Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

Time-Varying Input and State Delay Compensation for Uncertain Nonlinear Systems

A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An integral term composed of previous control values facilitates a delay-free open-loop error system and the development of the feedback control structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals guarantees uniformly ultimately bounded tracking under the assumption that the delays are bounded and slowly varying

Adaptive Fractional-Order Sliding Mode Controller with Neural Network Compensator for an Ultrasonic Motor

Ultrasonic motors (USMs) are commonly used in aerospace, robotics, and medical devices, where fast and precise motion is needed. Remarkably, sliding mode controller (SMC) is an effective controller to achieve precision motion control of the USMs. To improve the tracking accuracy and lower the chattering in the SMC, the fractional-order calculus is introduced in the design of an adaptive SMC in this paper, namely, adaptive fractional-order SMC (AFOSMC), in which the bound of the uncertainty existing in the USMs is estimated by a designed adaptive law. Additionally, a short memory principle is employed to overcome the difficulty of implementing the fractional-order calculus on a practical system in real-time. Here, the short memory principle may increase the tracking errors because some information is lost during its operation. Thus, a compensator according to the framework of Bellman's optimal control theory is proposed so that the residual errors caused by the short memory principle can be attenuated. Lastly, experiments on a USM are conducted, which comparative results verify the performance of the designed controller.Comment: 9 pages, 9 figure

Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors

Over the years, researchers have addressed several control problems of various classes of nonlinear systems. This article considers a class of uncertain strict feedback nonlinear system with unknown external disturbances and asymmetric input dead-zone. Designing a tracking controller for such system is very complex and challenging. This article aims to design a finite-time adaptive neural network backstepping tracking control for the nonlinear system under consideration. In addition,  all unknown disturbances and nonlinear functions are lumped together and approximated by radial basis function neural network (RBFNN). Moreover, no prior  information about the boundedness of the dead-zone parameters is required in the controller design. With the aid of a Lyapunov candidate function, it has been shown that the tracking errors converge near the origin in finite-time. Simulation results testify that the proposed control approach can force the output to follow the reference trajectory in a short time despite the presence of  asymmetric input dead-zone and external disturbances. At last, in order to highlight the effectiveness of the proposed control method, it is applied to a quadrotor unmanned aerial vehicle (UAV)

Finite-Time Adaptive Fuzzy Tracking Control for Nonlinear State Constrained Pure-Feedback Systems

This paper investigates the finite-time adaptive fuzzy tracking control problem for a class of pure-feedback system with full-state constraints. With the help of Mean-Value Theorem, the pure-feedback nonlinear system is transformed into strict-feedback case. By employing finite-time-stable like function and state transformation for output tracking error, the output tracking error converges to a predefined set in a fixed finite interval. To tackle the problem of state constraints, integral Barrier Lyapunov functions are utilized to guarantee that the state variables remain within the prescribed constraints with feasibility check. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. In addition, all the signals in the closed-loop system are guaranteed to be semi-global ultimately uniformly bounded. Finally, two simulation examples are given to show the effectiveness of the proposed control strategy