Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

In this brief, the global output-feedback stabilization is addressed for a class of uncertain feedforward nonlinear systems. By integrating a dynamic event-triggered mechanism, a novel observer-based control scheme is established, where a time-varying gain is introduced to cope with large uncertainties and sampling errors in the system. Under this control scheme, the global convergence is ensured for the resulting closed-loop system states. Different from the related results, the system states are intermittently monitored by imposing suspension time after each sampling, so that the inter-event intervals have a uniform positive lower bound, and the Zeno behavior is automatically ruled out. Additionally, an internal dynamic variable is incorporated into the triggering mechanism to further extend the inter-event intervals. Finally, the obtained results are extended to a class of feedforward nonlinear systems with unknown time-varying growth rates. A simulation example is given by applying the proposed scheme to a nonlinear liquid level control (LLC) resonant circuit system.

ABSTRACTThis paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.

This paper investigates the problem of disturbance attenuation for a class of feedforward nonlinear systems whose output functions are not precisely known. A new control strategy based on a double-domination approach is proposed to cope with serious coexistence of various uncertainties, including unknown output function and external disturbances. The novelty lies in a distinct perspective to applying two domination gains in the constructions of the observer and the controller in the case when output functions are perturbed by unmeasurable errors, which was previously regarded as a rather difficult problem. A numerical simulation is carried out to illustrate the effectiveness of the proposed scheme.

Semi-global finite-time output feedback stabilization for a class of large-scale uncertain nonlinear systems

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

In this paper, by constructing appropriate Lyapunov–Krasovskii functionals (LKF) and applying the model transformation of time-delay systems, a design scheme of state feedback controller for a class of feedforward nonlinear systems with a delay in the input is proposed. The designed controllers have a very simple structure and do not involve any saturation or recursive computation, which is widely applied in designing a controller of feedforward nonlinear systems. Using the transformation of coordinates and the property of Hurwitz polynomial, the problem of designing controller can be converted into the problem of finding a parameter, which can be solved by solving the optimization problem with linear matrix inequalities (LMIs) constraints. A simulation example is given to show the effectiveness of the proposed design procedure.

In this work, by constructing an appropriate integral-type Lyapunov-Krasovskii functional (LKF) and applying a model transformation of time-delay systems, a design scheme of delay-free state feedback controller is provided for a class of feedforward nonlinear systems with both discrete delays and distributed delays. The designed controllers have simple forms and do not involve saturation or any recursive computation, which is widely applied in designing a controller of feedforward nonlinear systems. By using the transformation of coordinate and the property of Hurwitz polynomial, the problem of designing controller will be converted into that of determining a constant parameter, which can be gotten by appraising the nonlinear terms of the given systems.

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

We consider the problem of finite-time stabilization for nonlinear systems. In the previous work, it was proved that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system could be achieved by non-Lipschitz continuous state feedback. The proof was based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method proposed in, for the control of nonlinear systems that are impossible to be dealt with by any smooth feedback. A simpler design algorithm is given for the construction of a non-Lipschitz continuous, global finite-time stabilizer as well as a C/sup 1/ positive definite and proper Lyapunov function that guarantees finite-time stability.

Robust finite-time output feedback control of perturbed double integrator

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

H finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.