Linear Parameter-varying Framework Research Articles

Linear Parameter-Varying Polytopic Modeling and Control Design for Guided Projectiles

In this paper, a linear parameter varying (LPV) modeling and control design approach is applied to a new class of guided projectiles, aiming to exploit the advantages of the LPV framework in terms of guaranteed stability and performance. The investigated concept consists of a planar symmetric 155 mm fin-stabilized projectile equipped with a reduced amount of control actuators and characterized by a predominantly unstable behavior across the analyzed flight envelope. A dedicated modeling procedure allows reformulating the nonlinear projectile dynamics as a LPV polytopic system, employed for the controller design. The procedure intends to reduce the computational complexity and the conservativeness affecting the overall controller synthesis. A trajectory-tracking simulation scenario is performed in a realistic simulator environment to assess the performance of the resulting LPV polytopic autopilot across the entire flight envelope.

Event-Triggered Control for LPV Modeling of DC–DC Boost Converter

This study presents the event-triggered control (ETC) for linear parameter varying (LPV) model of boost converters. We examine the nonlinear dynamics of boost converters in the LPV framework. The proposed controller is duty-ratio-dependent and provides better performance while requiring less computation. Using the parameter-dependent Lyapunov function (PDLF), we demonstrate the stablity analysis of the proposed approach. Furthermore, we demonstrate that the inter-event time is lower bound by a positive constant, which indicates Zeno behavior free performance. In comparison to earlier time-invariant synthesis techniques, the LPV formulation offers for increased robustness and performance properties. Simulation and experimental results validate the effectiveness of the proposed method.

A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

ABSTRACT This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

A Hybrid Neural Network Approach for Adaptive Scenario-Based Model Predictive Control in the LPV Framework

This paper presents a hybrid neural network (NN) approach for adaptive scenario-based model predictive control (SMPC) design of nonlinear systems in the linear parametervarying (LPV) framework. In particular, a deterministic artificial neural network (ANN)-based LPV model is learned from data as the nominal model. Then, a Bayesian NN (BNN) is used to describe the mismatch between the plant and the LPV-ANN model. Adaptive scenarios are generated online based on the BNN model to reduce the conservativeness of scenario generation. Moreover, a probabilistic safety certificate is incorporated into the scenario generation by ensuring that the trajectories of scenarios contain the trajectory of the system and that all the scenarios satisfy the constraints with a high probability. Furthermore, conditions for the recursive feasibility of the SMPC are given. Experiments on the closed-loop simulations of a two-tank system demonstrate that the proposed approach can better model the behaviors of nonlinear systems than sole ANN/BNN models can, and the SMPC based on the hybrid NN (HyNN) model can improve the control performance compared to the SMPC with a fixed scenario tree.

An LPV-Based Online Reconfigurable Adaptive Semi-Active Suspension Control with MR Damper

This study introduces an online reconfigurable road-adaptive semi-active suspension controller that reaches the performance objectives with satisfying the dissipativity constraint. The concept of the model is based on a nonlinear static model of the semi-active Magnetorheological (MR) damper with considering the bi-viscous and hysteretic behaviors of the damper. The input saturation problem has been solved by using the proposed method in the literature that allows the integration of the saturation actuator in the initial system to create a Linear Parameter Varying (LPV) system. The control input meets the saturation constraint; therewith, the dissipativity constraint is fulfilled. The online reconfiguration and adaptivity problem is solved by using an external scheduling variable that allows the trade-off between driving comfort and road holding/stability. The control design is based on the LPV framework. The proposed adaptive semi-active suspension controller is compared to passive suspension and Bingham model with Simulink simulation, and then the adaptivity of the controller is validated with the TruckSim environment. The results show that the proposed LPV controller has better performance results than the controlled Bingham and passive semi-active suspension model.

Safe control of nonlinear systems in LPV framework using model-based reinforcement learning

This paper presents a safe model-based reinforcement learning (MBRL) approach to control nonlinear systems described by linear parameter-varying (LPV) models. A variational Bayesian inference Neural Network (BNN) approach is first employed to learn a state-space model with uncertainty quantification from input-output data collected from the system; the model is then utilised for training MBRL to learn control actions for the system with safety guarantees. Specifically, MBRL employs the BNN model to generate simulation environments for training, which avoids safety violations in the exploration stage. To adapt to dynamically varying environments, knowledge on the evolution of LPV model scheduling variables is incorporated in simulation to reduce the discrepancy between the transition distributions of simulation and real environments. Experiments on a parameter-varying double integrator system and a control moment gyroscope (CMG) simulation model demonstrate that the proposed approach can safely achieve desired control performance.

