Showing papers presented at "American Control Conference in 1991"

Systematic Design of Adaptive Controllers for Feedback Linearizable Systems

Abstract: A systematic procedure is developed for the design of new adaptive regulation and trackdng schemes for a class of feedback linearizable nonlinear systems. The coordinate-free geometric conditions, which characterize this class of systems, neither restrict the location of the unknown parameters, nor constrain the growth of the nonlinearities. Instead, they require that the nonlinear system be transformable into the so-called pure-feedback form. When this form is "strict", the proposed scheme guarantees global regulation and tracking properties, and substantially enlarges the class of nonlinear systems with unknown parameters for which global stabilization can be achieved. The main results of this paper use simple analytical tools, familiar to most control engineers.

Think Globally, Act Locally: Decentralized Supervisory Control

Abstract: Decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints but whose solution is described by local controllers. A necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behaviour of the closed-loop system lies in a given range. Where the range of behaviour can be described by regular languages, it can be effectively tested whether the decentralized control problem is solvable; in this case, a procedure is given to compute the associated supervisors.

Longitudinal Vehicle Controller Design for IVHS Systems

Abstract: This paper describes a combined throttle/brake control algorithm designed to control intervehicle spacing within a fully automated "platoon" of vehicles. The control algorithm is developed using a modified sliding control method due to the inherent nonlinearities that exist in current automotive vehicles. Tne controller is designed using a simplified four state vehicle model and then simulated on a more complete nine state model. Simulations are shown for a two vehicle platoon and for a four vehicle platoon. The four vehicle platoon simulations illustrate the need for "feedforward" platoon information to eliminate disturbance amplification within the platoon. It is shown that communicating the lead vehicle's velocity and acceleration to all platoon vehicles is sufficient to prevent this amplification.

Gaussian Networks for Direct Adaptive Control

Abstract: A direct adaptive tracking control architecture is proposed and evaluated for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs a network of gausian radial basis functions to adaptively compensate for the plant nonlinearities. Under mild assumptions about the degree of smoothness exhibited by the nonlinear functions, the algorithm is proven to be stable, with tracking errors converging to a neighborhood of zero. A constructive procedure is detailed, which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy. A stable weight adjustment mechanism is then determined using Lyapunov theory. The network construction and performance of the resulting controller are illustrated through simulations with an example system.

Reinforcement Learning is Direct Adaptive Optimal Control

Abstract: Control problems can be divided into two classes: 1) regulation and tracking problems, in which the objective is to follow a reference trajectory, and 2) optimal control problems, in which the objective is to extremize a functional of the controlled system's behavior that is not necessarily defined in terms of a reference trajectory. Adaptive methods for problems of the first kind are well known, and include self-tuning regulators and model-reference methods, whereas adaptive methods for optimal-control problems have received relatively little attention. Moreover, the adaptive optimal-control methods that have been studied are almost all indirect methods, in which controls are recomputed from an estimated system model at each step. This computation is inherently complex, making adaptive methods in which the optimal controls are estimated directly more attractive. Here we present reinforcement learning methods as a computationally simple, direct approach to the adaptive optimal control of nonlinear systems.

Gain Scheduling: Potential Hazards and Possible Remedies

Abstract: A common gain scheduling rule-of-thumb is to "schedule on a slow variable." In this paper, it is shown how current gain scheduling practice is necessarily limited to slow variations in the scheduling variable. These limitations are revealed to be consequences of fundamental control concepts. Furthermore, it is shown how a reformulation of the gain scheduling procedure can lead towards ultimately removing these restrictions.

Stability of Linear Feedback Systems with Random Communication Delays

Abstract: Integral control of large-scale systems implies application of control and information exchange via communication networks in which random delays may exist. The design of such systems rely on conservative sufficient stability tests for systems with random, time-varying delays. In this report, necessary and sufficient conditions are found for zero-state mean-square exponential stability of the considered class of control systems. Numerical tests for zero-state stability are outlined and illustrated by a simple example. Finally, the results are also demonstrated on specific hardware, multiprocessor real-time control network which has been recently developed.

Linear and nonlinear algorithms for identification in H ∞ with error bounds

Abstract: In this paper, a linear and a nonlinear algorithm are presented for the problem of system "identification in H∞", posed by Helmicki, Jacobson and Nett. We derive some error bounds for the linear algorithm which indicate that if the model error is not too high, then this algorithm has good guaranteed error properties. The linear algorithm requires only FFT (fast Fourier transform) computations. A nonlinear algorithm, which requires an additional step of solving a Nehari best approximation problem, is also presented that has the robust convergence property.

Adaptive Robotic Visual Tracking

Abstract: Current robotic systems lack the flexibility of dynamic interaction with the environment. The use of sensors can make the robotic systems more flexible. Among the different types of sensors, visual sensors play a critical role. This paper addresses some of the issues associated with the use of a visual sensor in the feedback loop. In particular, algorithms are proposed for the solution of the robotic (hand-eye configuration) visual tracking and servoing problem. We state the problem of robotic visual tracking as a problem of combining control with computer vision. We propose the use of sum-of-squared differences (SSD) optical flow for the computation of the vector of discrete displacements. These displacements are fed to an adaptive controller (self-tuning regulator) that drives implemented three different adaptive control schemes and the results are presented in this paper.

