Stability Of Predictive Control Research Articles

Stable predictive control of continuous stirred-tank reactors using deep learning

In this work, a Lyapunov-based predictive control method utilizing deep learning techniques is proposed for driving continuous-time nonlinear processes towards the desired equilibrium point. Initially, a neural ordinary differential equation model is developed to learn the continuous-time dynamics from discrete-time sampling data. Subsequently, the theoretical conditions that the control Lyapunov function (CLF) developed on the learned continuous-time system is feasible to act on the actual system through a zero-order-holder are analyzed. Building upon the theoretical analysis and the constructed continuous-time dynamics, a deep neural network control Lyapunov function (DNN-CLF) controller is developed. Importantly, the DNN-CLF is independent of the affine system formulation, effectively addressing the challenge of designing the CLF. Benefiting from the stability guarantee provided by the established DNN-CLF, it is integrated into the model predictive control (MPC) framework to develop Lyapunov-based MPC to further improve the control performance. To ensure safety, considering error propagation and associated risks with enlarging the feasible region of the CLF, tubes are constructed and integrated into the MPC scheme. Finally, a numerical simulation of a chemical process is conducted to validate the efficiency of the proposed method.

Input‐to‐state stable predictive control based on continuous projected kinky inference

Input‐to‐state stable predictive control based on continuous projected kinky inference

Generalized ESO based stable predictive tracking control for micro gas turbine cogeneration system

Control of micro gas turbine combined heating and power (MGT-CHP), i.e., cogeneration systems, is challenging because of large inertia, strong coupling, strict input constraints, nonlinearity, and complex disturbances. To overcome these problems, this paper develops an extended state observer (ESO) based stable predictive tracking control (SPTC) for MGT-CHP. Unlike traditional ESO-based control methods, ESO-SPTC guarantees overall optimality by using disturbance feedback compensation. A new discrete-time generalized ESO is developed for the ESO-SPTC to surmount higher-order disturbances and its bounded stability is demonstrated. Besides, the designed SPTC fully guarantees that the infinite horizon inputs fully satisfy the amplitude and rate constraints. The resulting ESO-SPTC can eliminate the impact of matched and unmatched disturbances in the output channel at a steady state. Simulation results on a numerical example and an 80 kW MGT-CHP verify the effectiveness of the control scheme.

Improving the Performance of Single-Intersection Urban Traffic Networks Based on a Model Predictive Controller

The use of a Model Predictive Controller (MPC) in an urban traffic network allows for controlling the infrastructure of a traffic network and errors in its operations. In this research, a novel, stable predictive controller for urban traffic is proposed and state-space dynamics are used to estimate the number of vehicles at an isolated intersection and the length of its queue. This is a novel control strategy based on the type of traffic light and on the duration of the green-light phase and aims to achieve an optimal balance at intersections. This balance should be adaptable to the unchanging behavior of time and to the randomness of traffic situations. The proposed method reduces traffic volumes and the number of crashes involving cars by controlling traffic on an urban road using model predictive control. A single intersection in Tehran, the capital city of Iran, was considered in our study to control traffic signal timing, and model predictive control was used to reduce traffic. A model of traffic systems was extracted at the intersection, and the state-space parameters of the intersection were designed using the model predictive controller to control traffic signals based on the length of the vehicle queue and on the number of inbound and outbound vehicles, which were used as inputs. This process demonstrates that this method is able to reduce traffic volumes at each leg of an intersection and to optimize flow in a road network compared to the fixed-time method.

Asymptotically Stable Predictive Control of Grid-Connected Converter Based on Discrete Space Vector Modulation

This paper presents an alternative implementation of the finite control set model predictive control (FCS-MPC) approach for a 3-O, two-level grid-connected power converter. The presented approach combines the concept of discrete space vector modulation into the FCS-MPC structure to improve the input current quality of the power converter. Further, with the help of Lyapunov's stability theory, it is shown that the predictive control law used in the present analysis ensures the stability of the overall system. However, the additional virtual voltage vectors can cause an unacceptable computational burden to the controller. To alleviate this issue, the proposed control approach uses a preselection technique that reduces the number of possible voltage vectors for the optimization process from 38 to 10, thereby allowing the proposed technique to be implemented in a standard control platform. Finally, measurement results are presented from an experimental prototype which demonstrates the efficacy of the proposed algorithm concerning the improvement of the input current quality.

