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ABSTRACT: We develop a Linear Matrix Inequality (LMI) tool for analyzing the stability and performance of adaptive controllers that employ sigma-modification. The formulation involves recasting the error dynamics composed of the tracking error and the weight estimator error into a linear parameter varying form. We show how stability, convergence rate, domain of attraction, and the transient and steady state behavior of the adaptive control system can be analyzed using the developed LMI tool. It is guaranteed that less conservative estimates for the convergence rate and the size of the ultimate bound for the tracking error are obtained compared to the standard analysis in the literature.
American Control Conference, 2009. ACC '09.; 07/2009
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ABSTRACT: An adaptive approach that augments existing decentralized linear controllers is considered. By employing a neural network as a centralized element, the approach greatly broadens the class of system for which linear decentralized controllers can be designed. The stability proof naturally follows from the viewpoint that a set of decentralized controllers are a special class of multi-input multi-output controllers of an existing central method. The approach is illustrated using an inverted flexible pendulum in which a neural network coordinates an acceleration controller with a controller for an rigid inverted pendulum.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: A neural synthesis method is considered for a class of multivariable nonaffine uncertain systems. The method extends the previous approach developed in a single-input single-output system to a multi-input multi-output system without resorting to a fixed-point assumption or boundedness assumption on the time derivative of a control effectiveness term. By assuming that the uncertain input matrix term is dominated by the known part of the input matrix, we show that a new inverting method can be developed taking nonaffineness into account for its synthesis procedure. Using Lyapunov's 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 double Van Der Pol system having nonaffine control terms illustrates the approach.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
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ABSTRACT: A backstepping based neural synthesis method is proposed to stabilize a class of non-affine systems, that include non-minimum phase systems as well. The method describes the class of systems in normal form, and uses two neural networks, while previous backstepping methods introduce a neural networks at each backward step. The neural weights are updated using tuning functions, and nonlinear damping terms prevent the functional reconstruction error from propagating to the next backward step. The method does not rely on a fixed-point assumption, nor does it assume that the time derivative of the control effectiveness is bounded (an assumption that is commonly employed when using the mean value theorem). All the signals of the closed-loop system are shown to be uniformly ultimately bounded. Simulation results illustrate the approach
Decision and Control, 2006 45th IEEE Conference on; 01/2007
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ABSTRACT: 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
American Control Conference, 2006; 07/2006
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ABSTRACT: For a class of single-input single-output non-affine non-minimum phase nonlinear systems, a neural control synthesis method based on backstepping combined with inverting design is considered. The method reduces the number of steps in designing a backstepping controller compared to previous approaches by seeking a state that stabilizes the unstable internal dynamics. The method does not need a fixed-point assumption nor the boundedness assumption on the time derivative of a control effectiveness term. Using Lyapunov's direct method, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Simulation results illustrate the approach
American Control Conference, 2006; 07/2006
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ABSTRACT: A neural control synthesis method is considered for a class of non-affine uncertain single-input, single-output 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 Lyapunov's 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 non-affine control terms illustrates the approach.
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 01/2006
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ABSTRACT: A flight control design is presented that combines model inversion control with an online adaptive neural network (NN). The NN cancels the error due to approximate inversion. Both linear and nonlinear NNs are described. Lyapunov stability analysis leads to the online NN update laws that guarantee boundedness. The controller takes advantage of any available knowledge for system inversion, and compensates for the effects of the remaining approximations. The result is a consistency in response which is particularly relevant in human operation of some unconventional modern aircraft. A tiltrotor aircraft is capable of converting from stable and responsive fixed wing flight to sluggish and unstable hover in helicopter configuration. The control design is demonstrated to provide a tilt-rotor pilot with consistent handling qualities during conversion from fixed wing flight to hover.
IEEE Transactions on Control Systems Technology 12/2005; · 1.77 Impact Factor
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ABSTRACT: This paper discusses estimation and guidance strategies for vision-based target tracking. Specific applications include formation control of multiple unmanned aerial vehicles (UAVs) and air-to-air refueling. We assume that no information is communicated between the aircraft, and only passive 2D vision information is available to maintain formation. To improve the robustness of the estimation process with respect to unknown target aircraft acceleration, the nonlinear estimator (EKF) is augmented with an adaptive neural network (NN). The guidance strategy involves augmenting the inverting solution of nonlinear line-of-sight (LOS) range kinematics with the output of an adaptive NN to compensate for target aircraft LOS velocity. Simulation results are presented that illustrate the various approaches.
American Control Conference, 2005. Proceedings of the 2005; 07/2005
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ABSTRACT: Experimental results are presented that illustrate a recently developed method for adaptive output feedback control. The method permits adaptation to both parametric uncertainty and unmodeled dynamics, and incorporates a novel approach that permits adaptation under known actuator characteristics including actuator dynamics and saturation. Only knowledge of the relative degree of the controlled system within the bandwidth of the control design is required. The controller design was tested by controlling the pitch axis of a three degrees-of-freedom (DOF) helicopter model, using attitude feedback through a low-resolution optical sensor.
