Recursive observer design and nonsmooth output feedback stabilization of inherently nonlinear systems

This paper investigates the problem of using output feedback to semi-globally stabilise a class of planar non-linear systems with unknown control coefficients. For any given bounded set of initial condition, a non-smooth output feedback controller using a reduced-order observer is explicitly constructed to stabilise the planar system in a finite time. We also show that the proposed non-smooth output feedback controller can be used to solve the problem of Maximum Power Point Tracking (MPPT) in Photovoltaic (PV) arrays for certain solar radiation and temperature.

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

Output feedback (OFB) controllers for switched systems have been typically developed for linear systems. Of the OFB controllers that have been designed for switched nonlinear systems, at least partial knowledge of the system parameters is required, or the system results in local stability. In this paper, an OFB, time-dependent, switched controller is developed for an Euler-Lagrange system with parametric uncertainty and exogenous disturbances. The time-dependent switching signal is designed using an average dwell-time scheme based on multiple Lyapunov functions such that the switched system achieves semi-global uniformly ultimately bounded (UUB) tracking with arbitrary switching sequences.

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This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

Global output feedback stabilization for a class of switched nonlinear systems is addressed. The tasks of finding a common Lyapunov function and designing state stabilizing feedback laws are solved simultaneously based on the adding a power integrator approach. Reduced-order compensators for the switched nonlinear system are constructed to estimate the unmeasurable states. Coupling the state feedback controllers with the developing nonlinear observers, global asymptotic stabilization of the switched nonlinear system under arbitrary switchings is achieved by the output feedback control.

Global stabilization of a class of partially known nonnegative systems

In this paper a necessary and sufficient condition for a nonlinear system of the form /spl Sigma/, given by x(k+1)=f(x(k))+g(x(k))u(k), y(k)=h(x(k))+J(x(k))u(k), to be lossless is given, and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero-state observable. Then, we investigate conditions under which /spl Sigma/ can be rendered lossless via smooth state feedback. In particular, we show that this is possible if and only if the system in question has relative degree /spl lcub/0,...,0/spl rcub/ and has lossless zero dynamics. Under suitable controllability-like rank conditions, we prove that nonlinear systems having relative degree /spl lcub/0,...,0/spl rcub/ and lossless zero dynamics can be globally stabilized by smooth state feedback. As a consequence, we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable. The global stabilization problem of the nonlinear system /spl Sigma/ without output is also investigated in this paper by means of feedback equivalence. Some of the results are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of nonlinear systems using NARMAX model

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

This paper is concerned with the output feedback \(\mathcal {H}_\infty \) control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It\(\hat{o}\)-type differential equation with state and disturbance contaminated by white noises. The design of the output feedback \(\mathcal {H}_\infty \) control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback \(\mathcal {H}_\infty \) controller. It is shown that the output feedback \(\mathcal {H}_\infty \) control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton–Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods.

In this paper, we investigate the finite-time stabilization of a class of nonlinear systems using output feedback. The system nonlinearities are only assumed to be Holder continuous with output-dependent Hôlder coefficients. A new continuous, finite-time, output-feedback controller design is proposed based on a finite-time observer. The jet engine control model is adopted to demonstrate the effectiveness of the proposed output-feedback design method.

Design of output feedback semiglobally practically input-to-state (SPIS) stabilizing controllers for nonlinear strict-feedback networked systems is considered. We first design continuous-time state feedback globally asymptotically (GA) stabilizing controllers and discrete-time reduced-order observers and combine the emulation of state feedback controllers and the designed observers to construct discrete-time output feedback controllers. Then we show that the designed controllers SPIS stabilize nonlinear strict-feedback networked control systems when transmission intervals are sufficiently small and communication networks satisfy suitable assumptions. A numerical example is also given to illustrate the efficiency of proposed design of controllers.

Asymptotic stabilization of nonlinear systems with long input delay via memoryless feedback: A linearization method

A preliminary result on the construction of norm estimators for general nonlinear systems that do not necessarily admit a IOSS-Lyapunov characterization is given. Furthermore, an output feedback stabilization scheme is presented that makes use of norm estimators. This construction extends some previous results allowing for more general nonlinearities. Two examples complete the work.