Efficient Robust Model Predictive Control Research Articles

An efficient robust model predictive control for nonlinear Markov jump systems with persistent disturbances using matrix partition

For a class of nonlinear Markov jump systems (MJSs), an efficient robust model predictive control (MPC) is designed with bounded persistent perturbations and hard constraints. Nonlinearity is considered as a description of polyhedral form. First, affine control inputs are introduced for the polytopic MJSs to provide the expected performance. Quadratic boundedness is then used to deal with bounded persistent perturbations to improve the robustness of the closed loop system. Then the large amount of online MPC computation problem is solved efficiently by matrix partitioning. The efficient MPC strategy not only ensures that the closed-loop system is stochastically stable but also reduces the amount of on-line computation and improves the efficiency of on-line computation. Finally, a numerical example and a nonlinear mechanical mass-spring-damper system are applied to elucidate the proposed algorithm.

Nonlinear curve fitting-based fast robust MPC algorithm for nonlinear system

In the existing efficient robust model predictive control (ERMPC) algorithms (see e.g. [14,31,32]), through offline optimization and online lookup table calculation, a fixed state feedback control law or a linear interpolated control law is applied to a system when the system state lies between two adjacent polyhedrons, which undoubtedly will result in conservativeness of the controller. Faced with this issue, an improved ERMPC algorithm is proposed in this paper, which considers the nonlinearity between the state feedback control laws with respect to polyhedrons and the norm distance from system state to origin, and can provide continuously variable state feedback control law varying with the state. First, a set of polyhedral parameters and their corresponding state feedback control law sequences are obtained offline by solving a set of LMIs optimization problems. Next, for each state feedback control law sequence, a nonlinear fitting function is established offline between the state feedback control law and its serial number. Then a simplified lookup table is constructed offline to save memory space and shorten online computation time of the controller. According to the simplified lookup table and information of the norm distance from system state to origin, we online establish the coordinate of current state in the nonlinear fitting curve for getting current feedback control law, which changes continuously with the state. The proposed ERMPC algorithm is successfully applied to an actual fast-responding linear one stage inverted pendulum (LOSIP) system to verify its effectiveness.

Control of LPV Modeled AC-Microgrid Based on Mixed H2/H∞ Time-Varying Linear State Feedback and Robust Predictive Algorithm

This paper presents a robust model predictive control (RMPC) method with a new mixed H2/<inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> linear time-varying state feedback design. In addition, we propose a linear parameter-varying model for inverters in a microgrid (MG), in which disturbances and uncertainty are considered, where the inverters connect in parallel to renewable energy sources (RES). The proposed RMPC can use the gain-scheduled control law and satisfy both the H2 and <inline-formula> <tex-math notation="LaTeX">$\text{H}\infty $ </tex-math></inline-formula> proficiency requirements under various conditions, such as disturbance and load variation. A multistep control method is proposed to reduce the conservativeness caused by the unique feedback control law, enhance the control proficiency, and strengthen the RMPC feasible area. Furthermore, a practical and efficient RMPC is designed to reduce the online computational burden. The presented controller can implement load sharing among distributed generators (DGs) to stabilize the frequency and voltage of an entire smart island. The proposed strategy is implemented and studied in a MG with two DG types and various load types. Specifically, through converters, one type of DGs is used to control frequency and voltage, and the other type is used to control current. These two types of DGs operate in a parallel mode. Simulation results show that the proposed RMPCs are input-to-state practically stable (ISpS). Compared with other controllers in the literature, the proposed strategy can lead to minor total harmonic distortion (THD), lower steady-state error, and faster response to system disturbance and load variation.

Efficient robust output feedback MPC

AbstractThis paper extends an efficient robust Model Predictive Control (MPC) methodology based on offline optimization of prediction dynamics in two respects. Firstly the case of output feedback via an observer is considered. Secondly, a method is proposed for imposing a bound on worst case performance using dynamic feedback which allows a nominal optimal feedback law to be implemented when this is feasible. The method is applicable to the case of uncertain systems which are not robustly stabilized by nominal LQ-optimal control. An efficient online optimization with feasibility and stability guarantees is proposed.

Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

Shimmy vibration is one of the major concerns in the aircraft landing gear design. In this paper, the influence of structural parameters on the shimmy dynamics is analyzed based on a nonlinear dynamical model. A computationally efficient robust model predictive control law is formulated for a linear parameter varying system with guaranteed closed-loop stability. Moreover, an attempt is made to apply the proposed robust model predictive control strategy to suppress the shimmy during the taxiing and landing of an aircraft. Compared with two current robust model predictive controls, the proposed shimmy controller can effectively suppress the shimmy with more efficient computation. To verify the efficiency of the proposed algorithm, the simulation results are presented and discussed. Nomenclature A,B,C = discrete state-space matrices Ac,Bc,Cc = continuous state-space matrices Aj,Bj = discrete state-space matrices ofjth vertex a = half contact length

Optimizing prediction dynamics for robust MPC

A convex formulation is derived for optimizing dynamic feedback laws for constrained linear systems with polytopic uncertainty. We show that, when it exists, the maximal invariant ellipsoidal set for the plant state under a dynamic feedback law incorporating any chosen static feedback gain is equal to the maximal invariant ellipsoidal set under any linear feedback law. The dynamic controller and its associated invariant set define a computationally efficient robust model predictive control (MPC) law with prediction dynamics belonging to a polytopic uncertainty set.

A SIMPLE TUBE CONTROLLER FOR EFFICIENT ROBUST MODEL PREDICTIVE CONTROL OF CONSTRAINED LINEAR DISCRETE TIME SYSTEMS SUBJECT TO BOUNDED DISTURBANCES

We present a simple tube controller for efficient robust model predictive control of constrained linear, discrete-time systems in the presence of bounded disturbances. The proposed control policy ensures that controlled trajectories are confined to a given tube despite uncertainty. The robust optimal control problem that is solved on-line is a standard quadratic programming problem of marginally increased complexity compared with that required for model predictive control in the deterministic case. We show how to optimize the tube cross section, how to construct an adequate tube terminal set and we establish robust exponential stability of a suitable robust control invariant set (the ‘origin’ for uncertain system) with enlarged domain of attraction.