Adaptive Output Feedback Control with an Adaptive Predictive Feedforward Input for Continuous-Time Systems

In this paper, adaptive output feedback based tow-degree-of-freedom control with an adaptive output predictive control as a feedforward input is proposed for linear continuous-time systems. The method can design a stable and simple output predictive control based adaptive controller with higher control performance for uncertain systems. A simple adaptive output estimator and predictor for uncertain systems will be proposed to design a robust predictive controller for continuous-time systems, and the stability of the obtained control system will be maintained by ASPR based adaptive output feedback. The effectiveness of the proposed method is confirmed through numerical simulations for simple second order uncertain system.

A Sustainable Power Plant Control Strategy Based on Fuzzy Extended State Observer and Predictive Control

The control of an ultra-supercritical (USC) boiler–turbine power plant is critical in maintaining the safety of the sustainable power grid. However, it is challenging due to the internal nonlinearity, hard manipulation constraints, and widespread uncertainties. To this end, a fuzzy extended state observer (FESO)-based stable fuzzy predictive control (SFPC) approach is developed in this paper. First, the control difficulties of the USC boiler–turbine unit are analyzed. Then, based on a Takagi–Sugeno (T–S) fuzzy model, a new FESO is developed for nonlinear systems to achieve a more precise observation performance. The gain of FESO is determined by solving a series of linear matrix inequalities, while guaranteeing the stability of FESO. Then, by combining the proposed FESO with the SFPC, an integrated FESO–SFPC algorithm is devised. The disturbance rejection ability of the FESO–SFPC algorithm is analyzed theoretically. Simulation results on a 1000 MW USC boiler–turbine power plant model further validate the effectiveness of the proposed method.

Stable robust predictive controller for nonlinear systems

Stability of robust model predictive controller for SISO nonlinear dynamical systems is established in this paper. The neural networks model with parameter uncertainties is used to approximate the process behaviour having different point functions. The control input action is obtained by solving online the minimax optimisation problem subject to the model uncertainties and the input constraints. We have also studied the stability of the closed loop system in the presence of model uncertainties by using the Lyapunov theory. A comparison study between the PID controller and the proposed robust predictive controller was performed to validate the feasibility of the use of the uncertain neural networks in control theory. A simulation example is presented in order to illustrate the efficiency of the proposed controller.

Stable robust predictive controller for nonlinear systems

Stability of robust model predictive controller for SISO nonlinear dynamical systems is established in this paper. The neural networks model with parameter uncertainties is used to approximate the process behaviour having different point functions. The control input action is obtained by solving online the minimax optimisation problem subject to the model uncertainties and the input constraints. We have also studied the stability of the closed loop system in the presence of model uncertainties by using the Lyapunov theory. A comparison study between the PID controller and the proposed robust predictive controller was performed to validate the feasibility of the use of the uncertain neural networks in control theory. A simulation example is presented in order to illustrate the efficiency of the proposed controller.

Non-smooth predictive control for mechanical transmission systems with backlash-like hysteresis

This paper proposes a non-smooth predictive control approach for mechanical transmission systems described by dynamic models with preceded backlash-like hysteresis. In this type of system, the work platform is driven by a DC motor through a gearbox. The work platform is represented by a linear dynamic sub-model connected in series with a backlash-like hysteresis inherent in gearbox. Here, backlash-like hysteresis is modeled as a non-smooth function with multi-valued mapping. In this case, the conventional model predictive control for such system cannot be implemented directly since the gradients of the control objective function with respect to control variables do not exist at non-smooth points. In order to solve this problem, a non-smooth receding horizon strategy is proposed. Moreover, the stability of predictive control of such non-smooth dynamic systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are presented for validating the proposed method.

Model Predictive Control for Linear Impulsive Systems

Linear Impulsive Control Systems have been extensively studied with respect to their equilibrium points which, in most cases, are no other than the origin. However, the trajectory of the system cannot be stabilized to arbitrary desired points which imposes a significant restriction towards their utilization in various applications such as drug administration. In this paper, we study the equilibrium of Linear Impulsive Systems in light of target-sets instead of the standard equilibrium point approach. We properly extend the notion of invariant sets which is crucial in designing asymptotically stable Model Predictive Controllers (MPC).