Cloud-based adaptive semi-active suspension control for improving driving comfort and road holding

The improvement of driving comfort and vehicle stability performance is essential for the vehicles, which can be actualized by adaptive semi-active suspension control. Cloud computing allows several features for autonomous vehicles. Implementing the adaptive suspension control using historical road data gathered in the cloud database is one of these features. This paper deals with the adaptive semi-active suspension control from the perspective of a Vehicle-to-Cloud-to-Vehicle integration. Measured and historical performance(vertical acceleration and tire deformation) and velocity data in different locations and road irregularities from other vehicles have been stored in the cloud database and used to design the dedicated scheduling variable. The novelty of this paper is developing the adaptive semi-active suspension control method with different scheduling parameter design approaches based on cloud application for the road adaptation capabilities of the suspension system. The control architecture is founded on the Linear Parameter-Varying framework, where the scheduling variable allows the trade-off between driving comfort and vehicle stability. The real data simulation demonstrates the operation of the introduced method in the TruckSim simulation environment and Matlab/Simulink. The results show that both vehicle stability and driving comfort has been improved.

Frequency Response Data-Driven LPV Controller Synthesis for MIMO Systems

The linear parameter-varying framework enables systematic control design approaches to meet increasing performance requirements and complexity of systems. The aim of this paper is to develop local frequency response data-based analysis and synthesis conditions for multiple-input multiple-output linear parameter-varying systems to facilitate fast tuning. Key advantages are local stability and performance guarantees and a global controller parameterization. The effectiveness of the proposed methods are evaluated based on a simulation example.

Design of shifting output-feedback controllers for LPV systems subject to time-varying saturations

This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.

Emerging approaches for nonlinear parameter varying systems

Emerging approaches for nonlinear parameter varying systems

Vehicle Semi-active Suspension Control with Cloud-based Road Information

Adaptive suspension control considering passenger comfort and stability of the vehicle has been researched intensively, thus several automotive companies already apply these technologies in their high-end models. Most of these systems react to the instantaneous effects of road irregularities, however, some expensive camera-based systems adapting the suspension in coherence with upcoming road conditions have already been introduced. Thereby, using oncoming road information the performance of adaptive suspension systems can be enhanced significantly. The emerging technology of cloud computing enables several promising features for road vehicles, one of which may be the implementation of an adaptive semi-active suspension system using historic road information gathered in the cloud database. The main novelty of the paper is the developed semi-active suspension control method in which Vehicle-to-Cloud-to-Vehicle technology serves as the basis for the road adaptation capabilities of the suspension system. The semi-active suspension control is founded on the Linear Parameter-Varying framework. The operation of the presented system is validated by a real data simulation in TruckSim simulation environment.

Road Quality Information Based Adaptive Semi-active Suspension Control

This paper introduces an adaptive semi-active suspension control by considering global positioning system-based and historical road information. The main idea of this study is to find a corresponding trade-off between comfort and stability at different road irregularities. The introduced semi-active controller is designed based on the Linear Parameter-Varying framework. The behavior of the designed controller can be modified by the use of a scheduling variable. This scheduling variable is selected by considering the various road category. TruckSim simulation environment is used in order to validate the introduced adaptive semi-active suspension control system by comparing it with the non-adaptive scenario. The results show that both driving comfort and vehicle stability have been improved with the proposed adaptive semi-active suspension control.

Finite Horizon Touchdown Analysis of Autolanded Aircraft under Crosswind

The paper presents a worst-case touchdown condition analysis of an autolanded aircraft under crosswind. Aircraft dynamics are generally considered altitude- and speed-dependent and, thus, well covered inside the linear parameter-varying framework. Following a specific parameter trajectory tracking the instrument landing system’s guidance signal, its dynamics amount to a finite horizon linear time-varying (LTV) system. This allows to explicitly respect the varying dynamics during the flare maneuver, changing control laws, and the finite horizon of the approach using a finite horizon LTV analysis. A time-varying trajectory uncertainty is proposed to respect the effects of different environmental conditions and aircraft parameters in the analysis. By representing the uncertainty as an integral quadratic constraint (IQC), recent advances in the worst-case gain analysis of finite horizon LTV systems can be utilized. The analysis condition is based on a parameterized Riccati differential equation, which leads to an efficiently solvable nonlinear optimization problem. Applying the robust LTV framework, worst-case touchdown conditions of an autolanded large airliner under crosswind wind are calculated. The obtained results are evaluated against Monte Carlo analyses of the nonlinear model.

Data-driven linear parameter-varying modelling of the steering dynamics of an autonomous car

Developing automatic driving solutions and driver support systems requires accurate vehicle specific models to describe and predict the associated motion dynamics of the vehicle. Despite of the mature understanding of ideal vehicle dynamics, which are inherently nonlinear, modern cars are equipped with a wide array of digital and mechatronic components that are difficult to model. Furthermore, due to manufacturing, each car has its personal motion characteristics which change over time. Hence, it is important to develop data-driven modelling methods that are capable to capture from data all relevant aspects of vehicle dynamics in a model that is directly utilisable for control. In this paper, we show how Linear Parameter-Varying (LPV) modelling and system identification can be applied to reliably capture personalised model of the steering system of an autonomous car based on measured data. Compared to other nonlinear identification techniques, the obtained LPV model is directly utilisable for powerful controller synthesis methods of the LPV framework.

