Stability Of Model Predictive Control Research Articles

Prediction Horizon-Varying Model Predictive Control (MPC) for Autonomous Vehicle Control

The prediction horizon is a key parameter in model predictive control (MPC), which is related to the effectiveness and stability of model predictive control. In vehicle control, the selection of a prediction horizon is influenced by factors such as speed, path curvature, and target point density. To accommodate varying conditions such as road curvature and vehicle speed, we proposed a control strategy using the proximal policy optimization (PPO) algorithm to adjust the prediction horizon, enabling MPC to achieve optimal performance, and called it PPO-MPC. We established a state space related to the path information and vehicle state, regarded the prediction horizon as actions, and designed a reward function to optimize the policy and value function. We conducted simulation verifications at various speeds and compared them with an MPC with fixed prediction horizons. The simulation demonstrates that the PPO-MPC proposed in this article exhibits strong adaptability and trajectory tracking capability.

Lyapunov-based model predictive control of dual-induction motors fed by a nine-switch inverter to improve the closed-loop stability

This study presents a novel Lyapunov-based model predictive control strategy for a nine-switch inverter-based multi-drive system. The drive system includes two ac motors and a single nine-switch inverter (NSI) that is capable of feeding the multiple induction motors. The model predictive control (MPC) is a popular feedback strategy in ac-drive applications due to its fast dynamic characteristics and the skill of handling multiple control goals. Although the MPC offers a rapid dynamic response to load variations, it suffers from closed-loop instability when the cost function is poorly designed. The unwise choice of the tuning parameters, cost function terms, and control constraints cause instability resulting in poor system performance. In particular, the formulation of the selected objective function greatly impacts the closed-loop stability since it tailors the closed-loop characteristics. A simple penalization of the control goal error in the cost function may not ensure asymptotic stability. Motivated by the MPC stability problem, the cost function is reformulated as a Lyapunov energy function to strengthen the closed-loop stability in this paper. The proposed method selects the control input that meets the Lyapunov stability criterion and applies it to the multi-motor driver. The proposed strategy ensures asymptotic stability and provides a robust motor operation by introducing the Lyapunov control constraints. The proposed feedback strategy is experimentally verified using a lab-scaled hardware test platform. The experimental results demonstrate that the suggested control routine offers an improved steady-state characteristic compared to the conventional MPC method. © 2017 Elsevier Inc. All rights reserved.

Model Predictive Control of Connected Spacecraft Formation

In this contribution we discuss the application of Model Predictive Control (MPC) to achieve a connected network formation of spacecrafts. A set of three spacecrafts are used to achieve in-plane formation which are initially in a connected network. Two scenarios including formation control and formation control with collision avoidance in a leader-follower configuration is addressed through simulation studies. The aspect of MPC stability and network connectivity is also addressed briefly in the context of formation control.

Parallel Hybrid Electric Vehicle Modelling and Model Predictive Control

This paper presents the modelling and calculations for a hybrid electric vehicle (HEV) in parallel configuration, including a main electrical driving motor (EM), an internal combustion engine (ICE), and a starter/generator motor. The modelling equations of the HEV include vehicle acceleration and jerk, so that simulations can investigate the vehicle drivability and comfortability with different control parameters. A model predictive control (MPC) scheme with softened constraints for this HEV is developed. The new MPC with softened constraints shows its superiority over the MPC with hard constraints as it provides a faster setpoint tracking and smoother clutch engagement. The conversion of some hard constraints into softened constraints can improve the MPC stability and robustness. The MPC with softened constraints can maintain the system stability, while the MPC with hard constraints becomes unstable if some input constraints lead to the violation of output constraints.

Finite Horizon Robust Nonlinear Model Predictive Control for Wheeled Mobile Robots

The control of mobile robotic systems with input constraints is still a remarkable problem for many applications. This paper studies the model predictive control-based kinematic control scheme after implementing the decoupling technique of wheeled mobile robots (WMRs). This method enables us to obtain the easier optimization problem with fixed initial state. The finite horizon in cost function of model predictive control (MPC) algorithm requires the appropriate terminal controller as well as the equivalent terminal region. The stability of MPC is determined by feasible control sequence. Finally, offline simulation results validate that the computation load is significantly reduced and also validate trajectory tracking control effectiveness of our proposed control scheme.

