Robust Stabilization Problem Research Articles

Global robust output regulation of a class of MIMO nonlinear systems by nonlinear internal model control

AbstractRecently, the global robust output regulation problem for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems which may not have well‐defined relative degree and are subject to a nonlinear exosystem has been studied based on a constructive nonlinear internal model. However, the proposed nonlinear internal model‐based control law is applicable to the case where the exogenous signals are reference input and/or measurable disturbance rather than unmeasurable disturbance. For this reason, this paper further studies the same control problem based on a general nonlinear internal model independent of the exogenous signal. It is shown that this control problem can be converted into a global robust stabilization problem of a more complicated MIMO nonlinear system with various uncertainties and well solved by a recursive state feedback controller design. Thus our approach applies to a broader class of output regulation problem of MIMO nonlinear systems.

Robust stability and stabilization of multi‐order fractional‐order systems with interval uncertainties: An LMI approach

AbstractThis paper concentrates on the robust stability and stabilization problems of multi‐order fractional‐order systems (MOFOSs) with interval uncertainties. Firstly, the new sufficient conditions for the stability of the nominal systems are given, which are suitable for robust analysis and controller design. Then, based on the above stability conditions, the robust stability conditions for the uncertain systems are proposed. Secondly, in order to stabilize the nominal systems and uncertain systems, the state feedback controllers are designed. All the results are in the form of linear matrix inequalities and can be applied in incommensurate cases. Finally, some numerical examples are provided to verify the effectiveness of our results.

Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept

This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials.

Nonfragile H ∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

Controlling synchronization in a complex network of nonlinear oscillators via feedback linearisation and H∞-control

Abstract This short communication proposes a strategy to induce complete synchronization in a complex network composed of a general class of nonlinear dynamical oscillators. To that end, we formulate complete synchronization as a robust stabilisation problem, and propose a multiple-input multiple-output feedback decoupling linearisation algorithm in combination with H ∞ -control, designed to achieve a stable synchronization even in the presence of model uncertainty. We illustrate the strategy via a case study, where a complex network composed of FitzHugh–Nagumo oscillators is considered.

A systematic approach towards robust stability analysis of integral delay systems with general interval kernels

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of the characteristic equation and the argument principle, an algorithm is generated, which is shown to outperform the Lyapunov-Krasovskii (LK) approaches with respect to conservatism in the presented examples. Despite the conventional manual use of the Nyquist criterion, the proposed algorithm is fully algebraic, cheaper and easily implemented in computer programs. The kernel matrix function in this method is not limited to the exponential type and can include any bounded real function as its elements.

Observer-based adaptive robust stabilization of dynamic positioning ship with delay via Hamiltonian method

In this paper, by applying the Hamiltonian function method, we study the observer-based adaptive robust stabilization problem for dynamic positioning (DP) ship with time delay, and present several new results on the issue. Firstly, the three degree of freedoms DP ship model with time delay is transformed into a Port-Controlled Hamiltonian (PCH) one, based on which we design its observer system. Then, by using the augmented technology and the Lyapunov stability theory, several observer-based robust stabilization controllers and observer-based adaptive robust stabilization controllers are designed for the DP ship with time delay, and some delay-independent and delay-dependent robust stabilization results are obtained. Finally, the simulation results show the effectiveness of the observer-based robust stabilization controller proposed in this paper.

LMI-Based Robust Stability Analysis of Discrete-Time Fractional-Order Systems With Interval Uncertainties

Robust stability problem of discrete-time fractional-order systems (DTFOSs) with interval uncertainties is investigated in this paper. Firstly, a new theorem for matrix root-clustering in union-region is established. Based on this theorem, the stability regions of DTFOSs are described as the union-region of closed sub-regions, and sufficient conditions for stability of DTFOSs are presented. Then, new sufficient conditions for robust stability of DTFOSs with interval uncertainties are derived. All the results are obtained in terms of linear matrix inequalities (LMIs) which are more tractable than the existing ones. Finally, numerical examples are given to show that our results are valid and less conservative than the existing ones.