Multivariable Generalized Predictive Control Design: Application for Couple of DC Motors

The paper presents method for design stable generalized predictive controller in the frequency domain and its application on model of couple DC motors. The frequency domain predictive methods are easier for application and can improve performance of control circuit. This way the presented predictive control method can be used in practice on real devices like FPGA without needs of complicated numerical calculations. Numerical results based on identification of real process are given to illustrate the effectiveness of the proposed method

Stable Adaptive Predictive Control System Design via Adaptive Output Predictor for Multi-rate Sampled Systems

This paper deals with a design problem of an adaptive predictive control for uncertain multi-rate sampled systems. In the proposed method, an adaptive predictive control using a simple adaptive output estimator, which has been previously proposed for single-rate sampled system, will be expanded to a multi-rate sampled system. A robust and model-free design method of feedforward compensators for designing the adaptive output estimator for predictive control and for setting an input constraint, “almost strictly positive real (ASPR) constraint” for stable control system will also be provided for the considered multi-rate systems. The effectiveness of the proposed method will be confirmed through an experiments of two-tank process control.

Stable predictive controller design with pole location specification

The paper presents a stable predictive controller design based on solving a linear matrix inequality. The main idea is the augmentation of the state-space model with model prediction to obtain predicted values of output and input signals. Performance specification is a desired closed-loop poles location in a circle in the complex plane. Structure of the practical implementation is provided. Simulation example of light intensity control proves applicability of the controller design.

Stable Predictive Control with Input Constraints Based on Variable Gain Approach

The paper presents a method of the predictive controller design which guarantees robust stability of the closed-loop system and minimizes the sum of squares of errors. Design is divided into the robust stabilization based on the robust PID controllers, optimal control with minimization of the cost function and soft input constraints handling with a variable gain. Stability is guaranteed in the presence of input constraints. Results are experimentally confirmed on the magnetic levitation model which is an unstable SISO process.

Constrained multivariable stable predictive control based on Toeplitz equation

A stable constrained multivariable predictive control algorithm based on the Toeplitz predictive equation is presented. An analytical method for transformation between left and right coprime factorization of multivariable system is put forward, and then an unconstrained control law and its stable condition are given. Furthermore, for the constrained multivariable controlled system, a predictive controller and its asymptotically stable condition are presented and proved. Finally, the constrained receding horizon optimization is transformed into a typical linear matrix inequality (LMI) problem and solved. The detailed control algorithm is depicted in a numerical example, and the simulation results reveal the effectiveness and practicability of the presented algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Design and Application of Stable Predictive Controller Using Recurrent Wavelet Neural Networks

This paper presents a design methodology for stable predictive control of nonlinear discrete-time systems via recurrent wavelet neural networks (RWNNs). This type of controller has its simplicity in parallelism to conventional generalized predictive control design and efficiency to deal with complex nonlinear dynamics. A mathematical model using RWNN is constructed, and a learning algorithm adopting a recursive least squares is employed to identify the unknown parameters in the consequent part of the RWNN. The proposed control law is derived based on the minimization of a modified predictive performance criterion. Two theorems are presented for the conditions of the stability analysis and steady-state performance of the closed-loop systems. Numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results for position control of a positioning mechanism show the efficacy of the proposed method with setpoint changes.

Rapid Load Following of an SOFC Power System via Stable Fuzzy Predictive Tracking Controller

The solid oxide fuel cell (SOFC) is widely accepted for clean and distributed power generation use, but critical operation problems often occur when the stand-alone fuel cell is directly connected to the electricity grid or the dc electric user. In order to address these problems, in this paper, a data-driven fuzzy modeling method is employed to identify the dynamic model of an integrated SOFC/capacitor system. A novel offset-free input-to-state stable fuzzy predictive controller is developed based on the obtained fuzzy model. Both the rapid power load following and safe SOFC operation requirements are taken into account in the design of the closed-loop control system. Simulations are also given to demonstrate the load following control performance of the proposed fuzzy predictive control strategy for the SOFC/capacitor power system.

Output tracking of constrained nonlinear processes with offset-free input-to-state stable fuzzy predictive control

This paper develops an efficient offset-free output feedback predictive control approach to nonlinear processes based on their approximate fuzzy models as well as an integrating disturbance model. The estimated disturbance signals account for all the plant–model mismatch and unmodeled plant disturbances. An augmented piecewise observer, constructed by solving some linear matrix inequalities, is used to estimate the system states and the lumped disturbances. Based on the reference from an online constrained target generator, the fuzzy model predictive control law can be easily obtained by solving a convex semi-definite programming optimization problem subject to several linear matrix inequalities. The resulting closed-loop system is guaranteed to be input-to-state stable even in the presence of observer estimation error. The zero offset output tracking property of the proposed control approach is proved, and subsequently demonstrated by the simulation results on a strongly nonlinear benchmark plant.

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.