Bong-Jun Yang

Adaptive Control of a Class of Nonaffine Systems Using Neural Networks

A neural control synthesis method is considered for a class of nonaffine uncertain single-input-single-output (SISO) systems. The method eliminates a fixed-point assumption and does not assume boundedness on the time derivative of a control effectiveness term. One or the other of these assumptions exist in earlier papers on this subject. Using Lyapunovs direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded, and that the tracking error converges to an adjustable neighborhood of the origin. Simulation with a Van Der Pol equation with nonaffine control terms illustrates the approach.

Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems

An adaptive output feedback control methodology is developed for a class of uncertain multi-input multi-output nonlinear systems using linearly parameterized neural networks. The methodology can be applied to non-minimum phase systems if the non-minimum phase zeros are modeled to a sufficient accuracy. The control architecture is comprised of a linear controller and a neural network. The neural network operates over a tapped delay line of memory units, comprised of the systems input/output signals. The adaptive laws for the neural-network weights employ a linear observer of the nominal systems error dynamics. Ultimate boundedness of the error signals is shown through Lyapunovs direct method. Simulations of an inverted pendulum on a cart illustrate the theoretical results.

A Loop Recovery Method for Adaptive Control

This paper presents a new modification term for use in adaptive control to improve an already existing design. By employing this term in a conventional adaptive law, the loop transfer properties of a reference model associated with a non-adaptive control design can be preserved. Consequently, this term increases the level of confidence of adaptive flight control systems for purposes of increased flight safety. The results are illustrated on an unmanned combat aerial vehicle dynamic model. I. Introduction n this paper we present an improved method of adaptation that enhances robustness of adaptive control systems. The method is arrived at by examining the loop transfer properties of an adaptive system when linearized about a given flight condition. The design approach modifies a conventional adaptive law with the goal of preserving the loop transfer properties of a reference model associated with a non-adaptive control design. The aim is to achieve an adaptive system that preserves the stability margins of a non-adaptive design, while at the same time providing the benefits of adaptation to modeling error. I

Augmenting Adaptive Approach to Control of Flexible Systems

This paper describes an approach for augmenting a linear controller design with a neural-network-based adap- tive element. The basic approach involves formulating an architecture for which the associated error equations have a form suitable for applying existing results for adaptive output feedback control of nonlinear systems. The approach is applicable to non-affine, nonlinear systems with both parametric uncertainties and unmodelled dy- namics. The effect of actuator limits are treated using control hedging. The approach is particularly well suited for control of flexible systems subject to limits in control authority. Its effectiveness is tested on a laboratory experiment consisting of a three-disk torsional pendulum system, including control voltage saturation and stiction. HIS paper describes an approach for augmenting a linear con- troller design with a neural-network (NN)-based adaptive el- ement. Previous adaptive output feedback control approaches have been applied within a control architecture that uses an inverting type of controller for the nonadaptive portion of the control system. 1,2 Considering that the vast majority of controllers are locally linear controllers, it would be highly desirable to retrofit such systems with an adaptive element, rather than to replace them with an inverting controller. In particular, within the aircraft and automobile industries there is a legacy of experience with existing control system archi- tectures, and these industries would much prefer to augment their controllers with an adaptive process, rather than replace them with a totally new architecture. This is particularly the case in applications calling for control of flexible systems. Several attempts to develop a method for adding an adaptive ele- ment to an existing controller architecture have recently appeared in the literature. 3−9 The methods 3−6 are restricted to state feedback and impose restrictive conditions with respect to properties of the reg- ulated variable and the manner in which the uncertainty affects the plant. For example, they might require that the regulated output has full relative degree (meaning that the number of times the regulated variable must be differentiated before the control appears equals the number of state variables needed to describe the plant dynamics) or that the plant uncertainty is matched (meaning that the uncertainty enters the plant dynamics in the same manner as the control). Be- cause the methods 3−7 are based on matching the state response of an idealized model with that of the true plant, they cannot be applied to a system of higher order than the model used in the design process. As a consequence, they are not robust to the unmodeled dynam- ics. The methods in Refs. 8 and 9 use an adaptive technique called input error method 10 for reconfigurable flight control. It requires, however, that the open-loop system is stable. State feedback is very restrictive, and flexible systems provide a good example in which a state feedback approach is not useful. The controller architecture proposed in this paper relies on re- cent developments in the area of nonlinear adaptive output feedback

