Generalized Data–Driven Predictive Control:Merging Subspace and Hankel Predictors

Data–driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems. Two main approaches exist within DPC: the subspace approach, which estimates prediction matrices (unbiased for large data) and the behavioral, data-enabled approach, which uses Hankel data matrices for prediction (allows for optimizing the bias/variance trade–off). In this paper we develop a novel, generalized DPC (GDPC) algorithm by merging subspace and Hankel predictors. The predicted input sequence is defined as the sum of a known, baseline input sequence, and an optimized input sequence. The corresponding baseline output sequence is computed using an unbiased, subspace predictor, while the optimized predicted output sequence is computed using a Hankel matrix predictor. By combining these two types of predictors, GDPC can achieve high performance for noisy data even when using a small Hankel matrix, which is computationally more efficient. Simulation results for a benchmark example from the literature show that GDPC with a reduced size Hankel matrix can match the performance of data–enabled predictive control with a larger Hankel matrix in the presence of noisy data.</p

Offset–free data–driven predictive control

This paper presents a tutorial overview of model predictive control (MPC), subspace predictive control (SPC) and data-enabled predictive control (DeePC), with emphasis on offset-free design. Based on recent results on offset-free SPC design and on the relation between SPC and DeePC, we show that when incremental inputs are used in the identification step (SPC) or in the Hankel matrix (DeePC), the resulting data- driven predictive controllers are offset-free. Moreover, they are equivalent with offset-free MPC in the deterministic case. For noisy data the equivalence does not hold and a regularized version of the DeePC algorithm is necessary. We show that regularized DeePC can be formulated as a Tikhonov regularized least squares problem. This enables systematic tuning of the regularization parameter. We compare the performance of the offset-free data-driven predictive controllers in an application example from high-precision mechatronics

Efficient Implementation and Sampling Period Analysis of MPC for Water Distribution Networks

In this paper we consider the design and implementation of Model Predictive Control (MPC) for water distribution networks (WDNs). First, we define the nonlinear differential algebraic equations that model a WDN, using both classical methods and simplified pump implementations. Then the cost function used in the MPC algorithm is formulated, where extra steps are taken to build a quadratic and convex cost function. The entire control problem is solved using a tailored sequential quadratic programming (SQP) method. The resulting control algorithm for WDNs is tested on a small distribution network to both illustrate the effectiveness and to perform additional tests on the effects of reducing the sampling period. The simulation results of this experiment indicate that the presented SQP-MPC can be implemented at faster rates than 1 hour and that this results in improved economic benefits

Parallel Shooting Sequential Quadratic Programming for Nonlinear MPC Problems

In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess sequential convergence over many initial trajectories in parallel. However, if none converge, the algorithm starts varying the Newton step size in parallel instead. Through this parallel shooting approach, it is expected that the number of iterations to converge to an optimal solution can be decreased. Furthermore, the algorithm can be further expanded and accelerated by implementing it on GPUs. We illustrate the effectiveness of the proposed Parallel Shooting Sequential Quadratic Programming (PS-SQP) method in some benchmark examples for nonlinear model predictive control. The developed PS-SQP parallel solver converges faster on average and especially when significant nonlinear behaviour is excited in the NMPC horizon.</p

Data-driven rate-based integral predictive control with estimated prediction matrices

This paper presents a data-driven approach to the design of predictive controllers. The prediction matrices utilized in standard model predictive control (MPC) algorithms are typically constructed using knowledge of a system model, such as state-space or input-output models. Instead, we directly estimate the prediction matrices relating future outputs with current and future inputs from measured data, off-line. Online, the developed data-driven predictive controller reduces to solving a quadratic program with a similar structure and complexity as linear MPC. Additionally, we develop a new procedure for estimating prediction matrices from data for predictive controllers with integral action, corresponding to the rate-based formulation (also called the velocity form model). The effectiveness of the developed data-driven predictive control algorithm is demonstrated in real-life control of a Buck DC-DC converter

Recursive data–driven predictive control with persistence of excitation conditions

In this paper we develop a recursive linear predictive control algorithm with integral action and plug-and-play capabilities. Typically, adaptive model predictive control requires a recursive estimation step for updating the prediction model and then builds prediction matrices on-line. In contrast to this approach, we develop a least-squares algorithm for recursively estimating the prediction matrices directly. We then exploit an analytic relation between standard and integral prediction matrices to recursively estimate the latter. Furthermore, to assess the convergence of the closed-loop estimation, we discuss various methods that generate a persistently exciting input. The efficiency of the recursive integral predictive controller is demonstrated on a motion control application

Data-driven rate-based integral predictive control with estimated prediction matrices

This paper presents a data-driven approach to the design of predictive controllers. The prediction matrices utilized in standard model predictive control (MPC) algorithms are typically constructed using knowledge of a system model, such as state-space or input-output models. Instead, we directly estimate the prediction matrices relating future outputs with current and future inputs from measured data, off-line. Online, the developed data-driven predictive controller reduces to solving a quadratic program with a similar structure and complexity as linear MPC. Additionally, we develop a new procedure for estimating prediction matrices from data for predictive controllers with integral action, corresponding to the rate-based formulation (also called the velocity form model). The effectiveness of the developed data-driven predictive control algorithm is demonstrated in real-life control of a Buck DC-DC converter