IEEE Transactions on Control Systems Technology 04/2005; · 1.77 Impact Factor
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ABSTRACT: This paper implements several methods for performing vision-based formation flight control of multiple aircraft in the presence of obstacles. No information is communicated between aircraft, and only passive 2-D vision information is available to maintain formation. The methods for formation control rely either on estimating the range from 2-D vision information by using extended Kalman Filters or directly regulating the size of the image subtended by a leader aircraft on the image plane. When the image size is not a reliable measurement, especially at large ranges, we consider the use of bearing-only information. In this case, observability with respect to the relative distance between vehicles is accomplished by the design of a time-dependent formation geometry. To improve the robustness of the estimation process with respect to unknown leader aircraft acceleration, we augment the EKF with an adaptive neural network. 2-D and 3-D simulation results are presented that illustrate the various approaches.
Decision and Control, 2004. CDC. 43rd IEEE Conference on; 01/2005
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ABSTRACT: A method of adaptive output feedback control design for an uncertain nonlinear system is presented. The control design augments a state observer based linear control law by an adaptive observer in a manner that adaptive estimation and control augmentation is achieved through a single neural network. In this process, we show how the unmatched uncertainty is tackled by an adaptive signal. The proposed synthesis can be applied to non-affine systems having parametric and dynamic uncertainties. The approach is also applicable to non-minimum phase systems if the non-minimum phase zero dynamics are considered in the linear control design. We illustrate the effectiveness of the approach using an inverted pendulum example.
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on; 01/2004
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ABSTRACT: A decentralized adaptive output feedback control design is proposed for large-scale interconnected systems. It is assumed that all the controllers share prior information about the system reference models. Based on that information, a linearly parameterized neural network is introduced for each subsystem to partially cancel the effect of the interconnections on the tracking performance. Boundedness of error signals is shown through Lyapunov's direct method.
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on; 01/2004
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ABSTRACT: The problem of approximation of unknown dynamics of a continuous-time observable nonlinear system is considered using a feedforward neural network, operating over delayed sampled outputs of the system. Error bounds are derived that explicitly depend upon the sampling time interval and network architecture. The main result of this note broadens the class of nonlinear dynamical systems for which adaptive output feedback control and state estimation problems are solvable.
IEEE Transactions on Automatic Control 10/2003; · 2.11 Impact Factor
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ABSTRACT: This paper addresses observer/controller design problems for nonlinear systems from the perspective of augmenting linear designs. In both problems, an adaptive element is added to the nominal design to provide a correction that accounts for modeling errors. The error signal for adaptive laws is generated through a linear observer of the nominal system's error dynamics. Ultimate boundedness can be shown through Lyapunov's direct method.
American Control Conference, 2003. Proceedings of the 2003; 07/2003
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ABSTRACT: We address adaptive output feedback control of uncertain nonlinear systems with noisy output measurements, in which both the dynamics and the dimension of the regulated systems may be unknown, and only the relative degree of the regulated output is assumed to be known. Given a smooth reference trajectory, the problem is to design a controller that forces the system measurement to track it with bounded errors. A recently developed method proposes the use of a linear error observer that estimates the tracking error and its derivatives. Since the observer is full order, it also estimates the states of the controller, even though these states are exactly known. It has been observed experimentally that the resulting adaptive control architecture is very sensitive to sensor noise. In this paper we provide a specific reduced order observer that significantly reduces sensitivity to sensor noise in adaptive control design. Experimental results on a three degrees of freedom laboratory model helicopter are used to illustrate the effectiveness of the reduced order observer design.
American Control Conference, 2003. Proceedings of the 2003; 07/2003
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American Control Conference, 2003. Proceedings of the 2003; 02/2003
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ABSTRACT: In this paper we address the problem of augmenting a linear observer with an adaptive element. The design of the adaptive element employs two nonlinearly parameterized neural networks, the input and output layer weights of which are adapted on line. The goal is to improve the performance of the linear observer when applied to a nonlinear system. The networks teaching signal is generated using a second linear observer of the nominal systems error dynamics. Boundedness of signals is shown through Lyapunov's direct method. The approach is robust to unmodeled dynamics and disturbances. Simulations illustrate the theoretical results.
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on; 01/2003
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ABSTRACT: A method of output feedback design of an adaptive controller is presented that can be used to augment a fixed-gain linear controller. The key feature is that it is applicable to non-minimum phase nonlinear systems, having both parametric uncertainty and unmodeled dynamics. Ultimate boundedness of error signals can be shown using Lyapunov's direct method. An example is provided to illustrate the effectiveness of the approach.
Decision and Control, 2002, Proceedings of the 41st IEEE Conference on; 01/2003
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Circuits and Systems, 2002. MWSCAS-2002. The 2002 45th Midwest Symposium on; 09/2002
