Focusing on the piezoelectric positioning stage, this paper proposes an adaptive estimated inverse output-feedback quantized control scheme. First, the quantized issue due to the of computer is addressed by introducing a linear time-varying quantizer model where the quantizer parameters can be estimated on-line. Second, by using the fuzzy approximator, the developed controller can avoid the identification of the parameters in the piezoelectric positioning stage. Third, by constructing estimated inverse compensator of the hysteresis, the hysteresis nonlinearities in the piezoelectric actuator are mitigated; Fourth, states observer is designed to avoid the measurements of the velocity and acceleration signals. The analysis of stability shows the signals in the piezoelectric positioning stage are uniformly ultimately bounded and the prespecified tracking performance of quantized control system is achieved by employing the error transformed function. Finally, a computer controlled experiments the piezoelectric positioning stage is conducted to show the effectiveness of the proposed quantized controller.

The Krasnoselskii-Pokrovskii (KP) model, as one of the popular operator-based hysteresis models, is commonly used to describe the hysteresis nonlinearities, especially in the smart materials-based actuators. Due to the complex formulation of the KP model, it is a great challenge to construct the inverse for the KP model. In this paper, an inverse multiplicative structure (IMS) is employed to find the inverse of the KP model. The merit of IMS is that this approach is simple to implement and the detailed knowledge of the hysteresis model is not required. However, the IMS technique cannot be directly applied to construct the inverse compensator for the KP model due to its complexity. Toward this problem, a new expression of the KP model is developed, where the input variable is expressed explicitly. With this new expression, the KP model can fit into IMS. Experiments are conducted to validate the effectiveness of the developed inverse compensator on a piezoelectric platform.

The micro/nano positioning system discussed in this paper includes a piezoelectric actuator (PEA) and flexure-hinge-based positioning mechanism. Due to the existence of the hysteretic nonlinearity in the PEA and the friction in the system, the accurate positioning of the piezo-actuated positioning system calls applicable control schemes for practical applications. To this end, an implementable adaptive controller is developed in the paper, where a minimized parameterization hysteresis model is employed to reduce the computational load. The formulated adaptive control law guarantees the global stability of the controlled positioning system, and the positioning error can approach to zero asymptotically. The advantages of the proposed method making on-line implementation feasible are that the traditional inversion of the hysteresis does not need to be constructed directly; the real values of the parameters of the positioning system neither need to be identified nor measured; only the parameters in the formulation of the controller are estimated online. Comparison with the feedforward plus proportional-integral feedback control scheme is conducted and experimental results show the effectiveness of the proposed method.

Flexible smart material actuators, such as dielectric elastomer actuators (DEA) and ionic polymer metal composites, have shown greatly potential applications in the field of soft biomimetic robots and rehabilitation robots due to their human-like muscle softness, large stretch, and high energy density characteristics. In this article, a fuzzy logic system (FLS) and barrier Lyapunov function (BLF) based adaptive pseudoinverse control scheme is proposed for a class of state-constrained hysteretic nonlinear systems, where all the states are always strictly limited in each constrained set. The main features of this article are: 1) the hysteresis nonlinearity in the actuators is considered and mitigated by the proposed pseudoinverse control algorithms, which implies that the direct hysteresis inverse model is not required, instead a searching mechanism of the actual control signal from the temporary control signal; 2) the all-state-constrained control problem of the Preisach hysteresis model is overcome when the control signal is coupled in the double integral functions with the aid of an FLS, BLFs, and the proposed hysteresis pseudoinverse algorithms; and 3) the DEA-based motion control platform is constructed, and the experiments are conducted to validate the effectiveness of our proposed control scheme.

This article aims to realize a precise position and attitude tracking control for the quadrotor using a proposed fuzzy approximator-based compound adaptive fuzzy quantized control scheme. In the control scheme, a quantized output-feedback control for position tracking and a state-feedback quantized control for attitude trajectory tracking are combined to deal with the underactuated and strong coupling problems of the quadrotor. The main contributions are: 1) the adaptive fuzzy quantized control is realized, then the strong nonlinearities caused by the quantizer are effectively mitigated, which implies that the control precision can be improved when a low communication rate is required in the real-time control system of quadrotor; 2) by applying the adaptive fuzzy dynamic surface control (DSC) technique to the underactuated quadrotor control system, the ``explosion of complexity'' problem in the backstepping method is overcome and the L∞ tracking performance is achieved with the proposed initializing technique inspired by Zhang et al. This guarantees that the attitude signals promptly converge to the desired trajectories, then the underactuated problem of the quadrotor is overcome by solving the designed adaptive fuzzy-quantized control equations; and 3) the experiments on the platform of the Quanser Qball-X4 quadrotor are conducted and the effectiveness of the proposed control scheme is validated.

This paper proposes a decentralized neural adaptive dynamic surface approximated inverse control (DNADSAIC) scheme for a class of large-scale time-delay systems with hysteresis nonlinearities as input. The decentralized control problem under the case only the outputs are measurable is solved by utilizing the radial basis function neural networks approximator and the hysteresis approximated inverse compensator. Also, with the help of finite covering lemma, the traditional Krasovskii functionals are dropped when coping with the delays, leading to the removal of the assumptions on the functions with time-delay states and the acquisition of the arbitrarily small L∞ tracking performance of each hysteretic subsystem with time delays. The analysis of stabilities guarantees all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded. Simulation results illustrate the efficiency of the proposed DNADSAIC scheme.