Real time model identification using multi-fidelity models in managed pressure drilling

Abstract Highly accurate model predictions contribute to the performance and stability of model predictive control. However, high fidelity models are difficult to implement in real time control due to the large and often nonconvex optimization problem that must be completed within the feedback cycle time. To address this issue, a switched control scheme that uses high fidelity model predictions in real time control is presented. It uses real time simulated data to identify a linear empirical control model. The real time model identification procedure does not interrupt the process, and is suitable for nonlinear processes where offline model identification is difficult. Controller stability is discussed, and the control scheme is demonstrated in a managed pressure drilling simulation. The switched controller provides improved performance over both a high fidelity model based controller and a nonadaptive empirical model.

Computational Simulations on Stability of Model Predictive Control for Linear Discrete-time Stochastic Systems

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the effectiveness of the obtained stability condition. Keywords—Computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems.

Mechanical Impedance Control of Rotatory Test Beds

In this paper, impedance control for rotatory test beds is presented and discussed. Its goal is highly realistic testing of rotating machinery such as combustion engines through hardware-in-the-loop simulation. As rotatory test beds are typical examples of elastic drive systems, modeling and control of the oscillations arising on the test bed are of great importance. Additionally, a so-called impedance model emulates real-world operating conditions and delivers the load for the unit under test, which is then imposed using an appropriate controller. Specifically, in this paper, model predictive control (MPC) was chosen as it allows for high dynamic control including a priori consideration of constraints. In addition to the MPC, a control Lyapunov function based controller is proposed, resulting in guaranteed closed-loop stability even when active constraints prevent the use of classic MPC stability criteria. Finally, simulations and experimental results achieved on a laboratory setup as well as on an industrial test bed illustrate the efficiency of the proposed control scheme.

Stability Analysis of Quadratic MPC With a Discrete Input Alphabet

We study stability of Model Predictive Control (MPC) with a quadratic cost function for LTI systems with a discrete input alphabet. Since this kind of systems may present a steady-state error, the focus is on practical stability, i.e., ultimate boundedness of solutions. To derive sufficient conditions for practical stability and characterize the ultimately invariant set, we analyze the one-step horizon solution and adapt tools used for convex MPC formulations.

Stability Analysis of Constrained Nonlinear Model Predictive Control with Terminal Weighting

This paper investigates stability of model predictive control (MPC) for nonlinear constrained systems. New stability results for the MPC algorithms with terminal weighting are proposed using the dynamic programming method, which gives new criteria for choosing state, control and terminal weighting in the performance index to achieve stability of MPC algorithms. Illustrative examples are given to show that by combining this condition with existing ones, much less conservative results can be generated.

On the stability of MPC with a Finite Input Alphabet

AbstractThis paper studies stability of Model Predictive Control for systems with a finite input alphabet. Since this kind of systems may present a steady-state error under closed-loop control, the forms is on stability in the sense of ultimate boundedness of solutions. To derive sufficient conditions for stability, two different approaches are presented. The first one approximates the finite input alphabet via saturation-control allowing us to analyze the problem from a robust control perspective. In the second approach, a direct analysis of the problem is carried out. The results thus obtained are shown to be less conservative regarding ultimate bounded set than those obtained via the robust control approach.

Robust and stable predictive control with bounded uncertainties

Min–Max optimization is often used for improving robustness in Model Predictive Control (MPC). An analogy to this optimization could be the BDU (Bounded Data Uncertainties) method, which is a regularization technique for least-squares problems that takes into account the uncertainty bounds. Stability of MPC can be achieved by using terminal constraints, such as in the CRHPC (Constrained Receding-Horizon Predictive Control) algorithm. By combining both BDU and CRHPC methods, a robust and stable MPC is obtained, which is the aim of this work. BDU also offers a guided method of tuning the empirically tuned penalization parameter for the control effort in MPC.

On the stability of constrained MPC without terminal constraint

The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented.

