Output Feedback Control of a Class of Under-Actuated Nonlinear Systems Using Extended High Gain Observer

This paper deals with output feedback stabilisation of a class of nonlinear systems with nonlinearity of the unmeasured state variables. The nonlinearity of the unmeasured state complicates the zero dynamics of the nonlinear system and makes the control design more difficult. In this paper, the zero dynamics analysed for the class of nonlinear systems with respect to the original output and then with respect to a virtual output. It is demonstrated that nonlinear systems with unstable zero dynamics may have stable zero dynamics with the virtual output. Based on the analysis, conditions are then identified for nonlinear systems which can be stabilised by control design with estimated state, including the estimated virtual output, and this removes a restriction of a recent result that requires the transformed system has no zero dynamics. Examples are included to demonstrate that the proposed control design can be used to stabilise nonlinear systems with unstable nonlinear zero dynamics.

In this paper, an output-feedback tracking controller is proposed for a class of nonlinear non-minimum phase systems. To keep the unstable internal dynamics bounded, the method of output redefinition is applied to let the stability of the internal dynamics depend on that of redefined output, thus we only need to consider the new external dynamics rather than internal dynamics in the process of designing control law. To overcome the explosion of complexity problem in traditional backstepping design, the dynamic surface control (DSC) method is firstly used to deal with the problem of tracking control for the nonlinear non-minimum phase systems. The proposed output-feedback DSC controller not only forces the system output to asymptotically track the desired trajectory, but also drives the unstable internal dynamics to follow its corresponding bounded and causal ideal internal dynamics, which is solved via stable system center method. Simulation results illustrate the validity of the proposed output-feedback DSC controller.

Adaptive output feedback event-triggered tracking control for nonlinear systems with unknown control coefficient

A self-organizing fuzzy controller to augment a sliding-mode control (SOFSMC) scheme for a class of nonlinear systems is proposed. The motivation behind this scheme is to combine the best features of self-organizing fuzzy control and sliding-mode control to achieve rapid and accurate tracking control of a class of nonlinear systems. The chatter encountered by most sliding-mode control schemes is greatly alleviated without sacrificing invariant properties. A stability analysis is presented; the design guidelines and the class of applicable systems are clearly identified. To verify the scheme, the authors performed experiments on its implementation in a magnetic levitation system. The results show that both alleviation of chatter and robust performance are achieved; the advantages of the scheme are indicated in comparison with the conventional sliding-mode design. >

In this paper, a robust output feedback stabilization for a class of Autonomous Underwater Vehicle (AUV) is investigated. Two cases for, nonlinear, decoupled equations of motion of AUV in steering plane are considered in this work. In the first scenario, where all states are measurable, semi-global asymptotic stability for a class of AUV is shown by proposing a state-feedback controller based on Sliding Mode Control (SMC). The stability analysis is evaluated under model uncertainties and parametric variations. Then for the second case, Extended High-Gain Observer (EHGO), augmented with Extended Kalman Filter (EKF) is used to estimate the immeasurable states. It is shown that the states of the closed-loop system with output feedback controller, approach the invariant manifold in finite time and stay there. Efficacy of the proposed controllers is demonstrated with the help of numerical simulations.

This paper is concerned with an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control of Takagi-Sugeno fuzzy systems with immeasurable premise variables. Takagi-Sugeno fuzzy systems can usually approximate nonlinear systems and can even describe a certain class of nonlinear system exactly. When we consider the output feedback control of Takagi-Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design of the underlying nonlinear system based on its fuzzy system description is difficult. In this paper, we consider an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control problem. In this problem, the premise variable may not be measurable. Thus we formulate an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> output feedback control problem of fuzzy systems as a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control of uncertain systems. Numerical examples are given to illustrate our theory

A robust, stabilizing output feedback controller for systems in the normal form, which could potentially include systems with unstable zero dynamics, is presented. The control scheme adopted herein incorporates "smoothed" sliding mode control-chosen for its robustness properties as well as its ability to prescribe or constrain the motion of trajectories in the sliding phase-and an extended high gain observer to estimate one of the unknown functions. Stabilization in the case of an unknown control coefficient and uncertain constant parameters is shown.

We design a controller for a class of underactuated nonlinear systems. First, we try to find an appropriate global change of coordinates to transform the dynamics of the system into a desired form which consists of a lower order nonlinear subsystem plus a chain of integrators. Then, we find a control Lyapunov function (CLF) and its associated control law for the lower order subsystem. Finally, using a backstepping procedure we derive the control Lyapunov function and the controller for the whole system. The obtained controller renders the origin semiglobally asymptotically stable. As an special case, we demonstrate this procedure for the Acrobot example which is a two-link planar robot with a single actuator at the elbow.

