Bounded Input Disturbances Research Articles

Boundary Control of a Nonhomogeneous Flexible Wing with Bounded Input Disturbances

This note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two coupled partial differential equations. Based on the proposed boundary control law, the well-posedness of the underlying Cauchy problem is first investigated by resorting to the semigroup theory. Then, a Lyapunov-based approach is employed to assess the stability of the closed-loop system in the presence of bounded input disturbances.

Estimation and Synthesis of Reachable Set for Singular Markovian Jump Systems

The problems of reachable set estimation and state‐feedback controller design are investigated for singular Markovian jump systems with bounded input disturbances. Based on the Lyapunov approach, several new sufficient conditions on state reachable set and output reachable set are derived to ensure the existence of ellipsoids that bound the system states and output, respectively. Moreover, a state‐feedback controller is also designed based on the estimated reachable set. The derived sufficient conditions are expressed in terms of linear matrix inequalities. The effectiveness of the proposed results is illustrated by numerical examples.

ISS Stabilization of Discrete-time LPV Systems with Interval Time-varying State Delay and Saturating Actuators

Abstract We address the problem of input-to-state stabilization of linear parameter-varying (LPV) discrete-time systems with delayed state and subject to saturated actuators and to l2-limited disturbance. It is assumed that the time-varying delay belongs to a known interval and its maximum variation between two consecutive instants has limited rate. We propose convex delay-dependent conditions for the synthesis of LPV state feedback controllers that do not require the real-time knowledge of the delay and ensure the local input-to-state stability of the closed-loop system for a set of initial conditions and subject to energy bounded disturbance input signals. The approach is based on rewriting the delayed system as a switched uncertain augmented delay-free system with a dead-zone non-linearity and on the application of the generalized sector condition to deal with the saturating actuators. To illustrate the efficiency of our approach, we present a numerical example.

Reachable set estimation for inertial Markov jump BAM neural network with partially unknown transition rates and bounded disturbances

This paper mainly focuses on the reachable set estimation problem of a time-varying delayed inertial Markov jump bidirectional associative memory (BAM) neural network with bounded disturbance inputs. The disturbances are assumed to be either unit-energy bounded or unit-peak bounded. Different from systems of the past studies, this paper is for inertial Markov jump BAM neural network with both time-varying delay and time-varying transition rates. The time-varying character of the considered transition rates is assumed to be piecewise-constant. In order to reduce the conservatism, the delay-partitioning technique is utilized to solve this reachable set estimation problem. As a result, it is obtained that the ellipsoid defined in this paper contains the reachable set Rup, which indicates the reachable set Rue is included. Further, we extend the results to the uncertain Markov jump BAM neutral network with partially unknown transition probabilities. Numerical examples are proposed to show the effectiveness of the given results.

Reachable Set Estimation of T–S Fuzzy Systems With Time-Varying Delay

In this paper, the reachable set estimation problem is investigated for delayed discrete-time Takagi–Sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions. A reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple-summable terms. The derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set, and all the states from other domain converge exponentially within another compact set. Moreover, a less conservative stability condition is also obtained. The effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples.

Reachable Set Estimation for Discrete‐Time Singular Systems

AbstractThis paper is concerned with the problem of reachable set estimation for discrete‐time singular systems with bounded input disturbances. Based on the Lyapunov method, a new sufficient condition is established in terms of linear matrix inequality (LMI) to guarantee that the reachable set of discrete‐time singular system is bounded by the intersection of ellipsoids. Then the result is extended to the problem for discrete‐time singular systems with time‐varying delay by utilizing the delay‐dependent approach and free weighting matrices. Two numerical examples are provided to demonstrate the effectiveness of the obtained results proposed in this paper.

