Xiangbin Liu

Immersion and Invariance Adaptive Control of Nonlinearly Parameterized Nonlinear Systems

A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity—or the related property of convexity—have already been explored by several authors with convexity being an a priori assumption that is valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. One consequence of this fact is that the controller does not rely on state—dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.

On adaptive control of nonlinearly parameterized nonlinear systems: Towards a constructive procedure

Abstract A new framework to design immersion and invariance adaptive controllers for nonlinearly parameterized, nonlinear systems was recently proposed by the authors. The key step is the construction of a monotone mapping, via a suitable selection of a controller tuning function, which has to satisfy some integrability conditions—this translates into the need to solve a partial differential equation (PDE). In this paper this result is extended providing some answers to the questions of characterization of “monotonizable” systems and solvability of the PDE. First, adding to the design a nonlinear dynamic scaling, we obviate the need to solve the PDE. Second, for the case of factorizable nonlinearities , the following results are established. (i) It is shown that the monotonicity condition is satisfied if a linear matrix inequality is feasible. (ii) Directly verifiable involutivity conditions that ensure the solution of the PDE are presented. (iii) An explicit formula for the required tuning function is given, provided the regressor matrix satisfies some rank conditions. Hence, adding a dynamic scaling, this yields a constructive solution to the problem.

Identification of nonlinearly parameterized nonlinear models: application to mass balance systems

A new framework to design parameter estimators for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity-or the related property of convexity-have already been explored by several authors with monotonicity (or convexity) being a priori assumptions that are, usually, valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. In order to dispose of degrees of freedom to render the function monotone we depart from standard (gradient or least-squares) estimators and adopt instead the recently introduced immersion and invariance approach for adaptation.

Robust adaptive failure compensation of hysteretic actuators for parametric strict feedback systems

It is well known that hysteresis often exists and failures may occur in practical actuators during system operation. The compensation for uncertainties caused by unknown hysteresis and unknown failures is an important problem in ensuring system stability and performances. However, available results based on adaptive approaches to address such a problem are still very limited. In this paper, an adaptive tracking control scheme is proposed to solve such a problem. Simulation results also illustrate the effectiveness of the control scheme.

Adaptive robust control of a class of uncertain nonlinear systems with unknown sinusoidal disturbances

In this paper, nonlinear observers are incorporated into the discontinuous projection based adaptive robust control (ARC) to synthesize performance oriented controllers for a class of uncertain nonlinear systems with unknown sinusoidal disturbances. In addition to magnitudes and phases, frequencies of the sinusoidal disturbances need not to be known as well, so long as the overall order is known. A nonlinear observer is constructed to eliminate the effect of unknown sinusoidal disturbances to improve the steady-state output tracking performance - asymptotic output tracking is achieved when the system is subjected to unknown sinusoidal disturbance only. The discontinuous projection based adaptation law is used to obtain robust estimate of all unknown parameters. In addition, a dynamic normalization signal is introduced to construct adaptive robust control laws to effectively deal with various uncertainties for a guaranteed robust performance in general. Compared with the existing internal model principle based robust adaptive designs for unknown sinusoidal disturbances, the model uncertainties considered in the paper can be of unmatched. Furthermore, in the presence of other disturbances and uncertainties in addition to the sinusoidal disturbances, the proposed approach achieves a guaranteed output tracking robust performance in terms of both the transient and the steady-state, as opposed to the robust stability results of the existing internal model principle based designs.

Immersion and invariance adaptive control of nonlinearly parameterized nonlinear systems

A new framework to design adaptive controllers for nonlinearly parameterized systems is proposed in this paper. The key step is the construction of a monotone function, which explicitly depends on some of the estimator tuning parameters. Monotonicity—or the related property of convexity—have already been explored by several authors with convexity being an a priori assumption that is valid only on some region of state space. In our approach monotonicity is enforced by the designer, effectively becoming a synthesis tool. One consequence of this fact is that the controller does not rely on state—dependent switching. In order to dispose of degrees of freedom to render the function monotone we depart from standard adaptive control and adopt instead the recently introduced Immersion and Invariance approach.

Fault-tolerant control of dynamic systems with unknown control direction-input nonlinearities-actuator failures

This paper aims at investigating fault-tolerant tracking control designs for uncertain multivariable systems involving unknown floating dynamics, fading actuators, input nonlinearities with non-symmetric saturation and dead-zones, and unknown control direction. A robust adaptive control approach with simple structure is proposed to cope with these factors concurrently, where the lack of knowledge of control sign is handled by incorporating in the control law a Nussbaum-type function. Furthermore, of practical interest, the adaptive compensation of the effects of the nonlinear inputs requires neither the knowledge of their parameters nor the construction of their inverse.