Time-varying Parameter Uncertainties Research Articles

Output-feedback-guaranteed cost control of fractional-order uncertain linear delayed systems

The control of fractional-order (FO) delayed systems is important in real-world applications, but it is still a challenging task. This paper studies the output-feedback-guaranteed cost control of a class of FO uncertain linear systems with time delay. Norm-bounded and time-varying parameter uncertainties are considered. A new definition of guaranteed cost control of FO system is proposed. Additionally, static and dynamic output-feedback delay-independent guaranteed cost controllers are designed. Two numerical examples are presented showing the effectiveness of the proposed schemes.

Robust stability analysis of stochastic switched neural networks with parameter uncertainties via state-dependent switching law

The problem of robust stability analysis for a class of stochastic switched neural networks (SSNNs) with time-varying parametric uncertainties is investigated in this paper. Some sufficient conditions are derived to guarantee the robust global asymptotical stability in mean square for the uncertain SSNNs by using state-dependent switching (SDS) method. It is shown that the robust stability of uncertain SSNNs composed of all unstable subnetworks can be achieved by using the designed SDS law. Moreover, the proposed sufficient conditions can be easily checked in terms of linear matrix inequalities (LMIs) for conveniently using Matlab toolbox. A numerical example is provided to demonstrate the effectiveness of the proposed SDS law.

Approximate feedback linearization based optimal robust control for an inverted pendulum system with time-varying uncertainties

In the present study, to attain an approximate feedback linearization based optimal robust control of an under-actuated cart-type inverted pendulum system with two-degree-of-freedom (2DOF) having time-varying uncertainties is desirable. To reach such a goal, at first, the governing dynamical equations of the cart-type inverted pendulum are presented. Then, using an approximate feedback linearization method, the dynamics of the nonlinear system are changed to those of the linear one. In order to simultaneously stabilize the both degrees of freedom, a robust sliding mode controller is designed for this under-actuated system. Finally, the control law is improved with aid of a novel adaptive approach based on an approximating function found via a multiple-crossover genetic algorithm so that the system always will be optimally robust against time-varying parametric uncertainties. The results are displayed to show how the proposed controller improves the settling time and overshoot of the system outputs. In addition, such an improvement in the values of the selected objective functions is clearly evident.

Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

Adaptive Self-Regulation PID Control of Course-Keeping for Ships

Abstract To solve the nonlinear control problems of the unknown time-varying environmental disturbances and parametric uncertainties for ship course-keeping control, this paper presents an adaptive self-regulation PID (APID) scheme which can ensure the boundedness of all signals in the ship course-keeping control system by using the Lyapunov direct method. Compared with the traditional PID control scheme, the APID control scheme not only is independent of the model parameters and the unknown input, but also can regulate the gain of PID adaptively and resist time-varying disturbances well. Simulation results illustrate the effectiveness and the robustness of the proposed control scheme.

Robust H∞ controller design for uncertain 2D continuous systems with interval time-varying delays

ABSTRACTThe design of delay-dependent robust controllers is solved here for a class of uncertain 2D continuous systems: those with interval time-varying delays and norm-bounded parameter uncertainties. By constructing a novel augmented Lyapunov–Krasovskii functional and then using the Wirtinger inequality, a new delay-dependent stability condition is developed, that uses the known lower and upper bounds of the time-varying delays to develop less conservative solutions that previous results in the literature. This condition is then applied to performance analysis and robust controller design, using linear matrix inequalities (LMIs). Two numerical examples are presented that illustrate the effectiveness of the proposed method.

Improving Tracking Performance of Nonlinear Uncertain Bilateral Teleoperation Systems With Time-Varying Delays and Disturbances

In this article, an adaptive nonsingular terminal sliding-mode (ANTSM) method is proposed for the motion tracking control of a bilateral teleoperation system. Efforts in this article seek to improve the position tracking performance of nonlinear systems subject to time-varying network delays, parametric uncertainties, and unknown external disturbances and frictions. Another issue addressed in this article is the common delay-induced phase shift of tracking profiles in many control methods, which is greatly reduced by introducing a novel mixed type of feedback signals in the ANTSM control design. Furthermore, the proposed adaptive control design with two online-estimated compensatory bounds removes the requirement of exact knowledge of network delays and disturbance bounds as a prior. In the master side, a force predictor is used to estimate the current environmental force for the reference signal generator. Therefore, the direct transmission of force signals is avoided. By comparing with the existing model-based and model-free methods, numerical simulation results with six-degree-of-freedom manipulators illustrate the merits of the developed robust and adaptive controllers. Experimental results with two Phantom Omni devices are also provided to demonstrate the effectiveness and the significant performance improvements of the proposed controllers.

