Robust Stabilization Problem Research Articles

Robust Altitude Stabilization of VTOL-UAV for Payloads Delivery

In this paper, we investigate the problem of robust altitude stabilization for the vertical take-off and landing (VTOL) of an unmanned aerial vehicle in the presence of external disturbances (e.g. wind gusts), payload variations, and noisy measurements. The design of the controller is simple; it is based on the minimization of the one-step-ahead predicted position errors. The stability analysis of the closed loop in the presence of external disturbances is presented. The analysis results prove that the tracking errors of attitude, take-off, hovering, and landing are uniformly bounded. Since the proposed control algorithm will be employed for goods delivery by drones, the robustness of this algorithm against low-frequency disturbances and payload variations is a major objective. To this end, integral action is included in the altitude loop to eliminate the induced steady-state error and to drop off the payload in the desired position successfully. Furthermore, the controller is given in the closed form to facilitate its implementation onboard to increase the autonomy of the flight. The numerical simulations are provided to show the effectiveness of the proposed algorithm.

Robust stabilization of time-varying delay systems with predictor-observer based controller

Abstract This papers deals with the problem of robust stabilization of a class of discrete systems with time-varying input delay and model uncertainties, where the state is assumed not to be fully accessible. Thus, a predictor-observer based controller is proposed. Furthermore, a control synthesis algorithm based on the Cone Complementarity Linearization (CCL) approach is provided to design the controller and observer gains, with the objective of improving robust performance against uncertainties in the process model and the input delay. Finally, different illustrative simulations are introduced to show the main benefits of this strategy.

An Explicit Method for Stability Analysis of 2D Systems Described by Transfer Function

In this paper, we propose a method to test the stability of two-dimensional (2D) linear discrete systems described by transfer function. And a complete region of disturbance parameters is solved to ensure the considered system with perturbations stability. Different from any other traditional algebraic methods, the algorithm of this method is explicit, which a large number of higher-order polynomial iterative operation doesn’t need to be carried out. By the fractional linear transformations, new condition is given in Hurwitz theorem, which doesn’t involve fractional calculation. The method is non-conservative for stability analysis and solving stable parameter region of 2D systems. It simplifies some existing methods. The computational cost is reduced. And it is better to solve the stability problems for 2D systems with disturbances. Examples illustrate the efficiency for testing the stability of higher-order 2D system and solving the robust stability problem of uncertain 2D systems.

Robust Performance Analysis on Dynamic Control of Unmanned Aerial Vehicle System Using Bode Plot

The paper focuses on the robust performance analysis on dynamic control of unmanned aerial vehicle system with numerical computation. The objectives of this work are to find the appropriate solution for robust stability problems for dynamic control of unmanned aerial vehicle (UAV) system which is critical challenge in the space technology. The background of the theoretical work on digital control system is very important to study the problem of dynamic control system at present. The idea behind the control system stability analysis on digital technology is very important candidate in space technology. The specific purpose on analyzing the performance of dynamic of digital control system for space technology is solved in this paper. The mathematical model of target system is mentioned and analyzed based on the classical control method with digital technology. The related work for modeling of the control system is mentioned and expressed the detailed background for the analysis. The simulation results confirm that the proposed system met the robust performance for digital control of UAV system for reality. The analysis has been carried out based on feedback control system stability for dynamic system as well. The simulation results for stability analysis have been carried out by using MATLAB programming languages.

Robust delay-dependent stability of uncertain inertial neural networks with impulsive effects and distributed-delay

The robust stability problem of uncertain inertial neural networks with impulsive effects and distributed-delay is considered in the present paper. The average impulsive interval and differential inequality for delay differential equations are used to obtain the global exponential stability of the inertial neural networks. The robust distributed-delay-dependent stability criteria here are proposed in terms of both linear matrix inequalities and algebraic inequalities. Our results can not only be used to obtain the stability of the uncertain inertial neural network with impulsive disturbance, but also be utilized to design the impulsive control for the uncertain inertial neural networks. The novel criteria complement and extend the previous works on uncertain inertial neural network with/without impulsive effects. Typical numerical examples are used to test the validity of the developed stability criteria finally.

Robust Impulsive Stabilization of Uncertain Nonlinear Singular Systems with Application to Transportation Systems

We consider the robust asymptotical stabilization problem for uncertain singular systems. We design a new impulsive control technique to ensure that the controlled singular system is robustly asymptotically stable and hence derive the corresponding stability criteria. These sufficient conditions are expressed in the form of algebra matrix inequalities and can be implemented numerically. We finally provide a numerical example of a transportation system to illustrate the effectiveness and usefulness of the proposed criteria.

