Constrained Control and Estimation of Homogeneous Reaction Systems Using Extent-Based Linear Parameter Varying Models

International audience

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.

We introduce a controller design methodology for nonlinear systems via complementary Linear Parameter Varying (LPV) controller and observer structures. The recently developed method is able to control physiological systems even with complex nonlinearities — without using Linear Matrix Inequalities (LMI) or other techniques requiring iterations. The developed method is based on the classical state feedback theorems, matrix similarity theorems and supplementary controller and observer structure which efficiently uses the mathematical properties of the parameter space of the LPV system. The main benefits of the proposed method is that the controller design does not require mathematical tools needing iteration thus high computational capacity. We used a nonlinear compartmental model in order to demonstrate the application of the method. The results showed that the developed complementary LPV controller and observer structures perform well on both the LPV systems and the original nonlinear system as well.

This paper presents a novel function of energy-optimal adaptive cruise control (EACC) for electric vehicles based on model predictive control (MPC), which optimally plans the host car's speed trajectory for higher energy efficiency through taking the surrounding traffic information and the road conditions ahead into account. To cope with the nonlinearity of the system dynamics, nonlinear MPC (NMPC) is designed in this paper. Afterwards, the nonlinear equality constraints are relaxed so that the optimization problem has a convex feasible set. Moreover, it is proven that the nonlinear problem can be recast as a second-order cone programming (SOCP) problem. The performance of NMPC is evaluated in the real driving condition and compared to both linear MPC and receding horizon dynamic programming (RH-DP). In order to enable real-time control, the interior point method is used to solve both linear and nonlinear MPC problems and the computation time is investigated in this paper.

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

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.

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

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.

An off-line Model Reduction-based Technique for On-line Linear MPC Applications for Nonlinear Large-Scale Distributed Systems

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

This paper investigates the stabilization problem for a class of discrete-time linear parameter-varying (LPV) systems with Markovian switching by using a parameter-dependent Lyapunov function method. A key point of this work relaxes discrete-time Markovian jump systems whose subsystems are described by discrete-time linear time-invariant (LTI) dynamics to discrete-time LPV systems with Markovian switching whose subsystems are described by discrete-time LPV dynamics. Meanwhile, the special assumption of completely known transition probability is relaxed to more general case that transition probability are partly known. Moreover, the proposed control technique for the discrete-time LPV systems with Markovian switching is used to solve the stabilization problem of turbofan-engine. Firstly, a state-feedback 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.

This paper presents a nonparametric identification method for state-space linear parameter-varying (LPV) models using a modified support vector machine (SVM) approach. While most LPV identification schemes in the state-space form fall under the general category of parametric methods, regularization-based SVMs provide a viable alternative to model scheduling dependencies, without the need of specifying the dependency structure and with an attractive bias-variance trade-off. In this paper, a solution is proposed for nonparametric identification of LPV state-space models in terms of least-squares SVMs (LS-SVM) and is then extended in a way that the proposed estimation is robust to errors in the noise model estimation. The so-called instrumental variables (IV) method has been used in linear system identification for quite some time, and has recently seen its application in the identification of both nonlinear and LPV systems in the input-output (IO) form. The IV method reduces the bias in estimated LPV state-space models in case the noise model is not estimated properly or is unknown. In the proposed method of this paper, the attractive bias-variance trade-off properties of LS-SVMs are combined with statistical properties of IV-based methods to give robust estimates of the functional dependencies. Numerical examples are provided to compare the performances of the proposed IV-based technique with the LS-SVM-based LPV model identification methods.

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.

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.

An important feature of linear model predictive control (MPC) is the ability to provide offset-free control through integral action. Linear MPC can utilize a steady-state target optimizer (SSTO) in conjunction with a dynamic optimization in order to manage systems that are non-square, have integrating modes, or encounter infeasible setpoints. Integral action does not ensure that the feasible steady-state target is closest to the true optimum when the desired setpoint is infeasible. This paper describes the modifications necessary to linear state-space MPC algorithms in order to address this problem (assuming systems with no integrating modes). The solution employs features of the integrated system optimization and parameter estimation (ISOPE) algorithm: the SSTO cost is modified by a term that results in matching of the true plant and model conditions necessary for optimality. This work combines well with prior work which has determined the situations where the modification is actually necessary.