Robust output feedback control of uncertain switched Euler-Lagrange systems

Output feedback control of switched nonlinear systems using multiple Lyapunov functions

In this paper, a nonlinear robust output feedback control is proposed for a class of autonomous underwater vehicles. In specific, we consider the nonlinear mathematical model of a heavy-weight torpedo and design a sliding mode controller to achieve robust stabilization of the closed-loop system in the presence of environmental disturbances and parametric uncertainties. Lyapunovs method is used to present the closed-loop stability analysis of the system. Then, the state feedback sliding mode control law is extended to an output feedback control design using a fourth order observer. It is highlighted that the performance of the state feedback control is recovered arbitrarily fast by the proposed output feedback controller in the presence of parametric uncertainties and environmental disturbances. Finally, the performance of the proposed control design is shown using simulation.

In this paper we develop a nonsmooth output feedback framework for local and/or global stabilization of a class of inherently nonlinear systems, which may not be achieved by any smooth feedback controller. A systematic design algorithm is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Holder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design procedure, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented fashion. Such nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems with unstabilizable/undetectable linearization. One of them is the global stabilizability of a chain of odd power integrators by Holder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems studied in Qian and Lin (2001), where only global stabilizability by nonsmooth state feedback was proved to be possible.

This study employs the free-weighting matrix approach to investigate the output feedback control of a linear discrete-time system with an interval time-varying delay. First, the delay-dependent stability is analyzed using a new method of estimating the upper bound on the difference of a Lyapunov function without ignoring any terms; and based on the results, a design criterion for a static output feedback (SOF) controller is derived. Since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility SOF control problem. Furthermore, the problem of designing a dynamic output feedback controller is formulated as one of designing an SOF controller. Numerical examples demonstrate the effectiveness of the method and its advantage over existing methods.

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

Both dynamic state feedback as well as output feedback tracking control designs are presented in this paper for constrained robot systems under parametric uncertainties and external disturbances. The previous studies on tracking control design, not considering the velocity measurements, address only the unconstrained robot design. In contrast, a dynamic output feedback controller based on a linear and reduced-order observer that uses only position measurements is proposed here for the first time to treat the trajectory tracking control problem of constrained robot systems. Both adaptive state feedback control schemes and adaptive output feedback control schemes with a guaranteed H∞ performance are constructed. It is shown that all the variables of the closed-loop system are bounded and a pre-assigned H∞ tracking performance is achieved, in the sense that the influence of external disturbance on the tracking motion error can be attenuated to any specified level. Moreover, it is also shown that the motion and force trajectories asymptotically converge to the desired ones as the dynamic model of robot systems is well-known and the external disturbance is neglected. Finally, simulation examples are presented to illustrate the tracking performance of a two-link robotic manipulator with a circular path constraint by the proposed control algorithms. © 1998 John Wiley & Sons, Ltd.

In the paper the problem of adaptive backstepping control of an uncertain nonlinear plant represented in the parametric output feedback canonical form is addressed. The state of the plant is not accessible for measurement and its parameters are not known. New modular backstepping state feedback design with high-order tuners recently proposed in [7], [8], [9] provides improvement of the transient performance of the closed-loop system by appropriate compensation of the deteriorating effect caused by the transients of the adjustable parameters. The main focus of the present paper is to extend the approach proposed in [7], [8], [9] to the case of output-feedback control. It is proved and demonstrated via simulation that the output-feedback adaptive controller designed accelerates the tuning of controller parameters.

In this paper, output feedback direct adaptive robust NN control is investigated for a class of nonlinear discrete-time systems in strict-feedback form. To construct output feedback control, the original strict-feedback system is transformed into a cascade form, which the output feedback of the nonlinear discrete-time system can be carried out. Then with employment of the inputs and outputs, the output feedback direct adaptive robust NN control is developed. The HONNs is exploited to approximate unknown function, and a stable adaptive NN controller is synthesized. The proposed algorithm improves the rubostness of the discrete-time nonlinear systems. It is proven that all the signals in closed-loop system are uniformly ultimately bounded (UUB). A simulation example is presented to illustrate the effectiveness of the proposed algorithm.Keywordsoutput feedbackrubostnessdirect adaptive NN controldiscrete-time nonlinear system

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.

In this paper, a new stabilization condition of switched fuzzy systems is proposed. The dynamic output feedback control problem is addressed for a class of switched fuzzy Systems. The dynamic output feedback with sufficient conditions and the design method of controller is given using multiple Lyapunov function method and switching law. The closed-loop system asymptotically stable is given by the designed controller. Adopting the dynamic output feedback control law, the order of the closed-loop system is reduced, which is helpful to improve the reliability of the system. Finally, simulation results verify the effectiveness of the conclusion.

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

A novel neural network (NN) -based output feedback controller with magnitude constraints is designed to deliver a desired tracking performance for a class of multi-input-multi-output (MIMO) discrete-time strict feedback nonlinear systems. Reinforcement learning in discrete time is proposed for the output feedback controller, which uses three NN: 1) a NN observer to estimate the system states with the input-output data; 2) a critic NN to approximate certain strategic utility function; and 3) an action NN to minimize both the strategic utility function and the unknown dynamics estimation errors. The magnitude constraints are manifested as saturation nonlinearities in the output feedback controller design. Using the Lyapunov approach, the uniformly ultimate boundedness (UUB) of the state estimation errors, the tracking errors and weight estimates is shown.

This paper considers the analytical design and stability analysis of an output feedback flight control problem for a rigid fighter aircraft which has a highly nonlinear dynamic. In this paper, a robust technique known as Universal Integral Regulator (UIR) has been chosen to solve the tracking problem due to the possibility to demonstrate the stability of the system and analytically compute the control parameters. The UIR is a combination of Continuous Sliding Mode Control (CSMC) and a Conditional Integrator (CI) which provides integral action only inside the boundary layer, enhancing the transient response of the system and providing an equilibrium point where the tracking error is zero. The general procedure consists firstly of rewriting the aircraft dynamics in the control-affine form, then the relative degree of the system is computed and the system is transformed to normal form. An output feedback controller using a CSMC controller is proposed, and a sliding surface considering a CI is designed. The controller parameters are designed analytically, taking into account two approaches. The first approach does not consider uncertain parameters and the second one treats a stability derivative as a parametric uncertainty. Simulations were performed in order to validate the design procedure of the control technique and to demonstrate the robustness of the UIR. Detailed step by step information about the computing of the controller parameters was done and an analytical analysis of stability was developed to demonstrate the convergence of the sliding surface, conditional integrator and tracking error dynamics.