E-mail: asideris@uci.edu

Office: EG 3205

Phone: (949) 824-8139

### 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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Last Updated: May 12, 1995