Decentralized robust output-feedback control of uncertain nonlinear interconnected systems with disturbances

International audience

The problem of dynamic output feedback control stabilization is considered for a class of multi-time delays uncertain nonlinear systems. Based on LMI and proper Lyapunov functions, a sufficient condition for the existence of robust output feedback controller is proposed, which ensures that the closed-loop system is robust stable. The dynamic output feedback controller is designed by the feasible solution of the matrix inequality with constraint. At last, by using matrix orthogonal complement, the parameters solving methods of output feedback controller is also provided.

Distributed containment output-feedback control for a general class of stochastic nonlinear multi-agent systems

In this paper, the output feedback control problem is considered for a class of uncertain nonlinear time-delay systems. The system nonlinearities satisfy linear growth condition on unmeasured states multiplied by unknown growth rate and output polynomial function. With appropriate Lyapunov-Krasovskii functional, a memoryless adaptive output feedback controller is developed to guarantee global stability of the nonlinear time-delay systems. The precise knowledge of the time-delay is not required to be known a priori. Furthermore, only one dynamic gain is designed, which makes the controller easier to implement. A numerical example is used to illustrate the effectiveness of the proposed method.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

Robust tracking control of uncertain nonlinear systems with adaptive dynamic programming

Stability for uncertain nonlinear dissipative systems

Robust adaptive fuzzy filters output feedback control of strict-feedback nonlinear systemsIn this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of single input single output (SISO) strict-feedback nonlinear systems without measurements of states. The nonlinear systems addressed in this paper are assumed to possess unstructured uncertainties, unmodeled dynamics and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds is available. In recursive design, fuzzy logic systems are used to approximate unstructured uncertainties, and K-filters are designed to estimate unmeasured states. By combining backstepping design and a small-gain theorem, a stable adaptive fuzzy output feedback control scheme is developed. It is proven that the proposed adaptive fuzzy control approach can guarantee the all the signals in the closed-loop system are uniformly ultimately bounded, and the output of the controlled system converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by a simulation example and some comparisons.

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

Robust adaptive output-feedback control of a class of uncertain nonlinear systems

This paper investigates non-fragile exponential H∞ control problems for a class of uncertain nonlinear networked control systems (NCSs) with randomly occurring information, such as the controller gain fluctuation and the uncertain nonlinearity, and short time-varying delay via output feedback controller. Using the nominal point technique, the NCS is converted into a novel time-varying discrete time model with norm-bounded uncertain parameters for reducing the conservativeness. Based on linear matrix inequality framework and output feedback control strategy, design methods for general and optimal non-fragile exponential H∞ controllers are presented. Meanwhile, these control laws can still be applied to linear NCSs and general fragile control NCSs while introducing random variables. Finally, three examples verify the correctness of the presented scheme.

A general class of uncertain nonlinear systems with uncertain input unmodeled dynamics is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions and coupled with a set of uncertain nonlinear appended dynamics as well as uncertain dynamic input nonlinearities. The dynamic input nonlinearities include an uncertain non-affine function and a dynamic perturbation through an uncertain input unmodeled dynamics subsystem. The input unmodeled dynamics subsystem is coupled with the entire system state including the unmeasured state of the uncertain nonlinear appended dynamics coupled with the nominal triangular system. The control design is based on dual controller/observer dynamic high-gain scaling with an additional dynamic scaling based on a singular-perturbation-like redesign to address the non-affine and uncertain nature of the input appearance into the system dynamics. The proposed approach yields a global robust adaptive output-feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure.

Decentralized Output Feedback Control of Interconnected Uncertain Delay Systems

This paper presents a finite-time fault-tolerant fuzzy adaptive controller for uncertain interconnected nonlinear systems in strict-feedback form. The controller addresses input saturation, state-dependent actuator faults, external disturbances, and unavailable states for measurement. To avoid any unexpected alteration due to failures, the proposed control scheme design addresses all types of actuator faults that are bias, drift, and loss of accuracy as additive faults, as well as a multiplicative fault that results in loss of effectiveness with nonaffine state-dependency. Restrictions on control gains and unmatched interconnections are eliminated, and the explosion complexity caused by recursive back-stepping designs is avoided. Fuzzy Systems approximate the unknown ideal control laws along side the acutator faults and disturbances. The stability analysis guarantees that tracking errors converge to a small compact set around the origin in finite time. Simulation results on a quad-rotor UAV and a mathematical system confirm the effectiveness of the proposed approach.

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