MPC FOR MAX-PLUS-LINEAR SYSTEMS WITH GUARANTEED STABILITY

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Previously, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the max-plus algebra. In this paper we consider the stability of MPC for these max-plus linear (MPL) systems, and we derive an MPL-MPC equivalent of the conventional end-point constraint. We show that with this end-point constraint the optimized cost function can be seen as a Lyapunov function for the system and can thus be used to prove stability.

Model predictive control of linear systems with nonlinear terminal control

AbstractIn terminal weighting based model predictive control (MPC) algorithms, the terminal weighting term is used to cover the performance cost under the terminal control for guaranteeing stability. Therefore, the terminal control is crucial in choosing the terminal weighting term and also determining/estimating the stability region. However, most of the existing MPC algorithms are developed based on linear terminal control which restricts the achievable performance and stability of MPC. For linear systems, an MPC algorithm with nonlinear terminal control is presented in this paper, where the gain of the terminal control varies with the terminal state. An offline algorithm is proposed to determine the nonlinear gains and to choose the associated terminal weighting term. It is shown that, compared with the MPC algorithms with fixed linear terminal gain, a nonlinear terminal control results in a much larger stability region, which is confirmed by a numerical example. Copyright © 2004 John Wiley & Sons, Ltd.

A note on calculation of polytopic-invariant feasible sets for linear continuous-time systems

A common way of guaranteeing stability in model predictive control (MPC) is to add into the open-loop optimization problem a terminal constraint set which is invariant and feasible. This note presents an algorithm for calculation of low-complexity polytopic-invariant sets for linear continuous-time systems with complex conjugate closed-loop eigenvalues. Asymmetrical amplitude and rate control input constraints are considered.

A note on calculation of polytopic-invariant feasible sets for linear continuous-time systems

A common way of guaranteeing stability in model predictive control (MPC) is to add into the open-loop optimization problem a terminal constraint set which is invariant and feasible. This note presents an algorithm for calculation of low-complexity polytopic-invariant sets for linear continuous-time systems with complex conjugate closed-loop eigenvalues. Asymmetrical amplitude and rate control input constraints are considered.

Robust Model Predictive Control of Linear Time Invariant System with Disturbances

In recent few years authors investigate methods for establishing and solving stability of model predictive control (MPC) with linear time-invariant systems. In this paper a modification of a predictive control scheme to ensure robust feasibility and stability for a case of discrete time linear systems with disturbances is submitted. A new cost function, which penalizes a deviation of state trajectories from a robust invariant set and deviation from some ideal control law is presented. The cost allows formulation of robustly stable MPC that can be solved via min-max optimization using a single linear program. The theory of robust invariant sets is investigated and applied. Further an algorithm for finding robust invariant and feasible sets, that are used in the new linear cost function, is presented. These suggested robust invariant sets have suitable properties and are less computational intensive. A min-max formulation of MPC than involves minimization of the maximum of disturbance influence, which range over a given polytope of possible disturbance realizations, is presented. In general, the solution of this problem is computationally demanding with large number of unknown parameters. The appropriate use of the performance criteria with respect to the receding horizon strategy, low complexity robust invariant sets and feedback policy with consideration of only the extreme realizations of disturbance signals can decrease this number of parameters. An efficient solution of the robust min-max optimization defined for mixed 1/∞ norm is given.

A Note to Calculation of Polytopic Invariant and Feasible Sets for Linear Continuous-Time Systems

A common way of guaranteeing stability in model predictive control (MPC) is to add into the open-loop optimization problem a terminal constraint set which is invariant and feasible. This note presents an algorithm for calculation of low-complexity polytopic invariant sets for linear continuous-time systems with complex conjugate closed-loop eigenvalues. Non-symmetrical amplitude and rate input constraints are considered.

Enlarged terminal sets guaranteeing stability of receding horizon control

The purpose of this paper is to relax the terminal conditions typically used to ensure stability in model predictive control, thereby enlarging the domain of attraction for a given prediction horizon. Using some recent results, we present novel conditions that employ, as the terminal cost, the finite-horizon cost resulting from a nonlinear controller u=−sat( Kx) and, as the terminal constraint set, the set in which this controller is optimal for the finite-horizon constrained optimal control problem. It is shown that this solution provides a considerably larger terminal constraint set than is usually employed in stability proofs for model predictive control.