Adaptive Controller Design for Tracking and Disturbance Attenuation in Parametric-Strict-Feedback Nonlinear Systems

This paper discusses a design method of a robust adaptive disturbance attenuating controller for nonlinear systems with uncertainty. The control scheme proposed by Shen et al. (1998) for nonlinear systems with relative degree 1 is extended to nonlinear systems with relative degree more than 1.

In this paper, we present robust adaptive controller design for a special class of linear system, which is composed of two SISO linear subsystems, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , under noisy output measurements and sequentially interconnected with additional feedback. We formulate the robust adaptive control problem as a nonlinear H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> -optimal control problem under imperfect state measurements, and then solve it using game-theoretic approach. The cost-to-come function analysis is carried out to derive the estimators and identifiers of S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and integrator backstepping methodology is applied recursively to obtain the control law, which guarantees the boundedness of closed-loop signals, and achieves asymptotic tracking under some assumptions. Moreover, the closed-loop system admits a guaranteed disturbance attenuation level with respect to the exogenous disturbance inputs, where the ultimate attenuation lower bound for the achievable performance level is equal to the noise intensity in the measurement channel of S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> .

In the paper, based on a combination of the robust control approach and an adaptive control technique, a design procedure of a new robust adaptive controller is proposed for power system load-frequency control with system parametric uncertainties. The system parametric uncertainties are obtained by changing parameters by 30% to 50% simultaneously from their typical values. In the design of the proposed controller, only the bounds of system parameters are required. The motivation of combining the robust control with an adaptive control is to use the robust control approach to deal with the small parametric uncertainties and to use the adaptive control for large parametric uncertainties so that stability of the overall system and good performance can both be achieved for all admissible uncertainties. The simulation results demonstrate that for the example system the proposed load-frequency controller can achieve good performance even in the presence of the generation rate constraint (GRC).

A nonlinear feedback control design for the adaptive robust H/sub /spl infin// control problem for nonlinear systems with gain bounded uncertainty is presented. An existing control scheme developed for nonlinear systems with relative degree of one is extended to the case where nonlinear systems have general relative degree. A Lyapunov function is constructed that ensures not only the stability of the closed-loop system but also satisfies the dissipation inequality ensuring L/sub 2/-gain performance. Then the controller can be obtained by the recursive use of the existing control scheme. A closed-form solution for the nonlinear H/sub /spl infin// control problem is provided without using a Hamilton-Jacobi inequality in the general relative degree case. Sufficient conditions which nonlinear systems should satisfy for solvability of the problem are provided.

Global adaptive neural network control of nonlinear time-varying systems with unknown control coefficients and model uncertainties

Liquid sloshing in moving or stationary containers and flexible uncertainty caused by the slosh are considered to be the most probable causing unexpected coupling effects on the dynamics of many systems such as aerospace, ground vehicles, and high speed industries arms. The coupling of dynamic liquid slosh in a container system with the uncertainty caused by the sensors or dampers is rare documented and this coupling can be considered as a highly nonlinear system. In this paper, an investigation is presented to demonstrate a new approach for enabling the reduction of the liquid slosh and uncertainty by implementing adaptive robust wavelet control technique. Starting by creating the mathematical dynamic model for the nonlinear slosh coupled by uncertainty, adaptive robust control based wavelet transform is applied for calculating optimal motion that minimize residual slosh and uncertainty. Subsequently the adaptive robust control based wavelet network approximation and the appropriate parameter algorithms for the container system with slosh and uncertainty are derived to achieve the feedback linearization, adaptive control, and H∞ tracking performance. The simulation results show that the effects of slosh errors and external uncertainty can be successfully attenuated within a desired attenuation level.

This paper deals with the tracking control of multi-inut/multi-output nonlinear parametric strict-feedback systems in the presence of additive disturbances and parametric uncertainties. For such systems, robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation. In this work, under the assumption the disturbances are C2with bounded time derivatives, we present a C0robust adaptive control construction that guarantees the tracking error is asymptotically driven to zero.

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Hydraulic system is widely used in industry where large actuation forces are needed such as electro-hydraulic positioning system, active suspension control, and so on. One of the main problem in hydraulic system is the nontriviality, for instance, the deadbands in valve operation, frictions of links, saturations, pressure dynamics, etc. both system unknown nonlinearities and external disturbances should be considered in controller design. For underwater hydraulic manipulator, because of the environment of sea and the large nonlinearities of the hydraulic manipulator system, both system unknown nonlinearities and external disturbances should be considered in controller design. A lot of control methods have been proposed to solve the problem properly, such as sliding mode control, adaptive control, fuzzy adaptive control, adaptive robust control, ect. However, due to limited knowledge about hydraulic manipulator system, it is hard to precisely estimate the nonlinearities for a possible higher performance. In this paper, a neural network adaptive robust control method is proposed to help control an underwater hydraulic manipulator. In order to achieve better performance using adaptive robust control strategy, unknown nonlinearities in the system are approximated by the outputs of radial basis function neural network (RBFNNs). A projection law has been used to bound the NN weights when they are tuning on-line to avoid possible adaptive divergence, and the tracking transient performance is guaranteed by robust control law. Simulation results illustrate that manipulator has a good tracking performance.

Robust and adaptive control of an unknown plant: A benchmark of new format

This paper reports a new robust adaptive tracking controller for multi-input/multi-output nonlinear parametric strict-feedback systems in the presence of parametric uncertainty and any unknown continuous bounded additive disturbance. The proposed solution uses a new projection-like adaptation that allows the application of the standard tuning function approach, thereby avoiding over parametrization and the need for extra nonlinear damping-type terms in the control. The robust adaptive control is shown to guarantee practical tracking in the presence of the disturbance and asymptotic tracking when the disturbance disappears.

Robust adaptive boundary control of a flexible marine riser with vessel dynamics

This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi‐strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the ‘explosion of terms’ problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley &amp; Sons, Ltd.

In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H/sup /spl infin// optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed-loop system without any persistency of excitation assumption on the reference signal. Due to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jw-axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance, inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example.

Adaptive robust motion control of linear motors for precision manufacturing