Function Based Model Predictive Control Research Articles

Control Lyapunov–Barrier function based model predictive control for stochastic nonlinear affine systems

AbstractA stochastic model predictive control (MPC) framework is presented in this paper for nonlinear affine systems with stability and feasibility guarantee. We first introduce the concept of stochastic control Lyapunov–Barrier function (CLBF) and provide a method to construct CLBF by combining an unconstrained control Lyapunov function (CLF) and control barrier functions. The unconstrained CLF is obtained from its corresponding semi‐linear system through dynamic feedback linearization. Based on the constructed CLBF, we utilize sampled‐data MPC framework to deal with states and inputs constraints, and to analyze stability of closed‐loop systems. Moreover, event‐triggering mechanisms are integrated into MPC framework to improve performance during sampling intervals. The proposed CLBF based stochastic MPC is validated via an obstacle avoidance example.

Barrier Lyapunov Function Based Model Predictive Control of a Morphing Waverider With Input Saturation and Full-State Constraints

With the fast development in aeronautical technology, aircraft are evolving towards a wider speed ranging from subsonic, transonic, and supersonic to hypersonic speeds. The variable-sweep-wing morphing waverider provides an effective way to meet the demanding wide-speed and long-range flight requirements. However, the special morphing mechanism, variable stability margin, and the aero-thermal heating of the morphing waverider, altogether impose difficulties and challenges on its flight tracking control problem, especially under parameter uncertainties, input saturation, and state constraints. To handle this issue, a six-degrees-of-freedom (6DOF) Barrier-Lyapunov-Function (BLF) based nonlinear model predictive controller (NMPC) consisting of two loops is proposed in this paper based on the control-oriented model of a symmetric-sweep-wing morphing waverider. Specifically, a virtual control signal of three-axis angular rates is provided by the BLF based outer-loop NMPC to not violate the flight constraints, combined with an auxiliary system according to the desired angle of attack, sideslip angle, and bank angle. Then, the desired virtual control signal is modified by a saturation function and a first-order command filter, and the control commands are generated by the BLF based inner-loop NMPC to deal with the input saturation by an auxiliary system. Meanwhile, a nonlinear disturbance observer is applied to estimate the morphing moments considering parameter uncertainties. The stability of the overall closed-loop system is analyzed by the Lyapunov stability theory. Finally, the performance of the controller is investigated via extensive and comparative numerical simulations.

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

AbstractA design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed‐loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling‐hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed‐loop system. The effectiveness of the proposed method is illustrated through a chemical process example.

Improved Model Predictive Control with Prescribed Performance for Aggregated Thermostatically Controlled Loads

Aggregate thermostatically controlled loads (ATCLs) are a suitable candidate for power imbalance on demand side to smooth the power fluctuation of renewable energy. A new control scheme based on an improved bilinear aggregate model of ATCLs is investigated to suppress power imbalance. Firstly, the original bilinear aggregate model of ATCLs is extended by the second-order equivalent thermal parameter model to optimize accumulative error over a long time scale. Then, to ensure the control performance of tracking error, an improved model predictive control algorithm is proposed by integrating the Lyapunov function with the error transformation, and theoretical stability of the proposed control algorithm is proven. Finally, the simulation results demonstrate that the accuracy of the improved bilinear aggregate model is enhanced; the proposed control algorithm has faster convergence speed and better tracking accuracy in contrast with the Lyapunov function-based model predictive control without the prescribed performance.

Laguerre function-based model predictive control for multiple product inventory systems

ABSTRACT This paper describes Laguerre function-based model predictive control for a multiple-product inventory system. In periodic review inventory systems the control law is designed for replenishment orders to fill the stock. The orders for the products are issued such that the demand for the product is met and desired stock is maintained. The demand for the products is unknown prior and does not affect the system dynamics but the supplies and the arriving orders for their replenishment do affect the system. Model predictive control (MPC) is well known for constraint handling and Laguerre function based MPC is aimed to reduce the number of parameters in control thus enhancing computational efficiency. A set of discrete orthonormal basis function is introduced into the design to reduce the number of parameters. The control law for replenishment orders is derived to maintain desired stocks of the products in the inventory and to optimise the profit from the sale. Simulation results on a two product inventory system are shown for validation.