A New Robust Control Strategy for a Wind Energy Conversion System Based on a T-S Fuzzy Model

This paper discusses the design of a robust fuzzy Maximum Power Point Tracking (MPPT) control for a variable speed Wind Energy Conversion System (WECS) powered by a Permanent Magnet Synchronous Generator (PMSG). In fact, The main objective of this research work is to ameliorate the energy conversion efficiency of the WECS in spite the existence of a time-varying wind and model parameter uncertainties, by appropriately regulating the duty cycle of a boost converter used to control the studied device.  For this purpose, the Takagi–Sugeno (T-S) fuzzy model with parametric uncertainties is exploited for a fuzzy representation of the nonlinear WECS. Next, a T-S reference model relying on the MPPT algorithm is proposed to rapidly calculate the reference signals. Then, a fuzzy controller is developed to compute the duty cycle needed to ensure a robust tracking and a fast convergence to the maximum power for different wind speed changes. Afterward, the stability analysis of the closed-loop control system is proven by the Lyapunov theory and the H∞ performance. Besides, the controller gains are well determined by solving a Linear Matrix Inequality (LMI) problem. Finally, the robustness and the effectiveness of the suggested fuzzy control scheme are confirmed through both simulation results and experimental tests.

An Event-Triggered Approach to Robust Fault Detection for Nonlinear Uncertain Markovian Jump Systems with Time-Varying Delays

In this paper, the problem of robust fault detection is investigated for nonlinear uncertain Markovian jump systems subject to time-varying delays, Lipschitz nonlinearities and parameter uncertainties under the event-triggered protocol. The event-triggered mechanism is introduced to adjust the transmission frequency of the data sent to the remote module. An event-based fault detection method is presented to guarantee the sensitivity of residual to fault and the attenuation of the effect from the disturbance on the residual. In this way, the considered fault detection problem is solvable by testifying the feasibility of $$H_\infty $$ filtering problem. By constructing the mode-dependent Lyapunov functional, new sufficient criteria are derived in terms of the linear matrix inequality technique, which insures the stochastic stability with prescribed performance for addressed MJSs. In the end, a numerical example is exploited and the validity of newly presented event-based fault detection method is shown.

Modified adaptive second order sliding mode control: Perturbed system response robustness

Sensitivity to parameters, which is negative for any system; for an aircraft is destructive. In this respect, an Adaptive Second-order Sliding Mode Control (AS-SMC) is proposed to manage the unknown time-varying aircraft parameter uncertainty and un-modeled coupling perturbations. The employed adaptivity relaxes the required knowledge of the perturbation bound, the suggested sliding surface improves the system stability and bypassing the SMC reaching phase enhances the performance robustness. The effectiveness of the scheme in providing low tolerance responses with respect to the basic controller is illustrated through extensive simulations. The response is more appreciated when the system operates in a high angle of attack/sideslip conditions.

Decentralized Fuzzy $H_\infty$-Iterative Learning LFC With Time-Varying Communication Delays and Parametric Uncertainties

Load frequency control (LFC) continues to be a major problem in multi-area power systems, which is compounded by communication network issues and parametric uncertainties, that degrade controller performance. In this contribution, a fuzzy $H_\infty$ -iterative learning controller (FILC) is designed for decentralized LFC with little knowledge of the local power area's model and no knowledge of the external power areas’ models. Further to this, time-varying communication delays, parametric variations, large disturbances, and non-identical power system area parameters are considered. The FILC strategy comprises a fuzzy strategy that quickly rejects large disturbances and drives the error to a designed tolerable band where an iterative learning control technique that is proven to be asymptotically stable with a prescribed $H_\infty$ performance achieves zero-error convergence. The proposed FILC is compared with that of the well-known PI algorithm for a three-area power system. Results indicate that the FILC performs significantly better than the PI controller under practical combinations of network problems, overlapping large disturbances in multiple areas and parameter variations.