Dynamics of interval Cohen‐Grossberg neural networks with time‐varying delays based on LMI computation

SummaryThe problem of the global robust exponential stability of delayed interval Cohen‐Grossberg neural networks is considered. By constructing suitable Lyapunov functional and using the linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the existence, uniqueness and robust exponential stability of the equilibrium point. Based on LMI computation, numerical examples are employed to show that the new results are less restrictive and less conservative than some existing results in the literature.

Mean square consensus of uncertain discrete-time stochastic multi-agent systems with x-dependent noise

ABSTRACTIn this paper, the mean square consensus control problem is investigated for linear uncertain discrete-time multi-agent systems with x-dependent noise and time-varying delays. Under undirected connected topology, the robust consensus problem of multi-agent systems is converted into the robust stabilisation problem for the discrete-time stochastic systems. By utilising Lyapunov functional and the linear matrix inequality method, some new sufficient conditions are derived to guarantee the consensus of uncertain discrete-time stochastic multi-agent systems. Based on the state feedback controller protocol with time-varying delays, a new consensus criterion is established for the discrete-time stochastic multi-agent systems with parameter uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the proposed results.

Further results on robust stability for uncertain neutral systems with distributed delay

This paper studies the problem of robust stability for uncertain neutral systems with distributed delay. By utilizing the incorporation of a new integral inequality technique and a novel Lyapunov–Krasovskii functional, some reduced conservative delay-dependent stability conditions for asymptotic stability are established. Then some special cases of neutral systems are discussed. Based on these delay-dependent stability conditions, the condition for robustness is obtained for uncertain linear delayed systems. All these stability conditions are given in terms of linear matrix inequalities (LMIs), which can easily be computed by the LMI toolbox of Matlab. Finally, several examples are discussed in detail to display the usefulness and superiority of the obtained results.

Robust stability of Markov jump linear systems through randomized evaluations

The paper presents a method for checking the robust mean square stability of continuous-time Markov jump linear systems. The robustness arises in the analysis due to the assumption that the Markovian transition probability matrix is partially known. The corresponding infinite-dimensional robust stability problem, difficult to solve, is then converted into a probabilistic problem, amenable to the numerical viewpoint, taking advantage of the randomized (scenario) approach. The paper shows examples—including a real-time electronic-circuit application—for which the results from the literature fail to determine the robust stability but the randomized approach gives a positive answer.

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.

Robust exponential stability of switched delay interconnected systems under arbitrary switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and unbounded delay is addressed. On the assumption that the interconnected functions of the studied systems satisfy the Lipschitz condition, by resorting to vector Lyapunov approach and M-matrix theory, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems under arbitrary switching are obtained. The proposed method, which neither require the individual subsystems to share a Common Lyapunov Function (CLF), nor need to involve the values of individual Lyapunov functions at each switching time, provide a new way of thinking to study the stability of arbitrary switching. In addition, the proposed criteria are explicit, and it is convenient for practical applications. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the proposed theories.

An off‐policy iteration algorithm for robust stabilization of constrained‐input uncertain nonlinear systems

SummaryThis paper studies the robust stabilization problem of constrained‐input nonlinear systems with mismatched uncertainties. Initially, the robust stabilization problem is converted into a constrained H2 optimal control problem by providing a proper infinite‐horizon cost function for the auxiliary system. It is demonstrated that the solution of the constrained H2 optimal control problem can force the original system to be stable in the sense of uniform ultimate boundedness. Then, under the framework of reinforcement learning, an off‐policy iteration algorithm is proposed to solve the constrained H2 optimal control problem. The off‐policy iteration algorithm is implemented by using two kinds of approximators. That is, the critic approximator is applied to approximate the optimal cost function and the actor approximator is used to approximate the augmented optimal control. The method of weighted residuals together with the Monte‐Carlo integration technique is employed to determine the weight parameters of critic and actor approximators. Finally, two examples, including a pendulum system, are presented to validate the proposed control algorithm.

