Direct Adaptive Control Law Research Articles

Direct Adaptive Control for Stochastic Systems with Risk-Sensitive Indices

We propose a direct adaptive control law based on the adaptive dynamic programming (ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive indices. A control design methodology is employed to iteratively solve the generalized algebraic Riccati equation by using the online information of the state and input, and to directly learn the optimal control law. We prove the convergence of the online ADP algorithm and show that the direct adaptive control law approximates the optimal control law as time goes on. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our algorithm.

Trajectory-Driven Adaptive Control of Autonomous Unmanned Aerial Vehicles with Disturbance Accommodation

This paper presents the development of direct adaptive control laws to enable an autonomous unmanned aerial vehicle (UAV) to track reference trajectories in the presence of external disturbances. A maneuver database of reference trajectories is computed offline from a linear UAV dynamic model using an optimization routine. Each maneuver in the database is therefore represented as a state trajectory, as well as the control input sequence that generates that trajectory. The trajectory tracking control laws are designed to enable a UAV to follow reference trajectories from this maneuver database. A disturbance accommodating control law is first developed and applied for the tracking of reference trajectories while the UAV is subjected to a persistent external disturbance. This control design requires a state-space disturbance generator model and the derivation of ideal trajectories from a reference model, which requires the solution of a set of matching conditions. A direct adaptive controller is then developed to enable the UAV to track reference trajectories while subject to modeling error and external disturbances. The adaptive controller also requires a disturbance model and the existence of ideal trajectories, but it does not require the explicit solution of the matching conditions. Simulation results for the disturbance accommodating controller and the adaptive controller are presented using a linear six-degree-of-freedom dynamic model that is representative of typical UAV dynamics. The results show that, although both controllers track reference trajectories and provide disturbance rejection, the adaptive controller is better suited for handling modeling errors or uncertainties.

Adaptive Control of Mildly Nonlinear Infinite-Dimensional Systems on Hilbert Space Using a Robust Version of the Lyapunov-Barbalat Theorem

Abstract: This paper presents an exponential stability result for mildly nonlinear distributed parameter systems. Given a mildly nonlinear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we will use this infinite-dimensional Lyapunov-Barbalat Lemma to show that there is an exponentially stabilizing direct adaptive control law with disturbance rejection and robustness properties.

Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results.

Takagi-Sugeno Fuzzy System based Stable Direct Adaptive Control of Nonlinear Systems

paper proposes a novel idea for stable direct adaptive control of nonlinear systems using Lyapunov function with fuzzy approach. Stable direct adaptive control law consists of an ideal control, and a sliding mode control. Sliding mode controller is used to ensure the stability of Lyapunov function. Stability of direct adaptive control law is tested on two nonlinear systems. Non linear systems analyzed are ball beam system and cart pole system. A computer simulation is performed on nonlinear systems by using MATLAB. Keywordssystem, Lyapunov function, adaptive control, ball beam system and cart pole system.

The Simplicity of Robust Direct Adaptive Control with Disturbance Rejection for Linear Infinite-Dimensional Systems: An Introduction

Our purpose in this paper is to provide an introduction to direct adaptive control in infinite dimensions and to prove the remarkable simplicity of infinite dimensional adaptive control even in infinite dimensions. However, we will show that the mathematical foundations are much more stringent in infinite dimensional theory. Consequently, this paper will emphasize some important fundamentals and will not be comprehensive. Much more can be done, but here we hope to provide a starting point for further exploration. Given a linear continuous-time infinite-dimensional plant on a Hilbert space and disturbances of known and unknown waveform, we show that there exists a very simple stabilizing direct adaptive control law with certain disturbance rejection and robustness properties. The closed loop system is shown to be exponentially convergent to a neighborhood with radius proportional to bounds on the size of the disturbance. The plant is described by a closed densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. To illustrate the use of the control law, we apply the result to a partial differential equation example of an unstable diffusion system, but other applications are possible.

Aircraft failure detection and identification over an extended flight envelope using an artificial immune system

AbstractAn integrated artificial immune system-based scheme that can operate over extended areas of the flight envelope is proposed in this paper for the detection and identification of a variety of aircraft sensor, actuator, propulsion, and structural failures/damages. A hierarchical multi-self strategy has been developed in which different self configurations are selected for detection and identification of specific abnormal conditions. Data collected using a motion-based flight simulator were used to define the self for a wide area of the flight envelope and to test and validate the scheme. The aircraft model represents a supersonic fighter, including model-following direct adaptive control laws based on non-linear dynamic inversion and artificial neural network augmentation. The proposed detection scheme achieves low false alarm rates and high detection and identification rates for all the categories of failures considered.

Adaptive Formation Control for Rovers Traveling over Unknown Terrains

A novel adaptive formation-control strategy for a group of rovers navigating over unknown terrain is presented. A leader‐follower formation control architecture is employed. Direct adaptive control laws and a formation speed adaptation strategy are developed that 1) bring the rovers into a prescribed formation from arbitrary in-plane locations and 2) enable the group to navigate over unknown and changing terrain, while staying in formation in the presence of actuator saturation. On-line estimates of generic friction parameters account for terrain surface variations. The leader specifies a reference motion for the entire fleet, including both straight-line and turning maneuvers. In saturation events, the formation speed is reduced based on the maximum sustainable speed of the slowest saturated rover using internal fleet communication, allowing the formation error to stay bounded and small. A formal proof for asymptotic stability of the formation system under nonsaturated conditions is given. A simulation example is presented that demonstrates formation initialization, formation-keeping, and formationswitching in both actuator saturation and nonsaturation circumstances. Nomenclature cn = follower’s adaptive controller feedback gain E nj = follower’s tracking-error state vector en = follower’s tracking-error vector e nj = follower’s scalar tracking-error in inertial directions Fn = rover’s control force magnitude F max n = rover’s actuator saturation limit fn = rover’s control force per unit mass g = acceleration due to gravity kn = follower’s adaptive controller feedback gain k P, k I = leader’s PI-controller feedback gains L = formation size mn = rover’s mass N = number of rovers in the fleet nn = unit vector normal to rover’s path pn = follower’s parameter-estimation gain Qn = follower’s separation distance (Euclidian or arc) QnS, Q nN = follower’s scalar separations along leader’s path-frame axes qn = follower’s separation vector from the leader q nX , qnY = follower’s scalar separations in inertial directions rn = rover’s inertial position vector sn = unit vector tangent to rover’s path (rover’s heading vector) t = time un = rover’s control-force unit vector Vn = aggregate Lyapunov function V nj = directional Lyapunov function

Design of an Adaptive Model Matching Controller for Nonminimum Phase Systems Using a Periodic Scheme

Using a periodic control scheme, a direct adaptive model matching controller is proposed for a discrete-time multivariable nonminimum-phase system. The linear error equation for estimating appropriate periodic feedback gains and, at the same time, appropriate pole-placing feedback gains is first obtained using a derivation of the inverse system representation. With these periodic feedback gains estimated through the recursive leastsquare estimation scheme and used in a direct adaptive control law, it is then shown that the overall control system is globally asymptotically stable and the desired model matching is asymptotically achieved.

An exponentially stable adaptive control law for robot manipulators

An exponentially stable direct adaptive control law for motion control of robot manipulators is presented. This control law utilizes the desired trajectory information instead of the actual manipulator joint signals for feedforward compensations and parameter adaptation. Computationally, it is extremely efficient. The exponential stability of the adaptive control algorithm is proven without requiring the persistent excitation condition and by fully considering the nonlinear dynamics of the manipulator in the analysis.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>