Non-fragile memory filtering of T-S fuzzy delayed neural networks based on switched fuzzy sampled-data control

This paper deals with the non-fragile memory filtering issue of T-S fuzzy delayed neural networks with randomly occurring time-varying parameters uncertainties and variable sampling rates. Compared with existing sampled-data control schemes, an improved switched fuzzy memory sampled-data control protocol is designed for the first time, which involves not only a signal transmission delay but also switched topologies. By developing some new terms and taking full advantage of the variable characteristics related to the actual sampling pattern, a modified loose-looped fuzzy membership functions (FMFs) dependent Lyapunov-Krasovskii functional (LKF) is constructed based on the information of the time derivative of FMFs. Meanwhile, some relaxed matrices chosen in LKF are not consequentially positive definite. Moreover, with the LKF methodology and employing the developed estimation technique, several optimized control algorithms with both a larger sampling period and upper bound of time-varying delays for achieving the stabilization of the resultant T-S fuzzy delayed neural networks are derived. Finally, a numerical example is presented to demonstrate the superiority and applicability of the theoretical results.

Robust Interval Type-2 Fuzzy Observer for Fault Detection of Networked Control Systems Subject to Immeasurable Premise Variables

In this paper, a novel observer design has been suggested for fault detection of networked control systems under random measurement delays. A randomly varying communication delay structure has been assumed in data transmission between the physical system and the observer. In order to increase the applicability of the proposed Takagi-Sugeno fuzzy observer, it has been contemplated to be under immeasurable premise variables. In addition, time-varying parameter uncertainties are added to the system, which contribute to the system uncertainties. Theoretical materials related to the system and the observer design with a predetermined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> index are provided resulting in less conservative constraints in the proof of asymptotical mean-square stability of the closed-loop system. Simulation results, which have been applied to a real-world system of tunnel diode circuit, have shown how the proposed observer would benefit from the use of interval type-2 fuzzy sets in dealing with uncertainties of the system.

Data-Driven Guaranteed Cost Control Design via Reinforcement Learning for Linear Systems With Parameter Uncertainties

Controllers learned from data are more practical and promising than the existing model-based ones and their capability can be enhanced if a priori information about the controlled plant is available. Under this viewpoint, a data-driven guaranteed cost control (GCC) design is investigated for linear systems with time-varying parameter uncertainties. Initially, the GCC design is shown to be equivalent to an $H_{\infty }$ state feedback control problem subject to a specific disturbance attenuation performance requirement. Then such an $H_{\infty }$ control problem is regarded as a zero-sum game and reduces to seek the stabilizing solution of a parameterized algebraic Riccati equation (ARE). Furthermore, to solve the ARE approximately, a modified simultaneous policy update algorithm (SPUA) and the corresponding data-driven variant based on off-policy reinforcement learning (RL) and experience replay technique is proposed. Finally, a numerical simulation for aircrafts with harsh uncertainties is illustrated to validate the merits of the proposed methods.

Adaptive iterative learning control for MIMO nonlinear systems performing iteration-varying tasks

The present work aims to develop a novel adaptive iterative learning control(AILC) method for nonlinear multiple input multiple output (MIMO) systems that execute various control missions with iteration-varying magnitude-time scales. In order to reduce the variations of the systems, this work proposes a series of time scaling transformations to normalize the iteration-varying trial lengths. An AILC scheme is then developed for the transformed control systems on a uniform trial length, which is shown to be capable of ensuring the asymptotic convergence of the tracking error. In other words, the proposed AILC algorithm is able to relax the constraint in conventional ILC where the control task must remain the same in the iteration domain. Additionally, the basic assumption in classic ILC that the control system must repeat on a fixed finite period is also removed. The convergence analysis of the AILC is derived rigorously according to the composite energy function (CEF) methodology. It is shown that the newly developed learning control strategy works well for control plants with either time-invariant or time-varying parametric uncertainties. To show the effectiveness of the AILC, three examples are illustrated in the end. Meanwhile, the proposed learning method is also implemented to a traditional X–Y table system.