Data-Driven Predictive Control for Linear Parameter-Varying Systems

Based on the extension of the behavioral theory and the Fundamental Lemma for Linear Parameter-Varying (LPV) systems, this paper introduces a Data-driven Predictive Control (DPC) scheme capable to ensure reference tracking and satisfaction of Input-Output (IO) constraints for an unknown system under the conditions that (i) the system can be represented in an LPV form and (ii) an informative data-set containing measured IO and scheduling trajectories of the system is available. It is shown that if the data set satisfies a persistence of excitation condition, then a data-driven LPV predictor of future trajectories of the system can be constructed from the IO data set and online measured data. The approach represents the first step towards a DPC solution for nonlinear and time-varying systems due to the potential of the LPV framework to represent them. Two illustrative examples, including reference tracking control of a nonlinear system, are provided to demonstrate that the data-based LPV-DPC scheme, achieves similar performance as LPV model-based predictive control.

Superheating control of an Organic Rankine Cycle for recovering waste heat from an engine cooling system

This paper proposes a set of strategies to control the superheat (SH) value of an Organic Rankine Cycle (ORC). This ORC corresponds to an experimental test bench aimed at developing a waste heat recovery system to be connected to the cooling circuit of a light-duty vehicle. Three strategies have been developed and tested experimentally. The first one is a linear control based on a PI controller valid for a given operating point. The second, valid for the same operating point, proposes an LPV (Linear Parameter-Varying) approach, less conservative and more accurate than the first one. Finally, a third strategy also using the LPV framework provides a controller valid in the full operating range of the test bench.

LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

In recent years, the Active Flutter Suppression (AFS) employing Linear Parameter-Varying (LPV) framework has become a hot spot in the research field. Nevertheless, the flutter suppression technique is facing two severe challenges. On the one hand, due to the fatal risk of flight test near critical airspeed, it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data. On the other hand, saturation of the actuator may degrade the closed-loop performance, which was often neglected in the past work. To tackle these two problems, a new active controller design procedure is proposed to suppress flutter in this paper. Firstly, with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates (SMILE) technique, a set of high-fidelity Linear Time-Invariant (LTI) models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system. And then, the unstable aeroelastic dynamics beyond critical airspeed are ‘predicted’ by extrapolating the resulting LPV model. Secondly, based on the control-oriented LPV model, an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation. Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored, the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter (BFF) when encountering the actuator saturation. However, the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system when encountering serious actuator saturation.

Shifting H∞ Linear Parameter Varying State-Feedback Controllers Subject to Time-Varying Input Saturations

This paper establishes a methodology based on linear matrix inequalities (LMIs) to design a shifting H∞ linear parameter varying (LPV) state-feedback controller for systems affected by time-varying input saturations. By means of the shifting paradigm, the instantaneous saturation values are linked to a scheduling parameter vector. Then, the disturbance rejection is dealt with the quadratic boundedness concept and the shifting H∞ methodology. The design conditions are obtained within the LPV framework using ellipsoidal invariant sets, thus obtaining an LMI-based feasibility problem that can be solved via available solvers. Finally, the main characteristics of the proposed approach are validated by means of an illustrative example.

Precompensation of Supply Dynamics of Dynamic Power Supply Transmitters Using a Linear Parameter-Varying Model

The use of a linear parameter-varying framework is proposed as a viable design tool for dynamic power supply transmitters. Accurate synchronization between the low- and high-frequency paths of these devices is an essential requirement for obtaining optimal results. Using this framework, the estimation of the low-frequency dynamics of the supply path is made possible for actual operational conditions. A precompensation model can, as a result, be designed to compensate for these unwanted dynamics, improving both the linearity and the energy efficiency of the resulting device. Moreover, the procedure does not require access to any internal nodes and can be implemented digitally without modification of the existing hardware. A measurement example demonstrates the advantages and improvements that become possible with the proposed technique.

Output integral sliding mode fault tolerant control scheme for LPV plants by incorporating control allocation

An integrated integral sliding mode fault tolerant control scheme is proposed for the linear parameter varying (LPV) plants in the output feedback framework. To estimate the unavailable plant states, an unknown input LPV observer is employed. The feedback and observer gains are designed using linear matrix inequalities approach to ensure closed-loop stability nominally and in the situation of actuator faults/failures. An integral sliding modes approach in the LPV framework together with control allocation maintains the nominal performance in the presence of permissible set of actuator faults/failures. A rigorous closed-loop stability analysis is carried out and to show the feasibility of the proposed approach it is tested in simulations on the non-linear plant of a passenger aircraft.