Off-line Model Predictive Control Research Articles

Dynamic Programming, Neuro-Dynamic Programming, Rollout Method and Model Predictive Control to Optimal Control of a Fermentation Process

This work presents the use of dynamic programming (DP), neuro-dynamic programming (NDP), rollout algorithm (RA) and model predictive control (MPC) for optimal control of batch cultivation of the yeast Kluyveromyces marxianus var. lactis MC5. DP is a widespread method for solving problems related to optimization and optimal process control. To reduce the “curse of dimensionality”, NDP has been implemented as an alternative. In NDP, a neural network is used to solve the dimensionality problem. A simpler NDP method, called RA, is used to approximate the optimal cost through the cost of a relatively good suboptimal policy, called the baseline policy. RA is a suboptimal method for deterministic and stochastic problems that can be solved by DP. In this paper we also present off-line MPC technique for tracking of constrained fermentation systems and it overcomes the problem by off-line optimizations prior to implementation. MPC is used to provide perturbation feedback and it is developed theoretical on base a controller as an illustration how we can avoid disturbances in the process optimisation. The developed control algorithm-combined NDP and MPC ensures maximum biomass production at the end of the process and feedback during disturbances and process stability and shows that robust stability can be ensured.

Offline model predictive control approach to micro-slip control in gearshifts of dual clutch transmission

Dual clutch transmission can avoid some noise vibration and harshness issues caused by other transmissions with single clutch. And applying micro-slip control on clutches can further improve the gearshift performance of transmission compared to the lock-up control. Considering the real-time characteristic of vehicle control, an offline model predictive controller designed by multi-parameter quadratic programming was creatively applied in dual clutch transmission to obtain both clutch torque at the same time with optimal control algorithm. In this way, while realizing the micro-slip state of the clutches, the fast response speed can be realized through the off-line controller, which makes it more feasible and practical for transmission control. A six degrees of freedom vehicle powertrain system model was built in MATLAB/Simulink to simulate the proposed control algorithm. The simulation results show that the micro-slip control avoid the negative torque compared to the lock-up control, which leads to a smoother shift process. In addition, compared with the proportional–integral–derivative micro-slip controller, the offline model predictive controller can achieve more stable control effects with less output torque fluctuation and shorter gearshift time.

LPV-Based Offline Model Predictive Control for Free-Floating Space Robots

In this article, an offline model predictive control (MPC) based on the linear parameter-varying (LPV) model is developed for free-floating space robots. Parameter set mapping is employed to obtain an LPV model with fewer scheduling parameters, which can enable easier control design and achieve more objectives by using linear control methods. In terms of the LPV system with external disturbance, an MPC method is proposed. Since large disturbance to the base attitude is not admissible in certain missions such as communication with the earth, a term related to the base angular velocity is considered as a part of the cost function of MPC. To deal with actuator saturation, input limitations are included in the constraints of MPC. Moreover, an offline algorithm is introduced to reduce the online computation. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

A New Approach to Off-Line Robust Model Predictive Control for Polytopic Uncertain Models

Concerning the robust model predictive control (MPC) for constrained systems with polytopic model characterization, some approaches have already been given in the literature. One famous approach is an off-line MPC, which off-line finds a state-feedback law sequence with corresponding ellipsoidal domains of attraction. Originally, each law in the sequence was calculated by fixing the infinite horizon control moves as a single state feedback law. This paper optimizes the feedback law in the larger ellipsoid, foreseeing that, if it is applied at the current instant, then better feedback laws in the smaller ellipsoids will be applied at the following time. In this way, the new approach achieves a larger domain of attraction and better control performance. A simulation example shows the effectiveness of the new technique.

Switched Offline Multiple Model Predictive Control with Polyhedral Invariant Sets

This paper presents a switched offline multiple model predictive control procedure for nonlinear processes to ease the online computational burden and reduce the number of submodels. We employ the gap metric to characterize the dynamic difference between linear models and establish a linear model bank to approximate the nonlinear system. Based on the robust MPC algorithm, we develop an offline model predictive controller for each submodel. The polyhedral invariant set is utilized to expand the work scope of each local controller. In the offline part, a series of discrete states are selected, the corresponding feedback gains are precomputed, and associated polyhedral invariant sets are constructed. In the online implementation, the control input is simply calculated by calling the feedback gain according to the current state. A switching rule is then designed to integrate the submodels and guarantee the stability of the whole system. Finally, the corresponding simulation example is presented to validate th...

Robust shrinking ellipsoid model predictive control for linear parameter varying system.

In this paper, a new off-line model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. A nest of shrinking ellipsoids is constructed by solving linear matrix inequality. By splitting the objective function into two parts, the proposed strategy moves most computations off-line. The on-line computation is only calculating the current control to assure the system shrinking into the smaller ellipsoid. With the proposed formulation, the stability of the closed system is proved, followed with two numerical examples to demonstrate the proposed method’s effectiveness in the end.

An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes

In this paper, a novel off-line model predictive control strategy for linear parameter varying systems is presented. The on-line computational burdens are reduced by pre-computing off-line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured. The real-time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two examples of continuous stirred tank reactors.

An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems

An off-line Model Predictive Control (MPC) method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances. In order to reduce the computational burdens and conservativeness of traditional polytopic MPC schemes, the present approach carries out off-line most of the computations and it makes use of closed-loop predictions to improve the control performance. This is done by recursively pre-computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on-line a simple and numerically low-demanding optimization problem subject to a set-membership constraint. Comparisons with three other recent off-line MPC approaches are also provided in the final example.

An off-line MPC strategy for nonlinear systems based on SOS programming

A novel moving horizon control strategy for input-saturated nonlinear polynomial systems is proposed. The control strategy makes use of the so called sum-of-squares (SOS) de-composition, i.e. a convexification procedure able to give sufficient conditions on the positiveness of polynomials. The complexity of SOS-based numerical methods is polynomial in the problem size and, as a consequence, computationally attractive. SOS programming is used here to derive an “off-line” model predictive control (MPC) scheme and analyze in depth his properties. Such an approach may lead to less conservative MPC strategies than most existing methods based on the global linearization approach. An illustrative example is provided to show the benefits of the proposed SOS-based algorithm.

New formulation of robust MPC by incorporating off-line approach with on-line optimization

This article addresses robust model predictive control (MPC) for systems with polytopic description. An existing off-line robust MPC enables the on-line computation as simple as searching a state feedback gain among the look-up table. We consider enlarging the region of attraction of the off-line MPC by incorporating free perturbation items. First, a larger ellipsoidal region of attraction is off-line constructed, in which a simple optimization problem is solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved on-line such that the overall region of attraction can be rendered as a much larger nonellipsoidal one. The proposed approach possesses all the merits of the off-line MPC and greatly enlarges the region of attraction. A simulation example is given to demonstrate the effectiveness.

Application of off-line model predictive control to pneumatic systems

Pneumatic systems usually have not only nonlinearity but also hard limits on the control input and output. To cope with these property and constraints, an off-line model predictive control method is applied to a pneumatic system. Unlike standard model predictive control methods, this method can deal with systems that have relatively fast dynamics because the on-line computation is reduced by computing a sequence of feedback gains in advance. Experimental results show the effectiveness of the control method.