A novel Q-modification term for adaptive control

A novel modification term is suggested for use in adaptive control. The development is of use in any setting in which uncertainty is linearly parameterized. The modification uses state and control time histories. The effect is justified through stability analysis, and illustrated on a dynamic model for wing rock

An Error Minimization Method in Adaptive Control

THIS paper presents a design approach based on error minimization in adaptive control for improving the rate of adaptation and allowing under certain conditions exponential convergence of the error dynamics. Global stability results are given for the case of perfectly parameterized uncertainty. The approach relies on the fact that the unknown weights in any linearly parameterized representation of uncertainty satisfy an integral equation involving the state and control variables. The equation is used to formulate an error minimization problem, the solution for which can be incorporated in the adaptive law. The paper extends an idea originally developed in (1) for the case of scalar uncertainty to the vector case. The results are conceptually similar to the notion of composite adaptation (2), and techniques developed for state estimation (3). The main difference is that these approaches use different signals. The effect of the modified adaptive components is illustrated on a dynamical model of an aircraft in which uncertainty is present both in control effectiveness and non-linear state dependent terms.

Adaptive output feedback control with input saturation

We consider the problem of adaptive output feedback control in the presence of saturating input characteristic. The adaptive control architecture augments an existing linear control design. The approach is applicable to non-affine, nonlinear systems with both parametric uncertainty and unmodeled dynamics subject to input saturation. Boundedness of signals is shown through Lyapunovs direct method. Experimental results with a 3-disk torsional pendulum are presented to demonstrate the approach.

Adaptive Output Feedback Control of a Flexible Base Manipulator

This paper considers augmentation of an existing inertial damping mechanism by neural network-based adaptive control, for controlling a micromanipulator that is serially attached to a macromanipulator. The approach is demonstrated using an experimental test bed in which the micromanipulator is mounted at the tip of a cantilevered beam that resembles a macromanipulator with its joint locked. The inertial damping control combines acceleration feedback with position control for the micromanipulator so as to simultaneously suppress vibrations caused by the flexible beam while achieving precise tip positioning. Neural network-based adaptive elements are employed to augment the inertial damping controller when the existing control system becomes deficient due to modeling errors and uncertain operating conditions. There were several design challenges that had to be faced from an adaptive control perspective. One challenge was the presence of a nonminimum phase zero in an output feedback adaptive control design setting in which the regulated output variable has zero relative degree. Other challenges included flexibility in the actuation devices, lack of control degrees of freedom, and high dimensionality of the system dynamics. In this paper we describe how we overcame these difficulties by modifying a previous augmenting adaptive approach to make it suitable for this application. Experimental results are provided to illustrate the effectiveness of the augmenting approach to adaptive output feedback control design.

Augmentation of an existing linear controller with an adaptive element

This paper describes an approach for augmenting an existing linear controller design with a neural network based adaptive element. The basic approach involves formulating an architecture for which the associated error equation has a form suitable for applying existing results for adaptive output feedback control of nonlinear processes. The approach is applicable to non-affine, nonlinear systems with both parametric uncertainty and unmodeled dynamics. There are no restrictions placed on the relative degree of the regulated output variable, and the uncertainties can be unmatched. New results related to disturbance cancellation in an adaptive context are presented. For simplicity, only the SISO case is treated. The overall approach is illustrated using a simple model for a flexible system.

On-Line Trajectory Optimization for Autonomous Air Vehicles

Abstract : Successful operation of next-generation unmanned air vehicles will demand a high level of autonomy. Autonomous low-level operation in a complex environment dictates a need for onboard, robust, reliable and efficient trajectory optimization. In this report, we develop and demonstrate an innovative combination of traditional analytical and numerical solution procedures to produce efficient, robust and reliable means for nonlinear flight path optimization in the presence of time-varying obstacles and threats. The trajectory generation problem is first formulated as an optimization problem using reduced-order dynamics that result from the natural time-scale separation that exists in the aircraft dynamics. Terrain information is incorporated directly into the formulation of the reduced-order dynamics, which significantly reduces the computational load and leads to a path planning solution that can be implemented in real-time. Various cases of terrain, pop-up obstacles/threats, and targets are simulated. A representative optimal trajectory is generated with in a high fidelity full-order nonlinear aircraft dynamics and compared with a solution obtained from a reduced-order optimization. The developed algorithm is flight demonstrated with a fixed-wing unmanned aircraft test-bed in which a neural network-based adaptive autopilot is integrated with the on-line trajectory optimization algorithm.