In this study the tracking problem for a class of non-linear uncertain systems is analyzed. The considered class of non-linear systems are restricted by those verifying the global Lipschitz condition on non-linearities making them linear-like. A new sliding mode neurocontroller is suggested to solve this problem. The controller desing includes the on-line state estimates construction and the corresponding tracking control based on sliding mode approach and the reconstructed dynamics generated by a special non-linear observer. A special sliding mode technique during the “off-line training” to estimate the right-hand side of the given dynamics in finite-time was applied. This procedure allows use of these estimates for the best (in LQ-sense) nominal weights selection in the neuro observer designed. A switching (sign) type term is incorporated in the observer structure to correct the current state estimates using just the on-line measurable output. This observer is supplied with a new learning procedure with switching structure. Two illustrative examples are presented: a benchmark problem related with a nominal linear system and a real chemical procedure dealing with the organic compounds elimination by ozone effect.

In this paper, we address the stabilization problem for nonlinear systems in a critical case. Namely, we study the class of canonical nonlinear systems. Canonical nonlinear systems or chain of power integrators is an important subject of research. Studying such systems is complicated by the fact that they cannot be mapped onto linear systems. Moreover, they have the uncontrollable first approximation. Previous results on smooth stabilization of such systems were obtained under the assumption that the powers in the right-hand side are strictly decreasing. In this work, we consider a case of non-increasing powers in the right-hand side for a three-dimensional system. A popular approach for studying such systems is the backstepping method, which is a method of step-wise stabilization. This method requires a sequential investigation of lower-dimensional subsystems. Backstepping enables the study of a wide range of nonlinear triangular systems but requires technically complex and cumbersome computations. Therefore, a natural question arises about constructing stabilizing controls of a simple form. Polynomial controls can serve as an example of such controls. In the paper, we demonstrate that linear controls can be considered as stabilizing controls. We derive sufficient conditions for the coefficients of the linear control that ensure the asymptotic stability of the zero equilibrium point of the corresponding closed-loop system. The asymptotic stability is proven using the Lyapunov function method, which is found as the sum of squares. The negative definiteness of the Lyapunov function derivative in a neighborhood of the origin guarantees asymptotic stability. In contrast to the case of strictly decreasing powers, additional conditions on the control coefficients, apart from their negativity, emerge. The obtained result extends to a broader class of nonlinear systems through stabilization by nonlinear approximation. This allows the consideration of systems with higher-order terms in the right-hand side. The effectiveness of the applied approach is illustrated by several model examples. The method used in this work to investigate the case of non-increasing powers can be applied to systems of higher dimensions.

The design of control laws for underactuated mechanical systems is challenging as their underactuated nature, poses problems in exact feedback linearization. This paper considers the stabilization problem of inertia-wheel pendulum, a widely studied benchmark nonlinear underactuated mechanical system. A novel nonlinear controller design for inertia wheel pendulum is presented; fusing recently introduced multiple surface controls with control Lyapunov function. The design procedure is simpler and more intuitive than already presented designs. Stability of the controller and advantages over dynamic surface control, energy shaping and backstepping controllers are analyzed theoretically and verified using numerical simulations.

A class of nonlinear systems is considered in IR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> whose system's function is, component-wise, given by the product of real powers of the state's entries. We call it the class of 'Π-algebraic' systems. It is shown that every Π-algebraic nonlinear system undergoes a quadratic embedding into a suitable (non associative) algebra. This means that a product can be defined in the state-space, which makes the latter a non associative algebra, whose associated quadratic differential equation has a subset of entries of its solution equal to the solution of the original nonlinear system. We also study a related control problem, where for a meaningful subclass of the considered systems it is shown that a state-feedback regulator can be build up, having exponential performance, which makes the y-axe in IR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> a globally asymptotically stable equilibrium set of the closed-loop system.

Byrnes-Isidori-based dynamic sliding-mode control for nonminimum phase hypersonic vehicles

This paper presents a unified fault isolation scheme for process faults and sensor faults in a class of nonlinear uncertain systems. The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a particular fault type. Based on the class of nonlinear systems and fault types under consideration, adaptive thresholds are derived for the isolation estimators, and fault isolability conditions are rigorously investigated, characterizing the class of process faults and sensor faults that are isolable by the proposed scheme.

Fuzzy stable inversion-based output tracking for nonlinear non-minimum phase system and application to FAHVs