Novel model reference adaptive control with application to wing rock example

In this study, we propose new adaptive laws for adjusting the controller parameters of the model reference adaptive control (MRAC) and MRAC with integral feedback schemes. The innovation presented in this study is considering a new form for the Lyapunov function candidate to prove the stability of the closed-loop system. In general, a Lyapunov function candidate contains two sets of quadratic expressions. The first set contains the state tracking error variable, while the second one consists of the controller parameter estimation errors. We prove that by choosing the tracking error quadratic expressions in the form of the exponential function, new adaptive laws that contain the tracking error quadratic expressions are obtained. The difference between the standard MRAC adaptive laws and the proposed new adaptive laws is the state tracking error exponential quadratic expression appears in the adaptive laws. It is shown that the adaptive laws obtained by the exponential quadratic Lyapunov function are similar to those obtained by the quadratic Lyapunov function except that the adaptive gains are variable with time. The advantage of using these new adaptive laws is improving the tracking performance of the closed-loop system, which has been proven analytically and verified by numerical simulations. Also, the robustness analysis of the proposed MRAC controller in the presence of the exogenous disturbance is studied. We consider the single degree of freedom of the wing rock example to evaluate the performance of the designed controllers.

Análisis de estabilidad de convertidores de segundo orden con la metodología de optimización de suma de polinomios cuadráticos

This paper presents a non-linear method based on sum-of-squares (SOS), to determine the stability of equilibrium points for the Buck, Boost, Buck-Boost and non-inverter Buck-Boost converters. These converters share a similar structure with a PI controller to regulate the output voltage. A quadratic Lyapunov function is proposed in all cases, and the conditions for stability are evaluated using convex optimization based on SOS models. The methodology is useful for academic purposes but also in practical applications like DC microgrids. Simulation results shows the advantages of the proposed method.

On Interval Observer Design for Continuous-Time LPV Switched Systems

State estimation for switched systems with time-varying parameters has received a great attention during the past decades. In this paper, a new approach to design an interval observer for this class of systems is proposed. The scheduling vector is described by a convex combination so that the parametric uncertainties belong into polytopes. The considered system is also subject to measurement noise and state disturbances which are supposed to be unknown but bounded.The proposed method guarantees both cooperativity and Input to State Stability (ISS) of the upper and lower observation errors. Sufficient conditions are given in terms of Linear Matrices Inequalities (LMIs) using a common quadratic Lyapunov function. Finally, a numerical example is provided to show the effectiveness of the designed observer.

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their time derivatives, which is the well-known issue of the common non-quadratic Lyapunov functions in the literature. Also, the memory fuzzy controller is chosen such that the artificial constant delay-dependent stability analysis conditions for a non-delayed closed-loop T–S fuzzy system are formulated in terms of linear matrix inequalities. To further reduce the conservatives, some slack matrices are introduced by deploying the descriptor representation and decoupling lemmas. Moreover, the design of the robust fuzzy controller is studied through the [Formula: see text] performance criteria. The main advantages of the proposed approach are its small conservatives and the global stability analysis, which distinguish it from the state-of-the-art methods. To show the merits of the proposed approach, comparison results are provided, and two numerical case studies, namely, flexible joint robot and two-link joint robot are considered.

Robust sliding mode observer design for simultaneous fault reconstruction in perturbed Takagi-Sugeno fuzzy systems using non-quadratic stability analysis

Appearing faults in a practical system is dispensable, and if it is not compensated, it results in poor system performance or even dysfunction of the system. The fault detection has become a promising challenging issue to guarantee the safety and reliability of systems. In this paper, a novel fuzzy-based sliding mode observer for the simultaneous actuator and sensor fault reconstruction of nonlinear systems subjected to external disturbance is proposed. The proposed approach employs the Takagi-Sugeno fuzzy model, sliding mode observer and non-quadratic Lyapunov function. First, by filtering the system output, a fictitious system whose actuator faults are the original actuator and sensor faults is constructed. Then, by considering the [Formula: see text] performance criteria, the effect of disturbance on the state estimations is minimized. It is proved that the estimations asymptotically converge to their actual values for non-perturbed systems. In the process of designing the observer gains, some transformation matrices are obtained by solving linear matrix inequalities. The proposed approach has some superiority over the existing methods. First, considering the non-quadratic Lyapunov function leads to relaxed results and good estimation performance. Second, using the sliding mode observer makes the proposed approach insensitive to the uncertainties and unknown inputs and determines the shape and size of the fault. Third, assuming the premise variables are immeasurable makes the presented approach more applicable. In conclusion, two practical systems are considered and simulation results illustrate the merits of the proposed approach in comparison with the recent methods from the fast and precise fault detection performance viewpoints.

STABILITY OF ZERO SOLUTION OF SYSTEM WITH SWITCHES CONSISTING OF LINEAR SUBSYSTEMS

In this paper, discusses the study of the stability of solutions of dynamic systems with switching. Sufficient conditions are obtained for the asymptotic stability of the zero solution of switching systems consisting of linear differential and difference subsystems. It is proved that the existence of a common quadratic Lyapunov function is sufficient for asymptotic stability.