Robust dissipativity and dissipation of a class of fractional‐order uncertain linear systems

This study addresses robust QSR-dissipativity and feedback dissipation of a class of fractional-order (FO) uncertain linear systems. Both the state and controlled output matrices are with time-varying norm-bounded parameter uncertainties. Firstly, some new notions of QSR-dissipativity and passivity for FO systems are introduced, the relationship between QSR-dissipativity and asymptotic stability and input-output stability are discussed, respectively. Then, a sufficient condition in the form of linear matrix inequality (LMI) is proposed to ensure that such system is robustly QSR-dissipative. According to this condition, a state feedback controller is proposed when the full states can be measured. Secondly, by employing LMI techniques and matrices singular value decomposition, sufficient conditions for the existence and a robust dissipation synthesis method are derived, respectively. Thirdly, a design method of dynamic output feedback controller is developed in order to guarantee that the closed-loop system is dissipative. Finally, some numerical examples are provided to show the application of the proposed methods.

Dissipativity analysis of stochastic fuzzy neural networks with randomly occurring uncertainties using delay dividing approach

This paper focuses on the problem of delay-dependent robust dissipativity analysis for a class of stochastic fuzzy neural networks with time-varying delay. The randomly occurring uncertainties under consideration are assumed to follow certain mutually uncorrelated Bernoulli-distributed white noise sequences. Based on the Itô's differential formula, Lyapunov stability theory, and linear matrix inequalities techniques, several novel sufficient conditions are derived using delay partitioning approach to ensure the dissipativity of neural networks with or without time-varying parametric uncertainties. It is shown, by comparing with existing approaches, that the delay-partitioning projection approach can largely reduce the conservatism of the stability results. Numerical examples are constructed to show the effectiveness of the theoretical results.

Optimal Portfolios under Time-Varying Investment Opportunities, Parameter Uncertainty, and Ambiguity Aversion

We study the implications of predictability on the optimal asset allocation of ambiguity-averse long-term investors and analyze the term structure of the multivariate risk–return trade-off considering parameter uncertainty. We calibrate the model to real returns of U.S. stocks, long-term bonds, cash, real estate, and gold using the term spread and the dividend–price ratio as additional predictive variables, and we show that over long horizons, the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. The ambiguity-averse long-term investor optimally tilts his or her portfolio toward a seemingly inefficient portfolio, which shows maximum robustness against estimation errors.

Distributed Robust PID Control For Leader Tracking in Uncertain Connected Ground Vehicles With V2V Communication Delay

The paper addresses the leader tracking problem for a platoon of connected autonomous vehicles in the presence of both homogeneous time-varying parameter uncertainties and vehicle-to-vehicle time-varying communication delay. To this aim, leveraging the multiagent systems (MAS) framework, a novel distributed robust proportional-integral-derivative control is proposed. The stability of the cohesive formation is analytically proved with a Lyapunov–Krasovskii approach by exploiting the descriptor transformation for time-delayed systems of neutral type. The delay-dependent robust stability conditions are expressed as a set of linear matrix inequalities allowing the proper tuning of the proportional, integral, and derivative actions implemented on each of the vehicles within the fleet. Extensive simulation analysis in different driving scenarios confirms the effectiveness of the theoretical derivation.

Robust $$H_\infty $$ H ∞ Filtering of Stochastic Switched Complex Dynamical Networks with Parameter Uncertainties, Disturbances, and Time-Varying Delays

This paper investigates the problem of stability analysis for switched complex dynamical networks with mixed time-varying delays and parameter uncertainties. The switched complex dynamical networks are composed of m modes that are switched from one to another based on time, state, etc. Although, the active subsystem is known in any instance, but the switching law such as transition probabilities are not known. The model for each mode is considered affine with matched and unmatched perturbations. The main purpose of the addressed problem is to design a filter error for the switched complex dynamical networks such that the dynamics of the error converges to the asymptotically irrespective of the admissible parameter variations with the gains. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented to ensure the $$H_\infty $$ performance of the complex dynamical system models. Finally, a numerical example is presented to illustrate the effectiveness of the proposed design method.