Tube-Based Output Feedback Robust MPC for LPV Systems With Scaled Terminal Constraint Sets.

A New Approach to Robust MPC Design for LPV Systems in Input-Output Form

International audience

In this paper, we consider the fault Detection and isolation (FDI) problem for faulty linear parameter-varying (LPV) systems subject to disturbances and propose a observer-based solution by using multiobjective optimization techniques. To simply the design process, a general faulty LPV system will be constructed from standard LPV description by converting actuator/system component faults into sensor faults at first. Then a bank of LPV FDI filters will be designed to identify each fault. Each FDI filter could generate a residual signal to track individual fault with minimum error and suppressing the effects of disturbances and other fault signals. The design of FDI filters will be formulated as multiobjective optimization problems in terms of linear matrix inequalities (LMIs) and can be solved efficiently. Two numerical examples are also presented to demonstrate the proposed fault detection and isolation approach on both LPV and LTI systems.

Stability analysis and stabilization of LPV systems with jumps and (piecewise) differentiable parameters using continuous and sampled-data controllers

ABSTRACTThe output feedback robust model predictive control (MPC), for the linear parameter varying (LPV) system with norm-bounded disturbance, is addressed, where the model parametric matrices are only known to be bounded within a polytope. The previous techniques of norm-bounding technique, quadratic boundedness (QB), dynamic output feedback, and ellipsoid (true-state bound; TSB) refreshment formula for guaranteeing recursive feasibility, are fused into the newly proposed approaches. In the notion of QB, the full Lyapunov matrix is applied for the first time in this context. The single-step dynamic output feedback robust MPC, where the infinite-horizon control moves are parameterised as a dynamic output feedback law, is the main topic of this paper, while the multi-step method is also suggested. In order to strictly guarantee the physical constraints, the outer bound of the true state replaces the true state itself, so tightness of this bound has a major effect on the control performance. In order to tighten the TSB, a procedure for refreshing the real-time ellipsoid based on that of the last sampling instant is given. This paper is conclusive for the past results and far-reaching for the future researches. Two benchmark examples are given to show the effectiveness of the novel results.

This paper investigates the guaranteed cost control problem for a class of linear parameter-varying (LPV) systems with Markovian switching under partly known transition rates. A key point of this work relaxes Markovian jump systems whose subsystems are described by linear time-invariant (LTI) dynamics to LPV systems with Markovian switching whose subsystems are described by LPV dynamics. Meanwhile, the special assumption of completely known transition rates is relaxed to more general case that transition rates are partly known. Moreover, the proposed control technique for the LPV systems with Markovian switching is used to solve the guaranteed cost control problem of turbofan-engine. Firstly, a guaranteed cost controller is designed, and the design problem can be reduced to a set of linear matrix inequalities (LMIs) feasibility problem. Then, a turbofan-engine example is given to demonstrate the applicability of the main results.

Linear parameter-varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different representations it appears that the time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. Therefore, representations used previously to define and specify LPV systems are not equal in terms of dynamics. In order to construct a parametrization-free description of LPV systems that overcomes these difficulties, a behavioral approach is introduced that serves as a basis for specifying system theoretic properties. LPV systems are defined as the collection of trajectories of system variables (like inputs and outputs) and scheduling variables. LPV kernel, input-output, and state-space system representations are introduced with appropriate equivalence transformations.

In recent years, automatic crane device is used in scenes of handling of objects at warehouse. Stacker crane is an example of automatic crane device. It has a Traveling body, a Forking mechanism and a Lifting mechanism. A Traveling body makes a Lifting body move along the horizontal axis. A Lifting mechanism makes a Forking mechanism move along vertical axis. It is able to carry a load into rack or takes out a load from the rack by using Forking mechanism. But, in action of Forking mechanism, vibration of Forking mechanism and variation of characteristic frequency of Forking mechanism causes several problems. In this study, the stacker crane is described in LPV (Linear Parameter Varying) system. And, using DMM (Dual Model Matching) method provides the LPV controller that can adjust plant that explained by LPV system. The results of simulation show the effectiveness of LPV controller when DMM controlled is applied.

Plug-and-play model predictive control based on robust control invariant sets

A robust synthesis algorithm is developed for a class of uncertain, linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal LPV system and a block structured uncertainty. The nominal part is a “gridded” LPV system with state matrices that are arbitrary functions of the parameter. The input/output behavior of the uncertainty is described by integral quadratic constraints (IQCs). The robust synthesis problem leads to a non-convex optimization. The proposed algorithm is a coordinate-wise descent similar to the well-known DK iteration for μ synthesis. It alternates between an LPV synthesis step and an IQC analysis step. Both steps can be efficiently solved as semidefinite programs. The derivation of the synthesis algorithm is less obvious for LPV systems as compared to its LTI counterpart due to the lack of a valid frequency response interpretation. The main contribution is the construction of the iterative synthesis algorithm using time domain dissipation inequalities and a scaled system analogous to that appearing in μ synthesis. It is shown that the proposed algorithm ensures that the robust performance is non-increasing at each iteration step. The effectiveness of the proposed method is demonstrated on a simple numerical example.

Input Estimation from Sparse Measurements in LPV Systems and Isotopic Ratios in Polar Firns

Robust model predictive control for stratospheric airships using LPV design

Linear Parameter Varying (LPV) system shows preferable performance in dealing with NonLinear (NL) systems and systems with time-varying parameters, based on a kind of wheel-legged robot with two-wheel and balance as Inverted Pendulum, this paper proposes a gain scheduling control method for balancing using LPV system on Equivalent model with Center Of Mass (COM). In order to ensure the stability and responsive of the system with possible values for all variable parameters, Higher Order Singular Value Decomposition (HOSVD) is used for constructing polytopic LPV system, then the robust controller is designed for the vertex systems forthputting Linear Matrix Inequality (LMI) approach, and the gain scheduling controller for global system is obtained by convex combination of vertex LTI systems. The simulation results show that the system can achieve the expected indicators.

SummaryThe present paper addresses an observer‐based output feedback robust model predictive control for the linear parameter varying system with bounded disturbance and noise subject to input and state constraints. The main contribution is that the on‐line convex optimization problem not only simultaneously optimizes the observer and controller gains to stabilize the augmented closed‐loop system but also incorporates the refreshment of bounds of the estimation error set. The optimization problem steers the nominal augmented closed‐loop system to converge to the origin, and the real augmented closed‐loop system bounded within robust positive invariant set converges to a neighborhood of the origin such that recursive feasibility of the optimization and robust stability of the controlled system are ensured. Two numerical examples are given to illustrate the effectiveness of the method.

A feedback control law is derived analytically for a linear parameter varying (LPV) discrete-time system with bounded rates of parameter variations subject to input-saturated constraints in this paper. As the uncertain region of such a LPV system in the future changes corresponding to the parameters which can be predicted in the future stage due to the information on the parameters value, magnitude bounds and the variation rate bounds, the control law is presented in the paper by solving a min-max MPC problem based on a dynamic programming viewpoint. By exploiting the dynamic nature of the min-max optimal problem and showing the convexity of the dynamic cost-to-go, the intrinsic structure of the feedback control law has been obtained which is proved to be efficient for an LPV system with bounded rates of parameter variations by an example at last.