Indirect Adaptive MPC for Discrete-Time LTI Systems With Parametric Uncertainties

In this note, we present a model predictive control (MPC) algorithm for uncertain time-varying systems with input constraints and state-delay. Uncertainty is assumed to be polytopic, and delay is assumed to be unknown but with a known upper bound. For a memoryless state-feedback MPC law, we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function. One is solvable and the other is not. We prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix. Based on these properties and optimality, we show that feasible MPC from the optimization problems stabilizes the closed-loop system. Then, we present an improved MPC algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed-loop system. Finally, a numerical example illustrates the performance of the proposed algorithm.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

Glycemic control can reduce the mortality and morbidity of intensive care patients. The CLINICIP (closed-loop insulin infusion for critically ill patients) project aimed to develop a closed-loop control system for this patient group. Following a stepwise approach, we combined three independently tested subparts to form a semiautomatic closed-loop system and evaluated it with respect to safety and performance aspects by testing it in subjects with type 1 diabetes mellitus (T1DM) in a first feasibility trial. Vascular microdialysis, a multianalyte infrared spectroscopic glucose sensor, and a standard insulin infusion pump controlled by an adaptive model predictive control (MPC) algorithm were combined to form a closed-loop device, which was evaluated in four T1DM subjects during 30-hour feasibility studies. The aim was to maintain blood glucose concentration in the target range between 80 and 110 mg/dl. Mean plasma glucose concentration was 110.5 ± 29.7 mg/dl. The MPC managed to establish normoglycemia within 105 ± 78 minutes after trial start and managed to maintain glucose concentration within the target range for 47% of the time. The hyperglycemic index averaged to 11.9 ± 5.3 mg/dl. Data of the feasibility trial illustrate the device being effective in controlling glycemia in T1DM subjects. However, the monitoring part of the loop must be improved with respect to accuracy and precision before testing the system in the target population.

In this work, we formulate a new, nonlinear, and time-variant transmitter equalization method based on the Model Predictive Control (MPC) algorithm. MPC is a class of control algorithms in which the current control action is obtained by solving, perhaps approximately, an online open-loop optimal control problem. One important advantage of the MPC in peak-power constrained link environment is its ability to cope with hard constraints on controls and states. Knowing the state of the channel enables a very fine nonlinear equalization. We utilize this flexibility to create various MPC formulations that control the entire eye-mask, receive signal dynamic range as well as the required quantization. Our MPC equalization significantly outperforms traditional transmitter techniques such as linear feed-forward and Tomlinson-Harashima equalizers, and gets very close to the optimized decision-feedback equalization at lower transmitter resolutions. We also describe the possible complexity reduction techniques that enable efficient implementation of our MPC algorithm in hardware.

This paper discusses the possibility of using a Jordan neural network as a model of dynamic systems and it presents a Model Predictive Control (MPC) algorithm in which such a network is used for prediction. The Jordan network is a simple recurrent neural structure in which only one value of the process input signal (from the previous sampling instant) and only one value of the delayed output signal of the model (from the previous sampling instant) are used as the inputs of the network. In order to obtain a computationally simple MPC algorithm, the nonlinear Jordan neural model is repeatedly linearised on-line around an operating point, which leads to a quadratic optimisation problem. Effectiveness of the described MPC algorithm is compared with that of the truly nonlinear MPC scheme with on-line nonlinear optimisation performed at each sampling instant.

This paper is concerned with a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm based on neural Wiener models. The model contains a linear dynamic part in series with a steady-state nonlinear part which is realised by a neural network. The model is linearised on-line, as a result the nonlinear MPC algorithm needs solving a quadratic programming problem. The algorithm gives control performance similar to that obtained in nonlinear MPC, which hinges on non-convex optimisation. In order to demonstrate accuracy and computational efficiency of the considered MPC algorithm, a polymerisation reactor is studied.

A novel approach to the design of a model predictive control (MPC) algorithm for a complex plant (with energy integration and mass recycles) is given. Sensitivity analysis and steady‐state optimization are used to determine the manipulated variables that have the strongest influence on the objective function of the operation. This allows a reduction of the number of variables that are optimized on‐line, as well as the use of detailed, first‐principle–based models in the MPC algorithm, thus resulting in more reliable predictions. Moreover, the same algorithm can be used to control plants of different size, without the need of a new calibration of the parameters of the model. The application of this procedure to a pressure‐swing distillation unit is given as an example. © 2006 American Institute of Chemical Engineers AIChE J, 2006

This paper presents a model predictive control (MPC) algorithm designed for the cooling system of a small commercial building under a time-dependent electricity price profile. The proposed approach includes a problem formulation in terms of cooling power, a variable-length prediction horizon and the consideration of the equipment duty cycle as a constraint in the optimization algorithm. The cooling system is equipped with an ice bank for thermal energy storage. A simple linear building thermal model is used to calculate the required amount of cooling power to maintain thermal comfort. The MPC algorithm uses this information to find the optimal operating points for the chiller and the ice bank to minimize the electric energy cost. The results of the MPC algorithm are compared against those of the reactive rule-based control algorithm currently in use in the building.