Robust Control for Discrete-Time T-S Fuzzy Singular Systems

This paper deals with the robust admissibility and state feedback stabilization problems for discrete-time T-S fuzzy singular systems with norm-bounded uncertainties. By introducing a new approximation technique, the initial membership functions are conveniently expressed in piecewiselinear functions with the consideration of the approximation errors. By utilizing the piecewise-linear membership functions, the fuzzy weighting-based Lyapunov function and the use of auxiliary matrices, the admissibility of the systems is determined by examining the conditions at some sample points. The conditions can be reduced into the normal parallel distributed compensation ones by choosing special values of some slack matrices. Furthermore, the authors design the robust state feedback controller to guarantee the closed-loop system to be admissible. Two examples are provided to illustrate the advantage and effectiveness of the proposed method.

Adaptive Robust Control for a Class of Uncertain Neutral Systems with Time Delays and Nonlinear Uncertainties

The problems of robust stabilization and adaptive robust controller design are considered for a class of uncertain neutral systems with time delays and nonlinear uncertainties. In this paper, Pade approximation is used to deal with input-delays, and the adaptation laws are proposed to estimate the norm of the unknown parameter uncertainties. Based on the improved Razumikhin-type theorem and the updated values, a class of delay-independent adaptive robust state feedback controllers is constructed to guarantee the uniform ultimate boundedness of uncertain neutral systems with input-delays and nonlinear uncertainties. Finally, the chemical two-stage dissolution tank is used to illustrate the effectiveness of the proposed method.

Control of Teleoperation Systems in the Presence of Varying Transmission Delay, Non-passive Interaction Forces, and Model Uncertainty

SUMMARYThis paper addresses robust stability and position tracking problems in teleoperation systems subject to varying delay in the communication medium, uncertainties in the models of manipulators, and non-passive interaction forces in the terminations. Fixed-structure nonlinear control law is developed based on the notion of Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) scheme. Then, utilizing the Lyapunov–Krasovskii theorem, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) to tune the controller parameters. Differently from literature, the objectives are achieved without requirement for any passive parts in the model of interaction forces. Comparative simulations and experimental results demonstrate the applicability and superiority of the proposed method.

Robust ℋ∞ and ℒ∞–ℒ∞ sampled-data dynamic output-feedback control for nonlinear system in T–S form including singular perturbation

ABSTRACT This paper pays attention to the robust sampled-data dynamic output-feedback stabilisation problems for a singularly perturbed nonlinear system in Takagi–Sugeno (T–S) form when the system suffers from parametric uncertainties and or disturbances. Two design conditions are proposed in terms of linear matrix inequalities such that the admissible controllers guarantee the prescribed and – disturbance-attenuation levels, respectively. The features of the development are that (i) the sampled-data syntheses are performed in a continuous-time domain and (ii) (even approximate) discrete-time modelling of the T–S fuzzy system is not involved.

Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol.

This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.

Robust stability of the global attractor of the reaction-diffusion system

In this paper we consider the problem of robust stability for a nonlinear system of equations in partial derivatives of the reaction-diffusion type. An undisturbed system is considered to have a global attractor. The main task is to estimate the deviation of the trajectory of the perturbed system from the global attractor of the perturbed system depending on the magnitude of the perturbations. Such an estimate can be obtained in the framework of the theory of input-to-state stability (ISS). The paper does not impose any conditions on the derivative of the nonlinear interaction function, so the unity of the solution of the initial problem is not ensured. The paper proposes a new approach to obtaining estimates of robust stability of the attractor in the case of a multivalued evolutionary decoupling operator. In particular, it is proved that the multivalued decoupling operator generated by weak solutions of a nonlinear reaction-diffusion system has the property of asymptotic gain (AG) with respect to the attractor of the undisturbed system.

