L.G. Bushnell

Stabilization of multiple input chained form control systems

Abstract This paper presents a control law for stabilizing multiple input chained form control systems. This extends an earlier result of Teel et al. (1994) on stabilizing the above class of systems which have two inputs. In addition, we generalize this law to dynamical control systems and construct a transformation from general chained form systems with multiple generators to a power form. A control law which stabilizes the origin of a three-input control system that models the kinematics of a fire truck is simulated, confirming the theoretical results.

Real-time mixed-traffic wireless networks

In this paper we introduce a new protocol, prioritized carrier sense multiple access with collision avoidance, for real-time wireless local area networking. Wireless networks increasingly will be called upon to carry mixed traffic, some portion of which will be devoted to real-time control and monitoring. Our protocol, based upon the IEEE 802.11 wireless standard, mixes real-time traffic with standard multimedia data in a way which assures loop stability. Scheduling the real-time traffic is the primary issue considered. Under our framework, we propose and validate several new algorithms for dynamically scheduling the traffic of wireless networked control systems: constant penalty, estimated error order and lag first-order schemes. All algorithms are compared via simulation and the results show that dynamic scheduling algorithms achieve better system performance on average than static scheduling algorithms like fixed-order polling. The results of a real experiment involving two dryer plants and three IEEE 802.11 nodes are reported with static scheduling employed as it lower bounds the closed-loop behavior.

Steering three-input nonholonomic systems: the fire truck example

In this article we steer wheeled nonholonomic systems that can be represented in a so-called chained form. Sufficient condi tions for converting a multiple-input system with nonholonomic velocity constraints into a multiple-chain, single-generator chained form via state feedback and a coordinate transfor mation are presented along with sinusoidal and polynomial control algorithms to steer such systems. Our example is the three-input nonholonomic system of a fire truck, or tiller truck. In this three-axle system, the control inputs are the steering velocities of both the first and third (or tiller) axles and the forward driving velocity of the truck. Simulation results are given for parallel parking, left hand turning, right hand turn ing, and changing lanes. Comparison is made to the same vehicle without tiller steering.

Predictors for networked control systems

In this paper we propose a way to improve the performance of networked control systems, which we define as systems with a feedback loop closed through a communication network. We propose two types of algorithms for estimating the plant outputs in between two successive transmission times: an open-loop structure predictor and a closed-loop structure predictor. We analyze both in detail and prove that they do not affect system stability. We conclude the paper with simulations showing the effect these predictors have on the system performance.

Fast Modifications of the SpikeProp Algorithm

In this paper we develop and analyze spiking neural network (SNN) versions of resilient propagation (RProp) and QuickProp, both training methods used to speed up training in artificial neural networks (ANNs) by making certain assumptions about the data and the error surface. Modifications are made to both algorithms to adapt them to SNNs. Results generated on standard XOR and Fisher Iris data sets using the QuickProp and RProp versions of SpikeProp are shown to converge to a final error of 0.5 -an average of 80% faster than using SpikeProp on its own.

Stability, linearization and control of switched systems

We derive Lyapunov stability and linearization properties for a class of switched systems. Based on these properties, we use an LMI method to design stabilizing controllers for switched systems. An example is given to illustrate the theoretical results.

Control of bifurcations and chaos in heart rhythms

Cardiac arrhythmias have been closely linked to a variety of bifurcations and chaos. In this paper control of bifurcations and chaos for nonlinear models of cardiac electro-physiologic activity is investigated. Both the Andronov-Hopf bifurcation and period doubling bifurcation are treated. Washout filter aided feedback controllers are employed to control the location and stability of the bifurcations, and the amplitude of the bifurcated solutions. Important features of the dynamic control laws include equilibrium preservation even in the presence of model uncertainty, and automatic targeting of the orbits to be controlled. An independent experiment of suppressing cardiac alternans in a piece of dissected rabbit heart demonstrates the viability and utility of the proposed bifurcation control approach. Controlling nonlinear cardiac dynamics may have important clinical implications as arrhythmias in the heart such as fibrillation and ectopic foci are life threatening. The controller designs described here can lead to the development of future smart clinical pacemakers.

Report on the fuzzy versus conventional control debate

highlight of the 1998 IEEE Conference on Decision and Control was a debate on “Fuzzy versus Conventional Control” held at one of the plenary sessions. Organized under the auspices of the CSS Membership Activities Board History Committee (Dr. Linda Bushnell, Chair), the debate featured Professor Lotfi Zadeh of the University of California at Berkeley taking the side of fuzzy control and Professor Michael Athans, recently retired from MIT, arguing the merits of conventional control. The debate activities consisted of three parts: the dinner beforehand, held Tuesday evening; videotaped interviews with Athans and Zadeh, requested at the dinner and conducted Wednesday morning; and the debate itself, held Thursday morning. Videotapes of both the debate and the interviews are available via the IEEE History Cent er (U R L : h tt p : // w w w. i ee e . org/ history-center/) for a small fee to cover the cost of reproducing and sending the tapes.

A multi-steering trailer system: Conversion into chained form using dynamic feedback

In this paper, we examine in detail the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, connected together with rigid bars. We define the state space and kinematic equations of the system, modeling the pair of wheels on each axle as able to roll but not slip. we then investigate how this system of kinematic equations may be converted into multi-input chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization. In order to convert the system to this multi-input chained form, we use dynamic state feedback. We draw some motivation from the very simple example of a kinematic unicycle and the relationships of the angular velocities therein, and we show how the dynamic state feedback that we use corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. We briefly discuss how some of the methods which have been proposed for steering and stabilizing two-input chained form systems can be generalized to multi-chained systems. for concreteness, we also present two different example systems: a fire truck (three axles) and a five-axle, two-steering system. Simulation results for a parallel-parking maneuver for the five-axle system are included in the form of margin movies.

Adaptive finite-time control of nonlinear systems

Global adaptive finite-time control problems for two special classes of nonlinear control systems with parametric uncertainties are considered. A simple design approach is given based on Lyapunov function and homogeneity. The feedback laws can be constructed in the form with fractional powers as shown in the design examples.