Robust dynamic output feedback stabilization for a class of nonlinear systems with state and input delay

A note on the problem of semiglobal practical stabilization of uncertain nonlinear systems via dynamic output feedback

New results on dynamic output state feedback stabilization of some class of time-varying nonlinear Caputo derivative systems

This paper investigates the problem of robust output feedback stabilization of uncertain Hamiltonian systems with saturating actuator and input delay. The uncertainties are assumed to be time invariant and belong to convex bounded polytopic domain. By employing Lyapunov-Krasovskii functional method and Wirtinger's inequality, some sufficient conditions are derived for stabilization of nonlinear Hamiltonian systems under consideration. A delay-independent condition in terms of linear matrix inequalities for control of the Hamiltonian systems is established first. And further, an output feedback controller synthesis scheme under the multiple Lyapunov functional framework is proposed which guarantees the robust stability of the closed-loop system when control saturation and delay effectively occur. Finally, numerical results are given to demonstrate the effectiveness of the proposed methodology.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

To guarantee the control performance of the discrete system under unmeasurable state and partial actuator failure, a robust dynamic output feedback predictive fault-tolerant control method derived from switching strategy is developed. A new iterative error switching model is established, which both ensures tracking performance and lays the foundation for the development of the next switching controller. Based on this model, output feedback switching fault-tolerant controller is developed. Compared with conventional fault-tolerant control methods, the designed controller can be used under the case of unmeasurable states, and it is more fault tolerant and less conservative. According to the Lyapunov stability theory, the robust stability analysis is carried out under normal and fault conditions, respectively. Then, depending on the findings of the stability analysis, sufficient conditions to guarantee the stability of the closed-loop normal and faulty system are derived. Finally, the suggested method's efficacy is confirmed using the injection moulding process as an example.

Magnetorheological fluid (MRF) dampers have been utilized in semi-active air suspension (SAAS) due to their attractive advantages. This paper investigates a novel robust fuzzy output feedback controller for semi-active air suspension with MRF damper (SAAS-MRFD), considering time delay and actuator saturation. An aero-thermodynamics theory is first utilized to describe the nonlinear air spring. The damping force of the MRF damper is represented by a hyperbolic tangent model. The interval type-2 (IT-2) Takagi–Sugeno (T-S) fuzzy method is second employed to capture those nonlinearities of the air spring and MRF damper. Considering the difficulty to measure all states, a novel dynamic output feedback (DOF) controller is developed by an appropriate Lyapunov–Krasovskii function and the reciprocally convex technique with consideration of time delay, actuator saturation, and output constraints. The effectiveness of the proposed controller is validated by both simulation and a quarter-car test rig (QCTR). The results indicate that the proposed controller has better performance in vibration reduction than the recent similar controllers in the literature.

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.

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

In this paper, the problem of delay-dependent robust dynamic output feedback stabilization for a class of uncertain singular time-delay system is investigated. Based on the delay-dependent stability criterion for nominal singular time-delay systems and the concept of generalized quadratic stabilization, the sufficient conditions of the existence of the feedback controller are obtained, which ensure that the closed-loop systems are regular, impulse free and robustly asymptotically stable. Moreover, the expression for the desired robustly stabilizing controller is given by using the LMIs and the cone complementarity linearization iterative algorithm.

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

This paper is concentrated on the problem of robust adaptive output feedback fault tolerant control for a class of nonlinear systems with Lipschitzian nonlinearities and faults. An adaptive fault estimator and a nonlinearity approximator via the measured output signals is introduced to establish an output feedback fault tolerant controller, so that the designed controller parameters are able to be updated on-line to compensate the fault effect on the nonlinear systems. The proposed control strategy guarantees the asymptotic stability of the closed-loop system with a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Numerical examples demonstrate the effectiveness of the proposed control scheme.

An observer-based adaptive neural-network robust control for a class of nonlinear time-delay systems with unmodeled dynamics. It is presented for a class of nonaffine nonlinear time-delay systems with external disturbance and unavailable states. By the implicit function theorem, Taylor’s formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems. The controller designed to attenuate the effect of external disturbance and approximation errors of the neural networks on tracking. The unknown time-delay is compensated by using appropriate Young inequality, the weight update laws based on Lyapunov stability theory can guarantee the system stability and asymptotic convergence of the tracking error to zero. Theoretical analysis and simulation results demonstrate the effectiveness of the approach.

In this paper, we consider the robust output containment problem of linear heterogeneous multi-agent systems under fixed directed networks. A distributed dynamic observer based on the leaders' measurable output was designed to estimate a convex combination of the leaders' states. First, for the case of followers with identical state dimensions, distributed dynamic state and output feedback control laws were designed based on the state-coupled item and the internal model compensator to drive the uncertain followers into the leaders' convex hull within the output regulation framework. Subsequently, we extended theoretical results to the case where followers have nonidentical state dimensions. By establishing virtual errors between the dynamic observer and followers, a new distributed dynamic output feedback control law was constructed using only the states of the compensator to solve the robust output containment problem. Finally, two numerical simulations verified the effectiveness of the designed schemes.

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this article introduces a dynamic fuzzy boundary output feedback (DFBOF) control under noncollocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi–Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI)-based sufficient conditions to ensure mean-square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Finally, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.

Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation