Linear Parameter-varying Systems Research Articles

Direct data-driven LPV control of nonlinear systems: An experimental result

We demonstrate that direct data-driven control of nonlinear systems can be successfully accomplished via a behavioral approach that builds on a Linear Parameter-Varying (LPV) system concept. An LPV data-driven representation is used as a surrogate LPV form of the data-driven representation of the original nonlinear system. The LPV data-driven control design that builds on this representation form uses only measurement data from the nonlinear system and a priori information on a scheduling map that can lead to an LPV embedding of the nonlinear system behavior. Efficiency of the proposed approach is demonstrated experimentally on a nonlinear unbalanced disc system showing for the first time in the literature that behavioral data-driven methods are capable to stabilize arbitrary forced equilibria of a real-world nonlinear system by the use of only 7 data points.

Zonotopic Set-Membership State Estimation for Switched LPV Systems

This paper addresses the state estimation problem for switched discrete-time Linear Parameter Varying (LPV) systems with mensurable and unmeasurable scheduling parameters. A zonotopic switched polytopic state estimator, considering parameter uncertainty, is proposed based on a Set-Membership Approach (SMA). Taking Average Dwell Time (ADT) into account, a new criterion is proposed to guarantee the convergence of the estimation. An application to vehicle lateral dynamics state estimation is used as case study. Simulation results reveal the effectiveness of the proposed algorithm and demonstrate advantages over the existing methods.

Gain-Scheduled Control of LPV Systems with Structural Constraints

In large-scale dynamic systems, consisting of the interconnection of several subsystems, the control law must obey a certain distributed structure defined by the information exchange pattern on a communication network. In case the system exhibits parameters which vary over time, the Linear Parameter Varying (LPV) paradigm provides a control-oriented framework for the design of robust or gain-scheduled control laws. Since each subsystem has only access to a partial knowledge of the overall set of parameters, due to the constraint imposed by the communication network, the controller gain must satisfy some structural constraints which increase the complexity of the design problem. This paper proposes a novel approach based on Linear Matrix Inequalities (LMIs) to deal with the distributed control of large-scale systems described by a LPV dynamics. LMI conditions are established for the design of a gain-scheduled controller ensuring exponential stability of the overall system with a prescribed decay rate, while satisfying the structural constraints imposed by the communication network. A simulation case study is presented to show the effectiveness of the proposed approach.

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

Distributed set-membership state estimation based on a zonotope method for linear parameter-varying systems

LMI-based Data-Driven Robust Model Predictive Control

Predictive control, which is widely used currently, bases on a model of the system to compute the applied input optimizing the future system behavior. If the nominal models are not given or are uncertain, data-driven model predictive control approaches can be employed, where control input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints for linear parameter-varying systems and Lur'e-type nonlinear systems. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.

A Kernel-Based Identification Approach to LPV Feedforward: With Application to Motion Systems

The increasing demands for motion control result in a situation where Linear Parameter-Varying (LPV) dynamics have to be taken into account. Inverse-model feedforward control for LPV motion systems is challenging, since the inverse of an LPV system is often dynamically dependent on the scheduling sequence. The aim of this paper is to develop an identification approach that directly identifies dynamically scheduled feedforward controllers for LPV motion systems from data. In this paper, the feedforward controller is parameterized in basis functions, similar to, e.g., mass-acceleration feedforward, and is identified by a kernel-based approach such that the parameter dependency for LPV motion systems is addressed. The resulting feedforward includes dynamic dependence and is learned accurately. The developed framework is validated on an example.

Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks

This work studies the finite-time control problem for discrete-time nonlinear Markov switching linear parameter varying (LPV) systems with denial-of-service (DoS) attacks. The aperiodic DoS attacks are introduced into the systems with partially unknown transition probabilities. First, considering the characteristics of aperiodic DoS attacks, an appropriate feedback controller is designed according to that whether it is attacked or not. Furthermore, the finite-time stability criteria of closed-loop system are derived by means of iterative technique and multiple Lyapunov functions. Finally, a turbofan engine model is taken as an example to verify the effectiveness and feasibility of the proposed finite-time control method.

DMVT-based observer design for general affine class of fractional-order nonlinear MIMO systems

In this article, a new observer design technique is proposed for the general affine class of fractional-order nonlinear multi-input/multi-output (MIMO) systems. This study is presented based on the differential mean value theorem. One significant characteristic of the suggested approach is that the nonlinear dynamic of observer error is converted into a linear parameter-varying system. Stability and convergence of observation error are shown using the Lyapunov direct method leading to feasibility and existence of a solution for some linear matrix inequalities. The performance and efficacy of the proposed method are evaluated through some illustrated simulations.

Formula omitted] gain-scheduled state-feedback design with experimental validation in a control moment gyroscope represented as a polynomial LPV model

The main contribution of this paper is a new H2 gain-scheduled state-feedback synthesis condition for continuous-time linear parameter-varying (LPV) systems where the parameters have bounded rates of variation. The matrices of the model as well as the control gain can have arbitrary polynomial dependence on the time-varying parameters. The synthesis conditions are formulated in terms of LMI relaxations combined with a search in a bounded scalar parameter, which can be used to obtain controllers with improved performance. As an experimental validation of the results, gain-scheduled controllers are designed and applied to a control moment gyroscope modeled as an LPV system with polynomial dependence on the time-varying parameters. Comparisons with a time-invariant controller, designed with the same performance criterion, are presented to illustrate the advantages of the proposed approach.

Robust observer design for LPV systems using Kronecker sum and direct searching

This paper addresses a robust Luenberger observer for an uncertain linear parameter varying (LPV) system based on the concepts of direct searching, Kronecker sum, and small gain theorem. An algorithm is proposed to investigate the situation of the different parts of the initial observer design space, in terms of suitability for being selected as the observer gain or needing elimination due to being an undesirable part. To find the undesirable parts of the design space, the singularity of the Kronecker sum matrix of the estimation error is checked by employing the small gain theorem concept. By excluding undesired parts from the entire design space and checking the remaining parts’ feasibility, a suitable solution can be found, appropriately. The performance of the proposed observer design method is illustrated by using numerical examples and an electric ground vehicle (EGV) system for the estimation of the vehicle sideslip angle and the yaw rate. The results prove the appropriateness of the designed observer using the proposed approach.

Robust Stability Analysis of Linear Parameter-Varying Systems With Markov Jumps

This article presents conditions to assure the mean-square stability of linear parameter-varying systems with Markov jumps. The model dynamics are driven not only by a Markov chain but also by time-varying parameters that take values in a polytopic set. No assumption is imposed on how the parameters vary within the polytopic set, i.e., the variation rate can be arbitrarily fast. The proposed conditions stem from a homogeneous polynomial Lyapunov function in the state space, adapted to account for Markov jumps. The stability certificate is sought through linear matrix inequalities. Numerical examples illustrate this article’s contribution.

Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

Sampled-Data Linear Parameter Variable Approach for Voltage Regulation of DC–DC Buck Converter

This paper addresses the new method for output voltage regulation of DC–DC buck converter nonlinear systems by a sampled-data linear parameter varying (LPV) controller. For this purpose, an output-error state-space affine LPV model is presented for DC–DC buck converter nonlinear systems. The sampled-data structure of the controller is considered as a time delay in the input, and stabilization conditions are obtained for LPV systems with affine dependence on the parameter by using a parameter-dependent Lyapunov–Krasovskii functional. Then, the design condition of the sampled-data LPV controller with an appropriate sampling period is derived to guarantee that the output voltage of the DC–DC buck converter can be adjusted to the desired voltage. Finally, simulation results are provided to show the validity of the presented approach in practical control applications where there are limitations on the value of the sampling period and the cost of the digital implementation.

A Survey of Output Feedback Robust MPC for Linear Parameter Varying Systems

For constrained linear parameter varying (LPV) systems, this survey comprehensively reviews the literatures on output feedback robust model predictive control (OFRMPC) over the past two decades from the aspects on motivations, main contributions, and the related techniques. According to the types of state observer systems and scheduling parameters of LPV systems, different kinds of OFRMPC approaches are summarized and compared. The extensions of OFRMPC for LPV systems to other related uncertain systems are also investigated. The methods of dealing with system uncertainties and constraints in different kinds of OFRMPC optimizations are given. Key issues on OFRMPC optimizations for LPV systems are discussed. Furthermore, the future research directions on OFRMPC for LPV systems are suggested.

Adaptive Event-Triggered Finite-Frequency Fault Detection With Zonotopic Threshold Analysis for LPV Systems.

This article investigates a class of multiobjective optimization fault detection observer design problems for linear parameter varying (LPV) systems considering the unknown but bounded disturbance with an adaptive event-triggered scheme. In this study, the actuator faults are considered in the low-frequency domain. First, to save the communication bandwidth and improve communication efficiency, an adaptively adjusted event-triggered (AAET) mechanism is proposed. Then, in order to make the designed observer gain satisfy both fault sensitivity and disturbance robust conditions, an H-/L∞ multiobjective optimization problem is proposed and solved by appropriate linear matrix inequalities. Next, the upper and lower bounds of the generated residual are calculated by the zonotope method when considering the estimation uncertainty. Fault detection can be achieved by judging whether the zero value belongs to the generated range of the residual signal. Finally, a simulation case is used to verify the effectiveness of the proposed method.

Recursive zonotopic set-membership approach for system-level prognostics with application to linear parameter-varying systems

A robust recursive zonotopic set-membership approach for remaining useful life forecasting with application to linear parameter-varying systems is proposed in this paper. The proposed approach addresses systems with degraded components formulated as a system-level prognostics problem. Thus, the critical degraded components of the system are augmented to the states resulting a nonlinear system that is reformulated as a linear parameter-varying model. Hence, joint estimation of states and parameters is adopted in a zonotopic set-membership scheme with an optimal linear matrix inequality-based tuning and assuming unknown-but-bounded noises and uncertainties. As a result, a recursive zonotopic set-membership approach is proposed for remaining useful life forecasting based on the prediction of the failure precursors of degraded systems. Finally, this approach is tested on a DC–DC converter case study with unknown degradation behaviors, and the obtained results show the estimation and the forecasting accuracy of this methodology.

A New Fuzzy Robust Control for Linear Parameter-Varying Systems

The linear parameter-varying (LPV) models have broad applications in advanced mathematics and modern control systems. This paper introduces a new method for controlling the LPV systems. This method includes the gain-scheduled state-feedback technique and a fuzzy system to calculate the state-feedback gain. The main goal of the control system is to stabilize the system and bring its states to equilibrium points. Linear matrix inequalities calculate feedback gains to stabilize the system. On the other hand, a fuzzy control system also produces a combined signal with the primary controller signal to speed up this operation. Lyapunov’s theory is used to guarantee the control system’s stability. Finally, to evaluate the performance of the proposed control system, the inverted pendulum has been investigated as a case study. The results show that the proposed method has good efficiency and performance.

A method for reducing implementation complexity in linear parameter-varying controllers

Gain-scheduling is a popular control technique to deal with nonlinear and time varying systems. The linear parameter-varying (LPV) system approach offers systematic tools to design gain-scheduled controllers. However, the implementation of these controllers might demand complex mathematical operations to be performed in real-time. This limits the hardware and the applications in which LPV controllers can be used. In this article, we analyze these limitations and propose a design methodology to reduce the implementation complexity of gain-scheduled LPV controllers. The methodology is illustrated with a nonlinear bicycle model used in electric vehicle control.

Adaptive Damping Control Scheme for Wind Grid-Connected Power Systems With Virtual Inertia Control

With the large-scale wind power integration into the power system, the inertia and damping characteristics of the system have been weakened, which is not conducive to fulfill the grid-friendly operation of wind power. Aiming at this, an adaptive control scheme combining virtual inertia control (VIC) and supplementary damping controller (SDC) is proposed in this paper. Firstly, the mathematical model of wind grid-connected power system with VIC is established. Secondly, the polytopic linear parameter varying (LPV) system is built to describe the uncertainty of system operating points, and the gap metric-based nonlinear evaluation method is used for polytope vertex configuration. Next, Youla-Kucera parametrization are extended to polytopic LPV system to design an adaptive damping control, in which VIC and SDC are coordinated to provide damping and virtual inertia simultaneously. Finally, the proposed adaptive control scheme is compared with several existing control techniques to validate its effectiveness and advantages in suppressing system oscillation in the modified IEEE 39-bus system integrated with 2 wind turbines.

A Direct Parameter-Error Codesign Approach of Discrete-Time Saturated LPV Systems

Considering a discrete-time linear parameter-varying systems with input constraints, this article deals with the codesign of a parameter-dependent state-feedback controller and a new parameter-dependent event-triggering mechanism. Two independent event-triggering policies are introduced at the sensor node to economize the limited network resources. They indicate whether the current state or the current scheduling parameters should be transmitted to the controller or not. In this sense, the controller scheduling parameters can differ from those of the system, yielding a certain degree of robustness concerning parameter deviations. Sufficient conditions, given in terms of linear matrix inequalities, ensure the regional asymptotic stability of the closed loop. To formulated them, we use the Lyapunov theory along with the generalized sector condition. Moreover, we formulate a convex optimization procedure indirectly reducing the transmission activity over the network. The proposed methodology effectiveness is attested through numerical examples and comparisons with related works from the literature.