Robust Stabilization for Uncertain Nonlinear Systems Subject to Feedforward Growth Constraint

This paper investigates the robust stabilization problem of a class of uncertain nonlinear systems with input matching uncertainty under linear feedforward growth conditions. Smooth robust controllers are obtained by state feedback and output feedback, respectively. In order to deal with input matching uncertainty, extra dynamics are designed inspired by the integral control and disturbance estimation. The proposed controllers guarantee that the states of controlled systems asymptotically converge to zero and all closed-loop signals are globally bounded. Finally, simulation examples are given to illustrate the usefulness of the state-feedback and output-feedback controllers proposed.

이산시간 불확실 특이시스템의 새로운 강인 유한시간 상태궤환 제어

In this paper, we consider the problem of robust finite-time singular stability(RFSS) and state feedback controller design method for discrete–time linear singular systems with norm-bounded parameter uncertainties. First, the FSS sufficient condition is derived by equivalently transformed closed-loop system. Second, a state feedback controller design method satisfying regular, causal, and RFSS is proposed by LMI(linear matrix inequality) technique on the basis of the obtained FSS condition and equivalent properties of the considering system. The presented conditions are strict LMI conditions in terms of finding all variables compared with previous results. Finally, a numerical example is given to illustrate the validity of the proposed method.

Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays

This paper investigates the delay-dependent robust stability problem of fuzzy stochastic Hopfield neural networks with random timevarying delays. Moreover, in this paper, the stochastic delay is assumed to satisfy a certain probability distribution. By introducing a stochastic variable with Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. Based on a LyapunovKrasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent stability criteria have been derived in terms of linear matrix inequalities (LMIs), which can be checked easily by the LMI control toolbox. Finally two numerical examples are given to illustrate the effectiveness of the theoretical results.

Event-triggered distributed self-learning robust tracking control for uncertain nonlinear interconnected systems

In this paper, a novel event-triggered self-learning robust tracking control scheme for a class of nonlinear interconnected systems with uncertain interconnections is developed based on adaptive dynamic programming (ADP). Initially, the robust tracking control problem of interconnected systems is transformed to the robust stabilization one of augmented interconnected systems. To address the uncertain interconnections as well as optimize the sample intervals, a group of auxiliary subsystems, each with a novel discounted cost function, are introduced, which enables the robust stabilization problem to be further converted to a group of two-player zero-sum differential games. Next, an event-triggered ADP algorithm is proposed to obtain the saddle point solutions, based on which the distributed event-triggered robust tracking control policies for the overall system are established. Specifically, the proposed event-triggered mechanism is asynchronous and distributed where the sample intervals are optimized to further reduce the computational burden and save the communication resources. Moreover, the tracking errors and the approximation errors of critic network weights are demonstrated to be uniformly ultimately bounded by using the Lyapunov approach. Finally, two simulation examples are provided to verify the effectiveness of the proposed method.

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

A Novel Connectivity-Preserving Control Design for Rendezvous Problem of Networked Uncertain Nonlinear Systems.

This article proposes a novel and robust connectivity-preserving rendezvous control design for a group of uncertain nonlinear multiagent systems with communication constraint where each agent has a limited sensing range. The control design can work under the assumption that the communication network is initially connected and is characterized by two distinguishing features. First, a new potential function is provided not only to maintain the existing and newly added links by the hysteresis rule but also to overcome the difficulty imposed by the nonlinear terms from system dynamics. Second, by constructing a series of lemmas, a connectivity-preserving stabilizing control law is presented to solve the robust stabilization problem with connectivity preservation for a time-varying nonlinear system, which is a special case of the augmented system with both dynamic and static uncertainties obtained via internal model design. After further incorporating the adaptive control technique, regardless of uncertain parameters and external disturbances in the multiple nonlinear subsystems, the leader-following rendezvous with connectivity preservation problem is finally solved by a distributed connectivity-preserving controller with parameter update law.