Longitudinal Control of a Platoon of Vehicles with no Communication of Lead Vehicle Information

Abstract: Evaluates the performance of longitudinal control laws with no communication of lead vehicle information. After using exact linearization methods, the authors propose a linear control law for each vehicle which uses only the information from the preceding vehicle in the platoon.

A Linear-Quadratic Game Approach to Estimation and Smoothing

Abstract: An estimator and smoother for a linear time varying system, over a finite time interval, are developed from a linear quadratic (LQ) game approach. The exogenous inputs composed of the measurement and process noise, and the initial state, are assumed to be finite energy signals whose statistics are unknown. The measure of performance is in the form of a disturbance attenuation function and the optimal estimator (smoother) bounds the attenuation function from above. The disturbance attenuation function is converted to a performance measure for a zero-sum LQ game and the exogenous inputs and the estimator are viewed as players in the game; the exogenous inputs attempt to worsen the estimate while the estimator tries to provide the most accurate estimate. The optimal estimator (smoother), restricted to a class of functions dependent on the measurement alone, is found to be unbiased and linear in structure. With a few mild assumptions, the results are extended to a linear time-invariant system on an infinite horizon, and the optimal estimator obtained is shown to satisfy an upper bound on the H ? norm.

Two Proposals to Improve Freeway Traffic Flow

Abstract: The first proposal organizes vehicles in platoons with manually driven lead car and the rest under automatic spacing control. A plausible model of the resulting traffic flow indicates that for an average platoon size of 20, the freeway capacity increases by a factor of four. The second proposal begins with a macroscopic model of freeway congestion and then presents a control law for reducing congestion. Simulation of the resulting closed loop model indicates dramatic reduction in congestion.

Adaptive Control of Robot Manipulators with Flexible Joints

Abstract: This paper presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value i.e. the results are not restricted to weak joint elasticity. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded.

Linear Time Periodic Systems: Transfer Function, Poles, Transmission Zeroes and Directional Properties

Abstract: A linear operator for LTP systems is presented, which is analogous to the LTI transfer function Properties such as poles, transmission zeroes, and their associated directional properties are described in terms familiar to the multivariable control theory

Intelligent Control Using Neural Networks

Abstract: The paper deals with the control of nonlinear dynamical plants in the presence of structural failures as examples of intelligent control. At any time, the system is assumed to be in one of a finite number of configurations. Corresponding to each configuration of the plant, a controller is assumed to exist such that the plant in that configuration together with the controller has a desired response. The objective of the paper is to propose a two-level controller structure where the higher level detects the configuration of the plant at any instant based on the response of the overall system and activates the corresponding controller at the lower level. Multilyer neural networks are used for the identification and control of the plant at the lower level and as pattern recognizers at the higher level. Simulation results are presented to complement the theoretical discussions.

Design and Modeling Issues for Integrated Airframe/Propulsion Control of Hypersonic Flight Vehicles

Abstract: TraditionaLly the systems integration process in aerospace controls is to make individually desig subsystems work together, that is, to ensure functional compatibility and minimize adverse interactions. With large hypersonic vehicles the aerodynamic, propulsion, structural, and controls features are intrinsically highly interactive dynamically over a wide range of frequencies. Consequently, systems integration activities must be enormously expanded in scope and degree to assure a successful result. In essence the new goal of dynamic systems integration is to carry out concurrent multidisciplinary design of the highly interactive systems to maximize overall aircraft performance in its broadest terms. Cooperative consolidation and interaction of functions and subsystems to achieve performance levels and design synergism greater than would be possible with independent, individual subsystem designs are the natural consequences desired.

Robust approximation and identification in H

Abstract: Robust approximation and identification of stable shiftinvariant systems is studied in the H∞ sense using a stable perturbation set-up. Issues of model set selection tion are addressed using the n-width concept: a concrete result establishes a priori knowledge for which a certain rational model set is optimal in the n-width sense. A general construction of interest to identification theory using ϵ-nets provides near-optimal identification methods tuned to the a priori knowledge about the system. A notion of robust convergence is defined so that any untuned identification method satisfying it has a generic well-posedness property for systems in the disk algebra. The existence of robustly convergent identification methods based on any complete model set in the disk algebra is established. It is also shown that the classical Fejer and de la Vallee-Poussin polynomial approximation operators provide robustly convergent identification methods. Furthermore, a result is given for optimal Hankel norm model reduction from experimentally obtained models.

