocity and radius is characterized, and is approximated by a linear model with linear or multilinear perturbations of some simple functions of the scheduling variables --- longitudinal velocity, yaw rate, cornering stiffness and the vehicle load. The operating range is determined by a hypercube in the space of these four variables. After redefining the scheduling variables without introducing excessive conservativeness, a group of linear systems are obtained, which correspond to the vertices of the whole linearized system family in the new parameter space.

For each of the extremal linear systems, LQG-type controllers are designed through an optimization problem with LMI (linear matrix inequality) constraints. Upon solution, a common quadratic Lyapunov function is obtained for the whole family of the linearized closed-loop systems. This guarantees the stability and some related performance of the final gain scheduled control system, which is nonlinear. A compensator is reconstructed from the solution of the optimization problem and the schedulinging variables. Combining the information of road geometry and reference velocity profile, a gain-scheduled feedback-feedforward controller is obtained. Since the cornering stiffness and vehicle load are not measured, they are estimated using least square method.

Simulation results show that controllers obtained with this method are very robust to parameter variations, and perform well in the presence of measurement noise and initial deviations.

Current research in this project is directed towards designing H-infinity-type gain-scheduled controllers with guaranteed performance in an L-2-gain sense.

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