Sparsity-Exploiting Anytime Algorithms for Model Predictive Control: A Relaxed Barrier Approach

We present and analyze a novel class of stabilizing and numerically efficient model predictive control (MPC) algorithms for discrete-time linear systems subject to polytopic input and state constraints. The proposed approach combines the previously presented concept of relaxed barrier function-based MPC with suitable warm-starting and sparsity-exploiting factorization techniques and allows to rigorously prove important stability and constraint satisfaction properties of the resulting closed-loop system independently of the number of performed Newton iterations. The effectiveness of the proposed approach is demonstrated by means of a numerical benchmark example.

Real-time Machine Learning-Based CLBF-MPC of Nonlinear Systems

In this work, a real-time Control Lyapunov-Barrier Function-based model predictive control (CLBF-MPC) system using recurrent neural network (RNN) models is developed for a general class of nonlinear systems to ensure closed-loop stability and operational safety accounting for time-varying disturbances. An RNN model is first constructed for the nominal system (i.e., without disturbances) and utilized in the design of CLBF-MPC to provide state prediction. Subsequently, to improve the closed-loop performance in terms of operational safety and stability in the presence of disturbances, online learning of RNN models is incorporated within the real-time implementation of CLBF-MPC to update the RNN models using the most recent process measurement data. The proposed adaptive machine-learning-based CLBF-MPC method is evaluated using a nonlinear chemical process example.

Control Lyapunov-Barrier function-based model predictive control of nonlinear systems

In this paper, we propose a Control Lyapunov-Barrier Function-based model predictive control (CLBF-MPC) method for solving the problem of stabilization of nonlinear systems with input constraint satisfaction and guaranteed safety for all times. Specifically, considering the input constraints, a constrained Control Lyapunov-Barrier Function is initially employed to design an explicit control law and characterize a set of initial conditions, starting from which the solution of the nonlinear system is guaranteed to converge to the steady-state without entering a specified unsafe region in the state space. Then, the CLBF-MPC is proposed and is shown to be recursively feasible, and stabilizing and to ensure the avoidance of a set of states in state–space associated with unsafe operating conditions under sample-and-hold control action implementation. Finally, we demonstrate the efficacy of the proposed CLBF-MPC method through application to a chemical process example.

A Lyapunov function based model predictive control for three phase grid connected photovoltaic converters

In this paper, a predictive direct power control (PDPC) method based on Lyapunov function approach is developed for control of grid connected photovoltaic (PV) converter. The predictive control algorithm utilizes the discrete model of the PV converter and predicts the future active and reactive power of the system by calculating a cost function for all voltage vectors. Subsequently, the optimal voltage vector that minimizes the cost function is selected to calculate the model variables in the next sampling instant. The proposed controller predicts error before the switching signal is applied to the high-gain multilevel PV converter and thus is able to choose the next switch event to minimize error between the commanded and actual converter operation. This technique improves the speed at which the controller can track rapid changes in solar insolation and results in an increase in the overall system output power. In the proposed technique, there is no need to adjust the control parameters under changing loads or model parameters uncertainties. Also, the use of many classical controllers is eliminated and only one PI controller is used for DC link voltage. Moreover, contrary to the conventional PDPC, the optimal switching vector is determined only based on active and reactive power and hence, the computation burden is significantly reduced and the convergence is speed up. The detail modeling and design of the proposed controller are verified through computer simulations under different operating conditions. Also, the robustness of the control approach is illustrated in the presence of parameters uncertainties and change in solar irradiations. Simulation results show that the proposed control strategy maintains the active and reactive powers as close as possible to the desired values under different operation mode.

Handling bounded and unbounded unsafe sets in Control Lyapunov-Barrier function-based model predictive control of nonlinear processes

Control Lyapunov-Barrier function (CLBF) has been used to design controllers for nonlinear systems subject to input constraints to ensure closed-loop stability and process operational safety simultaneously. In this work, we developed Control Lyapunov-Barrier functions for two types of unsafe regions (i.e., bounded and unbounded sets) to solve the problem of stabilization of nonlinear systems with guaranteed process operational safety. Specifically, in the presence of a bounded unsafe region embedded within the closed-loop system stability region, the CLBF-MPC is developed by incorporating CLBF-based constraints and discontinuous control actions at potential stationary points (except the origin) to guarantee the convergence to the origin (i.e., closed-loop stability) and the avoidance of unsafe region (i.e., process operational safety). In the case of unbounded unsafe sets, closed-loop stability with safety is readily guaranteed under the CLBF-MPC since the origin is the unique stationary point in state-space. The application of the proposed CLBF-MPC method is demonstrated through a chemical process example with a bounded and an unbounded unsafe region, respectively.

Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear Systems

In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further properties like performance and constraint satisfaction in dependence of the underlying relaxation. The proposed stabilizing MPC schemes are not necessarily based on an explicit terminal set or state constraint and allow to characterize the stabilizing control input sequence as the minimizer of a globally defined, continuously differentiable, and strongly convex function. The results are illustrated by means of a numerical example.

Energy Function-Based Model Predictive Control With UPFCs for Relieving Power System Dynamic Current Violation

This paper suggests a novel dynamic protection/control scheme with unified power flow controller (UPFC) to prevent transmission system overload. A transient energy function (TEF)-based model predictive control (MPC) methodology is developed to reduce control cost and enhance power grid resilience. First, a TEF and an associated cost function of UPFCs are constructed based on ac dynamic model with transmission over-current tripping model. Then the derived control constraint for MPC exploits the non-positive time derivative of the TEF with the accommodated admittance, which are optimally regulated by UPFC inputs, to mitigate dynamic current violation based on sensitivity analysis. With the proposed control method, the system can be driven to a stable state without current violation even if part of the UPFCs fails. Finally, the simulation results of 14 bus test case and 118 bus test case demonstrate the effectiveness of our proposed method, as well as the advantage over conventional MPC method.

Continuous-time linear MPC algorithms based on relaxed logarithmic barrier functions

In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. In particular, barrier function based continuous-time algorithms are considered, in which the control input is obtained as the sampled output of a continuous-time dynamical system. We present suitable barrier function relaxations as well as results on closed-loop stability and the satisfaction of state and input constraints. The results also apply to conventional barrier function based model predictive control schemes.

Constrained control Lyapunov function based model predictive control design

SUMMARYThis work considers linear systems with input constraints with the objective of designing a controller that guarantees stability from all initial conditions in the null‐controllable region (the set of initial conditions from where the system can be stabilized). To this end, a recently developed procedure for construction of constrained control Lyapunov functions is utilized within a Lyapunov‐based model predictive controller coupled with an auxiliary control design to achieve stabilization from all initial conditions in the null‐controllable region. Illustrative simulation results as well as an application to a nonlinear chemical process example is presented to demonstrate the efficacy of the results.Copyright © 2012 John Wiley & Sons, Ltd.

A Model Predictive Navigation Approach Considering Mobile Robot Shape and Dynamics

Most mobile robot navigation approaches assume the robot being point-like or consider only its bounding circle while looking for a collision-free path to a given goal position. A well-known method called the Dynamic Window Approach (DWA) introduced an interesting idea for solving the navigation problem by local optimization in the control space of the robot. Some extensions of the original DWA method can also be found in the literature, which enable its applicability to holonomic and non-holonomic robots and ensure a global and safe solution to the navigation problem. The method described in this paper has also been motivated by the basic idea of dynamic window and contributes to the previous variants by taking the robot shape into consideration as well. A navigation function based model predictive control scheme is utilized to choose the appropriate control for a safe and successful navigation.

Application of barrier function based model predictive control to an edible oil refining process

We use multivariable feedback control to reduce variations in flow and back-pressure associated with two industrial separator units forming part of an edible oil refining line. This provides plant operators with a mechanism for increasing process yield without reducing product quality. Actuator limits are a natural consideration in the controller design since increased production rates require actuators to operate on or near their limits. We use recentred barrier function model predictive control in this application and obtain favourable results.

Barrier function based model predictive control

A new formulation of nonlinear model predictive control (MPC) is developed by including a weighted barrier function in the control objective. While the barrier ensures that inequality constraints are strictly satisfied it also provides a smooth transition between points in the interior and those on the boundary of the constraint set. In addition, the resulting optimisation problem, to be solved at each control step, is effectively unconstrained and thus amenable to elegant optimisation techniques. The barrier must satisfy certain conditions in order that the state converges to the origin and we show how to construct such a barrier. Conventional MPC may be seen as a limiting case of the new class as the barrier weighting itself approaches zero. We pay particular attention to the novel approach of fixing the weighting parameter to some positive value—possibly large—and observe that this provides a degree of controller caution near constraint boundaries. We construct an ellipsoidal invariant set by exploiting the geometry of self-concordant functions and show nominal closed-loop stability for this class of controllers under full state feedback.