Robust finite-time stabilizers for five-degree-of-freedom active magnetic bearing system

In this paper, the robust finite-time stabilization problem for a fully suspended five-degree-of-freedom active magnetic bearing system is addressed in the presence of external disturbances and additive uncertainties. By developing the nonsingular terminal sliding mode control and defining new nonlinear sliding surfaces, three separate classes of stabilizers are proposed to regulate and place the suspended rotor in the desired positions of air gaps within adjustable finite times. The suggested nonlinear sliding surfaces and designed control inputs for each class of stabilizers are two major differences between these stabilizers. It is mathematically proven that five control voltages of this system, designed by each class of the suggested stabilizers, are able to locate the suspended rotor at the centers of air gaps in the adjustable finite time which is summation of two reaching and settling finite times. Moreover, several new inequalities are extracted for determining the reaching and settling finite times related to the three classes of stabilizers. These inequalities reveal the dependencies between optional parameters of the proposed stabilizers and the mentioned finite times. Finally, numerical simulations are provided to illustrate the efficiency and good performance of each class of the designed stabilizers.

Ellipsoidal Lyapunov-based hybrid model predictive control for mixed logical dynamical systems with a recursive feasibility guarantee

This paper proposes an ellipsoidal hybrid model predictive control approach to solve the robust stability problem of uncertain hybrid dynamical systems modelled by the mixed logical dynamical framework. In this approach, the traditional terminal equality constraint is replaced by an ellipsoid that results in a maximal positive invariant set for the closed-loop system. Then, a Lyapunov decreasing condition along with the robustness criterion is introduced to the optimization problem to achieve the robust stability of the closed-loop system. As the main advantages, the ellipsoidal terminal set proposed in this paper attains a larger domain of attraction along with the recursive feasibility guarantee. Moreover, the stability and robustness constraints are achieved by a lower prediction horizon, which leads to a smaller dimension optimization problem. In addition, to reduce the computational complexity of the corresponding optimization problem, a suboptimal version of the proposed algorithm is introduced. Finally, numerical and car suspension system examples show the capabilities of the proposed method.

Delay-dependent robust stability criteria for singular time-delay systems by delay-partitioning approach

ABSTRACTIn this paper, the problem of delay-dependent robust stability for singular time-delay systems is investigated. The parametric uncertainties are assumed to be norm bounded. Based on the idea of delay partitioning, A new Lyapunov–Krasovskii functional is proposed to develop new delay-dependent criteria, that ensures the considered system to be regular, impulse free and stable in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, some numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous works.

Adaptive NN Dynamic Surface Controller Design for Nonlinear Pure-Feedback Switched Systems With Time-Delays and Quantized Input

This paper deals with the problem of robust stabilization for a class of uncertain nonlinear pure-feedback switched time-delay systems with quantized input signal. In order to overcome the design difficulty caused by the quantization and unpredictable switchings, a nonlinear decomposition strategy for quantizer is employed in advance. In the controller design procedure, the unknown time-delay terms are compensated by utilizing Lyapunov–Krasovskii functionals, the desired virtual stabilizing functions and desired actual control input are approximated by applying radial basis function neural networks, and dynamic surface control technology are used to handle the issue of “explosion of complexity” in the traditional backstepping procedure. Furthermore, it is shown that the resulting closed-loop system are stable in the sense of semi-global uniformly ultimately bounded. Finally, to verify the effectiveness and applicability of the presented control scheme, an example is given to construct an adaptive neural controller for an electromechanical system.

Adaptive Parallel Simultaneous Stabilization of a Class of Nonlinear Descriptor Systems via Dissipative Matrix Method

This paper investigates the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method. Firstly, under an output feedback law, two nonlinear descriptor systems are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two resulting closed-loop systems. Then, the two systems are combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique. Based on the dissipative system, an adaptive parallel simultaneous stabilization controller and a robust adaptive parallel simultaneous stabilization controller are designed for the two systems. Furthermore, the case of more than two nonlinear descriptor systems is investigated. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the adaptive parallel simultaneous stabilization controllers obtained in this paper work very well.

New Relaxed Stability Conditions for Uncertain Two-Dimensional Discrete Systems

This paper is concerned with the problem of robust stability of uncertain two-dimensional (2-D) discrete systems described by the Roesser model with polytopic uncertain parameters. Based on a newly developed parameter-dependent Lyapunov–Krasovski functional combined with Finsler’s lemma, new sufficient conditions for robust stability analysis are derived in terms of linear matrix inequalities (LMIs). Numerical examples are given to show the effectiveness and less conservatism of the proposed results.

Robust set stabilization of Boolean control networks with impulsive effects

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.