Triple integral approach to reachable set bounding for linear singular systems with time‐varying delay

This paper is concerned with the reachable set estimation problem of singular systems with time‐varying delay and bounded disturbance inputs. Based on a novel Lyapunov–Krasovskii functional that contains four triple integral terms, reciprocally convex approach and free‐weighting matrix method, two sufficient conditions are derived in terms of linear matrix inequalities to guarantee that the reachable set of singular systems with time‐varying delay is bounded by the intersection of ellipsoid. Finally, two numerical examples are given to demonstrate the effectiveness and superiority of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Krein space-based H∞ adaptive smoother design for a class of Lipschitz nonlinear discrete-time systems

In this paper, the problem of H∞ adaptive smoother design is addressed for a class of Lipschitz nonlinear discrete-time systems with l2 bounded disturbance input. By comprehensively analyzing the H∞ performance, Lipschitz conditions and unknown parameter’s bounded condition, a positive minimum problem for an indefinite quadratic form is introduced such that the H∞ adaptive smoothing problem is achieved. A Krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form. The minimum of indefinite quadratic form is derived in the form of innovations through utilizing Krein space orthogonal projection and innovation analysis approach. Via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive, the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard Riccati difference equations. The quality of the estimator is checked on an example.

Leader-following control of perturbed second-order integrator systems with binary relative information

ABSTRACTIn this paper, we study the leader-following control problem for second-order integrator systems with bounded input disturbances using only binary relative position and velocity information. The leader is allowed to be dynamically evolving with a bounded acceleration which is unknown to any of the followers. With the proposed distributed controller, we prove that despite the fact that only very coarse relative information is available, robust finite-time leader-following control can be achieved by properly choosing the control gains. As an extension, robust finite-time formation control can also be achieved with the proposed control strategy using only binary relative information. Two simulation examples are provided to illustrate the results.

L∞-gain performance analysis for two-dimensional Roesser systems with persistent bounded disturbance and saturation nonlinearity

The l∞-gain approach has been an essential tool in one-dimensional system theory. However, limited results have been presented in the literature for the two-dimensional (2-D) l∞-gain approach. This paper investigates the l∞-gain performance for 2-D systems in the Roesser model with persistent bounded disturbance input and saturation nonlinearity. A linear matrix inequality (LMI)-based condition is established to reduce the effect of persistent bounded disturbance input on 2-D systems within a given disturbance attenuation level based on the discrete Jensen inequality, lower bounds lemma, and diagonally dominant matrices. We apply the obtained results to the l∞-gain performance analysis for 2-D digital filters with saturation arithmetic.

New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals

This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method.

New results on state bounding for discrete‐time systems with interval time‐varying delay and bounded disturbance inputs

This study considers the problem of state bounding for a class of discrete-time systems with interval time-varying delay and bounded disturbance inputs. By using an improved Lyapunov–Krasovskii functional combining with the delay-decomposition technique and the reciprocally convex approach, the authors first derive new delay-dependent conditions in terms of matrix inequalities to guarantee the existence of a ball such that, for any initial condition, the state trajectory of the system is either bounded within that ball or converges exponentially within it. On the basis of these new conditions, the authors then derive an improved ellipsoid reachable set bounding and a new result on exponential stability of discrete-time systems with interval time-varying delay. Numerical examples are presented to show the effectiveness of the obtained results and improvement over existing results.

Reachable set estimation and controller design for distributed delay systems with bounded disturbances

This paper is concerned with the problems of reachable set estimation and state-feedback controller design for linear systems with distributed delays and bounded disturbance inputs. The disturbance inputs are assumed to be either unit-energy bounded or unit-peak bounded. First, based on the Lyapunov–Krasovskii functional approach and the delay-partitioning technique, delay-dependent conditions for estimating the reachable set of the considered system are derived. These conditions guarantee the existence of an ellipsoid that contains the system state under zero initial conditions. Second, the reachable set estimation is taken into account in the controller design. Here, the purpose is to determine an ellipsoid and find a state-feedback controller such that the determined ellipsoid contains the reachable set of the resulting closed-loop system. Sufficient conditions for the solvability of the control synthesis problem are obtained. Based on these results, the problem of how to design a controller such that the state of the resulting closed-loop system is contained in a prescribed ellipsoid is studied. Finally, numerical examples and simulation results are provided to show the effectiveness of the proposed analysis and design methods.