Computationally efficient nonlinear predictive control based on neural Wiener models

In this paper, the unmanned vehicle trajectory tracking problems were studied. In order to improve the stability of unmanned vehicles, the trajectory tracking control algorithm based on model predictive control (MPC) algorithm was researched by adding the dynamic constraints of centroid, acceleration and tire side angle on the basis of vehicle dynamics model. The trajectory planning layer was established on top of the trajectory tracking control layer, and the Carsim/Simulink simulation platform was built. At different speeds and under different road adhesion conditions, the algorithm was verified and compared. The simulation results showed that the model predictive control algorithm with dynamic constraints was provided with excellent tracking performance under severe conditions and well adaptive to environment interference.

In this article, two new algorithms of the redundant force branch of 6-PUS/UPU parallel robot are proposed. They are model predictive control combining with proportional, integral, and differential algorithm and fuzzy combining with model predictive control algorithm. The shortcoming of the traditional model predictive control algorithm is complex adjustment, large amount of calculation, the dynamic performance effect of the system. The proposed PID model predictive control algorithm can make the controller parameters adjustment more convenient. However, PID model predictive control algorithm can’t obtain good control performance under sudden change in situation. Combining model predictive control algorithm with fuzzy theory, fuzzy model predictive control algorithm has better anti-interference ability than PID model predictive control algorithm and can reduce predictive horizon length as possible as it can. Simulation results show that fuzzy model predictive control algorithm can effectively improve real-time performance of control system, the dynamic tracking performance and robustness than the traditional model predictive control and PID model predictive control algorithm.

Two methods of prediction improvement in Model Predictive Control (MPC) algorithms utilizing fuzzy Hammerstein models are proposed in the paper. The first one consists in iterative adjustment of the prediction, the second one – in utilization of disturbance measurement. Though the methods can significantly improve control system operation, they modify the prediction in such a way that it is described by relatively simple analytical formulas. Thus, the prediction has such a form that the MPC algorithms using it are formulated as numerically efficient quadratic optimization problems. Efficiency of the MPC algorithms based on the prediction utilizing the proposed methods of improvement is demonstrated in the example control system of a nonlinear control plant with significant time delay.

When the structure information of a redundant manipulator is unknown, motion control methods that do not rely on its model are attractive. Due to the numerous advantages of model predictive control (MPC), such as the direct handling of constraints, this paper proposes a model-free MPC algorithm for redundant manipulators with unknown structure information. In this paper, a cerebellum-inspired model based on the echo state network (ESN) is employed to replace the kinematic model of the redundant manipulator, and an MPC algorithm based on the cerebellum model and neural dynamics (ND) approach is developed. Unlike existing studies, this work considers both performance optimization and system constraints of the redundant manipulator, and can achieve high-precision prediction and tracking by designing an online training algorithm for the cerebellum model. Furthermore, this paper proposes an ND-based correction algorithm to modify the prediction model and an ND solver to solve the MPC scheme. Theoretical analyses confirm the convergence of both the ND-based correction algorithm and ND solver. Simulation and experimental results consistently demonstrate that the proposed cerebellum-inspired MPC (CIMPC) algorithm is effective and outperforms comparison algorithms in terms of tracking performance.

Formulation of a model predictive control algorithm to enhance the performance of a latent heat solar thermal system

The constraints of output variables, input variables and intermediate variables exist widely in chemical process control. The inconsistency in different constraints may make constrained model predictive controller have no feasible solutions, which will bring harmful effect to practical production. To ensure the implementation of model predictive control, using its global optimization performance and constraint handling mechanism, a new particle-swarm optimization algorithm with the function of constraint handling, was proposed in this article. Taking into account the form of constraints and the constraints characteristics of MIMO (multi-input multi-output) predictive control system, this thesis, based on convex polyhedron geometry, discuss the feasibility of constrained model predictive control. Combined with duality theorem, the output constraints of system are transformed into constraints of input. After that, the constraints form which meets the requirements of control algorithm is obtained. Finally, particle swarm optimization algorithm is used to conduct the optimization of predictive control system. The simulation results of MIMO model with constraints showed the advantages and effectiveness of this algorithm.