Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

Robust linear controller design of uncertain discrete systems with time-varying delay

Disturbance rejection for nonlinear systems with mismatched disturbances based on disturbance observer

International audience

The robust stabilization problem for a class of uncertain linear time-delay systems containing sector saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. The new criterion of delay-dependent robust stabilizability for uncertain time-delay systems is presented and the corresponding robust memoryless state feedback controller is derived in terms of the solutions of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

In this paper, the tracking control problem is investigated for the helicopter under time-varying disturbance, input stochastic perturbation, and unmeasurable flapping motion states. Firstly, a state observer and a disturbance observer are constructed to estimate the unmeasurable states and the time-varying disturbance, and the estimation of the disturbance is used in the feedforward controller design. Secondly, under the input stochastic perturbation, a feedback controller is constructed to guarantee the stochastic stability of the closed-loop error system. Using the stochastic control theory and the linear matrix inequality technique, the stability of the closed-loop error system is analyzed, and the gain of the controller is acquired via a solvable sufficient condition. Finally, an example is presented to illustrate the effectiveness of the proposed method.

An anti-disturbance fault tolerant control (FTC) based on disturbance observer scheme is considered for a class of stochastic systems with faults and multiple disturbances in this paper. The disturbances are divided into two parts. One represents the stochastic disturbance with partial-known information which is formulated by an exogenous system. The other is independent Wiener process. A stochastic disturbance observer is designed to estimate exogenous disturbance using pole placement. And a composite fault diagnosis observer with disturbance observer is constructed to diagnose faults. Furthermore, a composite fault-tolerant controller is proposed to compensate modeled disturbance and accommodate faults. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the proposed scheme.

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities.

The problem of guaranteed cost (GC) control using static-state feedback controllers for uncertain linear discrete time-delayed systems subjected to actuator saturation is studied in this paper. The stability analysis of closed-loop systems is carried out using a Lyapunov-Krasovskii functional. Conditions for the existence of state-feedback GC controllers are developed using a linear matrix inequality (LMI)-based criterion. The approach ensures a sufficient performance bound over all the acceptable parameter uncertainties. The scheme of the optimal GC controller problem is framed as a convex optimization problem with LMI constraints. The design of GC controllers for discrete-time systems subjected to actuator saturation without considering the effect of state-delay is also discussed. The effectiveness of the proposed approach is illustrated using suitable examples.

In this article, a new scheme of designing decentralized extended proportional derivative (DEPD) controllers with combining novel disturbance observers is proposed for the issue of voltage control in islanded inverter-interfaced microgrids. A microgrid system under plug-and-play (PnP) functionality is described by an uncertain linear time-invariant system, and then, the stability of microgrid system is studied for voltage regulation based on the robust control theory and linear matrix inequality. The DEPD controller and the proposed disturbance observers are capable of minimizing undesirable oscillations in PnP operation of distributed generators and topology changes. To attenuate the effects of disturbances and uncertainties, a new nonlinear disturbance observer-based control strategy is provided in this article. The new disturbance observers proposed in this article can estimate any disturbances such as constant, harmonic, random walk, and any time-varying disturbances with slow varying rate. Some case studies and numerical simulations are investigated for evaluating the new control scheme via the MATLAB software. Simulations effectively validate the performance of the proposed approach.

This paper investigates the problem of robust H ∞ filter design for uncertain discrete piecewise time-delay systems based on a piecewise Lyapunov functional. The parametric uncertainties are assumed to be time-varying but norm bounded. The purpose is the design of a piecewise filter such that, for all admissible uncertainties, the resulting filtering error system is asymptotically stable and satisfies a prescribed H ∞ performance level. By introducing some different extra matrix variables, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of a desired piecewise filter is given. Two numerical examples are provided to demonstrate the effectiveness of the proposed design method.

The anti-disturbance output feedback tracking control problem is addressed for switched stochastic systems with multiple disturbances in this article. To deal with unknown disturbances and unmeasurable states, composite disturbance observer and state observer are designed simultaneously. Then, an output feedback tracking controller is designed based on outputs of two observers. By employing multiple Lyapunov function method, some sufficient conditions are given to analyse the mean square exponential stability with weighted H_∞ performance for the closed-loop system. Furthermore, the controller and observer gains are solved by linear matrix inequalities. At last, the validity of the presented scheme is demonstrated via two examples.

This paper proposes the sliding mode control using LMI techniques and adaptive recurrent fuzzy neural network (RFNN) for a class of uncertain nonlinear time-delay systems. First, a novel TS recurrent fuzzy neural network (TS-RFNN) is developed to provide more flexible and powerful compensation of system uncertainty. Then, the TS-RFNN based sliding model control is proposed for uncertain time-delay systems. In detail, sliding surface design is derived to cope with the non-Isidori-Bynes canonical form of dynamics, unknown delay time, and mismatched uncertainties. Based on the Lyapunov-Krasoviskii method, the asymptotic stability condition of the sliding motion is formulated into solving a Linear Matrix Inequality (LMI) problem which is independent on the time-varying delay. Furthermore, the input coupling uncertainty is also taken into our consideration. The overall controlled system achieves asymptotic stability even if considering poor modeling. The contributions include: i) asymptotic sliding surface is designed from solving a simple and legible delay-independent LMI; and ii) the TS-RFNN is more realizable (due to fewer fuzzy rules being used). Finally, simulation results demonstrate the validity of the proposed control scheme.

This technical note discusses the stability and stabilization problems for Takagi-Sugeno (T-S) fuzzy semi-Markovian jump systems (S-MJSs) in the discrete-time domain subjected to matched disturbances. The disturbance observer is designed to estimate the external disturbance. And then by combining the disturbance observer with model predictive control (MPC), a composite controller is proposed, such that, the stability of the closed-loop system can be guaranteed. By constructing a proper sojourn-time-dependent Lyapunov function, in the form of linear matrix inequalities (LMI), sufficient conditions for the existence of the composite anti-disturbance controller are framed. Finally, a set of numerical simulation examples are used to prove the effectiveness and feasibility of the proposed control strategy.