Stability analysis for a class of nonlinear discrete-time control systems subject to disturbances and to actuator saturation

This paper addresses the stability characterisation problem for a class of nonlinear discrete-time control systems subject to actuator saturation and energy bounded disturbance inputs. The considered class of systems covers all nonlinear discrete-time systems that can be modelled by rational difference equations. Based on quadratic and piecewise quadratic Lyapunov functions, conditions based on linear matrix inequalities are proposed to analyse the asymptotic stability (internal stability) and the ℓ2 input-to-state stability (external stability) of the closed-loop system. The proposed conditions are then incorporated into convex optimisation problems to either maximise an estimate of the region of attraction or a bound on the admissible ℓ2 disturbances, and also to obtain an estimate of the system ℓ2-gain for an admissible set of disturbances.

PD+ Based Output Feedback Attitude Control of Rigid Bodies

We address the problem of output feedback attitude control of a rigid body in quaternion coordinate space via a modified PD+ based tracking controller. Angular velocity is replaced by a low-gain dynamic extension. The controller ensures fast convergence to the desired operating point during transient maneuvers, while keeping the gains small. This contributes to diminishing the sensitivity to measurement noise hence, energy consumption may be expected to drop along with a decrease of the residual. More precisely, we show uniform practical asymptotic stability of the equilibrium point for the closed loop system in the presence of unknown, bounded input disturbances. Simulation results illustrate the performance improvement with respect to PD+ based output feedback control with static gains.

Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method. KeywordsAdaptive observer; linear matrix inequality, nonlinear systems; nonlinear observer; resilient observer; robust estimation.

Active FTC for Non-linear Aircraft based on Feedback Linearization and Robust Estimation

The current work concerns the development of a novel approach to robust fault estimation to achieve active Fault Tolerant Control (FTC) for a nonlinear aircraft system. The novelty lies in the combination of a feedback linearization controller, with a state/fault estimator. The active FTC system combines these to compensate for the faults acting in the control system. The paper focuses on the development of an active FTC scheme applied to a nonlinear unmanned airborne vehicle (UAV) system with different faults acting on three actuators and with wind turbulence affecting the vertical force. The aircraft dynamics are approximately linearized on-line using a dynamic inversion controller based on differential geometry theory. For the linearized system with bounded input disturbance, a robust state-space observer is designed to simultaneously estimate system states and actuator faults by solving a Lyapunov equation. The FTC scheme is achieved via a linear matrix inequality (LMI) approach, based on the estimated states/faults. The simulation results demonstrate the efficiency and robustness of the proposed design.

Robust Decentralized Formation Flight Control

Motivated by the idea of multiplexed model predictive control (MMPC), this paper introduces a new framework for unmanned aerial vehicles (UAVs) formation flight and coordination. Formulated using MMPC approach, the whole centralized formation flight system is considered as a linear periodic system with control inputs of each UAV subsystem as its periodic inputs. Divided into decentralized subsystems, the whole formation flight system is guaranteed stable if proper terminal cost and terminal constraints are added to each decentralized MPC formulation of the UAV subsystem. The decentralized robust MPC formulation for each UAV subsystem with bounded input disturbances and model uncertainties is also presented. Furthermore, an obstacle avoidance control scheme for any shape and size of obstacles, including the nonapriorily known ones, is integrated under the unified MPC framework. The results from simulations demonstrate that the proposed framework can successfully achieve robust collision-free formation flights.

Decentralized load frequency controller for a multi-area interconnected power system

This paper proposes a control scheme for the load frequency control (LFC) problem of multi-area power systems. These systems are treated as interconnected dynamical systems. In the design of the proposed controller, each local area network is overlapped with states representing the interconnections with the other local area networks in the global system. Then, a decentralized control scheme is developed as function of the local area state variables and those resulting from the overlapped states which represent an approximation of the interconnection variables. The proposed controller guarantees the asymptotic stability of the overall closed loop system. The simulation results indicate that the proposed control scheme works well. In addition, they show that the controlled system is robust to changes in the parameters of the power system and to bounded input disturbances acting on the system. Moreover, the simulation results show that the controlled system behaves well even when there is a maximum limit on the rate of change in power generation.

Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H∞ performance. The derived methods can be applied to the robust H∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).