Experiments in Robotic Catching

Abstract: Real-time coordination of visual information with high speed manipulator control is studied in the specific context of three-dimensional robotic catching All path-planning for the catch occurs in real-time during the half-second that the targeted object is airborne We use a trajectory-matching algorithm that combines an observer with a varying-strength filter, an error estimator, and an initial motion algorithm The results are demonstrated experimentally using a real-time vision system and a four-degree-of-freedom, cable-driven arm with a workspace of 42 cubic meters and speed capabilities of up to 20 mls

A Comparison of Controller Designs for an Experimental Flexible Structure

Abstract: This paper addresses control systems design and hardware testing for an experimental structure that displays the characteristics of a typical flexible spacecraft. The results of designing and implementing various control design methodologies are described. The merit of each design is based on its capacity for vibration suppression, its stability robustness characteristics with respect to unmodelled dynamics, and its ease of design and implementation. The design methodologies under investigation include Linear Quadratic Gaussian control, static and dynamic dissipative controls and H ? optimal control. Among the three controllers considered, it is shown, through computer simulation and laboratory experiments on the evolutionary structure, that the dynamic dissipative controller gave the best results in terms of vibration suppression and robustness with respect to modeling errors.

Local Training for Radial Basis Function Networks: Towards Solving the Hidden Unit Problem

Abstract: This work examines training methods for radial basis function networks (RBFNs) First, the theoretical and practical motivation for RBFNs is reviewed, as are two currently popular training methods Next a new training method is developed using well known results from functional analysis This method trains each kidden unit individually, and is thus called the local training method The structure of the method allows analysis of individual hidden units; moreover a covariance-related quantity is defined that gives insight into how many hidden units to employ Two examples illustrate the usefulness of the method Lastly, an ad hoc method to further improve RBFN performance is demonstrated

Geometry and the Dynamic Interpolation Problem

Abstract: In this paper we consider the dynamic interpolation problem for control systems in which certain dynamic variables of state trajectories are forced to pass through specific points by suitable choices of controls. This problem can be viewed as an extension of the spline problem. Following Noakes, Heinzinger and Paden [16], we give a derivation of suitable interpolating cubic splines on a Riemannian manifold extending the variational approach in Milnor [15]. For the special case of compact Lie groups, the relation with optimal control problems and singular Riemannian Geometry is spelled out in detail.

A Lyapunov Based Nonlinear Control Scheme for Stabilizing a Basic Compression System Using a Close-Coupled Control Valve

Abstract: The use of a closed loop control to allow surge free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described here directly addresses the nonlinear nature of the compressor characteristic using a Lyapunov based control law design formulation. The proposed approach is fairly generic, and should be of interest for gas turbine engine, as well as other applications.

Washout Filters in the Bifurcation Control of High Alpha Flight Dynamics

Abstract: Washout filters are employed in the design of stabilizing controllers for systems undergoing bifurcations. Moreover, the advantages of using washout filters are demonstrated in the control of a high angle-of-attack nonlinear aircraft model. In the bifurcation control of an F-8 model in [2], the performance of the controller depended on a priori computation of equilibrium curves. Moreover, the controller tended to result in reshaping non-nominal equilibrium branches. Since this could result in a nearby equilibrium point moving toward the trim condition, it is undesirable. In this paper, by complementing the technique of [2] with washout filters for the control of F-8 high alpha dynamics, a fixed controller can be used through a range of flight conditions, without affecting the set of open-loop equilibria. The stability of the equilibrium of interest is, however, significantly enhanced.

Lyapunov Stability of a Class of Discrete Event Systems

Abstract: Discrete event systems (DES) are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals. "Logical" DES are a class of discrete time DES with equations of motion that are most often non-linear and discontinuous with respect to event occurrences. Recently, there has been much interest in studying the stability properties of logical DES and several definitions for stability, and methods for stability analysis have been proposed. Here we introduce a logical DES model and define stability in the sense of Lyapunov for logical DES. Then we show that a more conventional analysis of stability which employs appropriate Lyapunov functions can be used for logical DES. This standard approach has the advantage of not requiring high computational complexity (as some of the others) but the difficulty lies in specifying the Lyapunov functions. The approach is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme, one of Dijkstra's "self-stabilizing" distributed Systems, and a load balancing problem in computer networks.

Strong Acid Equivalent Control of pH Processes: An Experimental Study

Abstract: The control of pH is widely recognized as a difficult problem The Strong Acid Equivalent approach for control of pH processes consists of defining an alternate equivalent control objetive, the Strong Acid Equivalent, which is linear in the states and using a linear control law in terms of this new control objective The Strong Acid Equivalent is then calculated on line from pH measurements given a nominal titration curve of the inlet stream A laboratory system has been built to implement this method Experimental results for the hydrochloric acid / sodium hydroxide and acetic acid / sodium hydroxide systems are given The results show the control which can be achieved with the Strong Acid Equivalent method

Adaptive Control of Nonlinear Systems Using Neural Networks - A Dead-Zone Approach

Abstract: Layered neural networks are used in a nonlinear adaptive tracking problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model with relative degree higher than one. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. Layered neural networks are used to model the plant and generate controls. Some error between the model and the plant is allowed. A dead-zone is specified in the updating rule. A local convergence result is given.

H ∞ control and filtering with sampled measurements

Abstract: In this paper, H∞ control and filtering problems for sampled-data systems are studied. Necessary and sufficent conditions are obtained for the existence of controllers and filters that satisfy a specified H∞ performance bound. And when these conditions hold formulae for controller and filter satisfying the H∞ bound are alos given.