Sensitivity-based multistep MPC for embedded systems

In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system

이동블록 및 잔류편차 제거 모델예측제어 기법의 최적성 향상

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부,2020. 2. 이종민.Model predictive control (MPC) is a receding horizon control which derives finite-horizon optimal solution for current state on-line by solving an optimal control problem. MPC has had a tremendous impact on both industrial and control research areas. There are several outstanding issues in MPC. MPC has to solve the optimization problem within a sampling period so that the reduction of on-line computational complexity is a one of the main research subject in MPC. Another major issue is model-plant mismatch due to the model based predictive approach so that offset-free tracking schemes by compensating model-plant mismatch or unmeasured disturbance has been developed. In this thesis, we focused on the optimality performance of move blocking which fixes the decision variables over arbitrary time intervals to reduce computational load for on-line optimization in MPC and disturbance estimator approach based offset-free MPC which is the most standardly used method to accomplish offset-free tracking in MPC. We improve the optimality performance of move blocked MPC in two ways. The first scheme provides a superior base sequence by linearly interpolating complementary base sequences, and the second scheme provides a proper time-varying blocking structure with semi-explicit approach. Moreover, we improve the optimality performance of offset-free MPC by exploiting learned model-plant mismatch compensating signal from estimated disturbance data. With the proposed schemes, we efficiently improve the optimality performance while guaranteeing the recursive feasibility and closed-loop stability.모델예측제어는 현재 시스템 상태에 대한 유한 구간 최적해를 도출하는 온라인 이동 구간 제어 방식이다. 모델예측제어는 피드백을 통한 공정 동특성과 제약 조건을 효과적으로 반영하는 장점으로 인해 산업 및 제어 연구 분야에 큰 영향을 미쳤다. 이러한 모델예측제어에는 몇 가지 해결되어야 할 문제가 있다. 모델예측제어에서는 샘플링 기간 내에 최적화 문제를 풀어내야 하기 때문에, 온라인 계산 복잡성의 감소가 주요 연구 주제 중 하나로 활발히 연구되고 있다. 또 다른 주요 문제는 모델에 기반한 예측을 이용하는 접근 방식으로 인해 모델-플랜트 불일치로 인한 오차를 해결해야 한다는 점이며, 모델 플랜트 불일치 또는 측정되지 않은 외란을 보상하여 잔류편차 없이 참조신호를 추적하는 연구가 활발히 이루어지고 있다. 이 논문에서는 모델예측제어에서의 온라인 최적화를 위한 계산 부하를 줄이기 위해 임의의 시간 간격에 걸쳐 결정 변수를 고정시키는 이동 블록 전략의 최적성 향상에 중점을 두었으며, 또한 잔류편차를 제거하기 위해 가장 표준적으로 사용되는 외란 추정기를 이용한 잔류편차-제거 모델예측제어 기법의 최적성 향상에 중점을 두었다. 이 논문에서는 이동 블록 모델예측제어의 최적 성능을 향상시키기 위한 두 가지 전략을 제시한다. 첫 번째 전략은 이동 블록 전략에서 일반적으로 고정된 채로 사용되는 기반 시퀀스를 상호 보완적인 두 기반 시퀀스의 선형 보간으로 대체함으로써 보다 우수한 기반 시퀀스를 제공하며, 두 번째 전략은 준-명시적 접근법을 활용하여 현재 시스템 상태에 적절한 시변 블록 구조를 온라인에서 제공한다. 또한, 잔류편차-제거 모델예측제어 기법의 최적 성능을 향상시키기 위해 추정 외란 데이터로부터 학습된 모델-플랜트 불일치 보상 신호를 온라인에서 이용하는 전략을 제안하였다. 제안된 세 가지 기법을 통해 모델예측제어의 반복적 실현가능성과 폐쇄-루프 안정성을 보장하면서 최적 성능을 효율적으로 개선 하였다.1. Introduction 1 2. Move-blocked model predictive control with linear interpolation of base sequences 5 2.1 Introduction 5 2.2 Preliminaries 9 2.2.1 MPC formulation 9 2.2.2 Move blocking 12 2.2.3 Move blocked MPC (MBMPC) 15 2.3 Move blocking schemes 16 2.3.1 Previous solution based offset blocking 17 2.3.2 LQR solution based offset blocking 18 2.4 Interpolated solution based move blocking 20 2.4.1 Interpolated solution based MBMPC 20 2.4.2 QP formulation 26 2.5 Numerical examples 29 2.5.1 Example 1 (Feasible region) 30 2.5.2 Example 2 (Performance in regulation problem) 33 2.5.3 Example 3 (Performance in tracking problem) 36 3. Move-blocked model predictive control with time-varying blocking structure by semi-explicit approach 43 3.1 Introduction 43 3.2 Problem formulation 46 3.3 Move blocked MPC 48 3.3.1 Move blocking scheme 48 3.3.2 Implementation of move blocking 51 3.4 Semi-explicit approach for move blocked MPC 53 3.4.1 Off-line generation of critical region 56 3.4.2 On-line MPC scheme with critical region search 60 3.4.3 Property of semi-explicit move blocked MPC 62 3.5 Numerical examples 70 3.5.1 Example 1 (Regulation problem) 71 3.5.2 Example 2 (Tracking problem) 77 4. Model-plant mismatch learning offset-free model predictive control 83 4.1 Introduction 83 4.2 Offset-free MPC: Disturbance estimator approach 86 4.2.1 Preliminaries 86 4.2.2 Disturbance estimator and controller design 87 4.2.3 Offset-free tracking condition 89 4.3 Model-plant mismatch learning offset-free MPC 91 4.3.1 Model-plant mismatch learning 92 4.3.2 Application of learned model-plant mismatch 97 4.3.3 Robust asymptotic stability of model-plant mismatch learning offset-free MPC 102 4.4 Numerical example 117 4.4.1 System with random set-point 120 4.4.2 Transformed system 125 4.4.3 System with multiple random set-points 128 5. Concluding remarks 134 5.1 Move-blocked model predictive control with linear interpolation of base sequences 134 5.2 Move-blocked model predictive control with time-varying blocking structure by semi-explicit approach 135 5.3 Model-plant mismatch learning offset-free model predictive control 136 5.4 Conclusions 138 5.5 Future work 139 Bibliography 145Docto

Robust Model Predictive Control via Scenario Optimization

This paper discusses a novel probabilistic approach for the design of robust model predictive control (MPC) laws for discrete-time linear systems affected by parametric uncertainty and additive disturbances. The proposed technique is based on the iterated solution, at each step, of a finite-horizon optimal control problem (FHOCP) that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances, followed by a specific command selection rule implemented in a receding horizon fashion. The scenario FHOCP is always convex, also when the uncertain parameters and disturbance belong to non-convex sets, and irrespective of how the model uncertainty influences the system's matrices. Moreover, the computational complexity of the proposed approach does not depend on the uncertainty/disturbance dimensions, and scales quadratically with the control horizon. The main result in this paper is related to the analysis of the closed loop system under receding-horizon implementation of the scenario FHOCP, and essentially states that the devised control law guarantees constraint satisfaction at each step with some a-priori assigned probability p, while the system's state reaches the target set either asymptotically, or in finite time with probability at least p. The proposed method may be a valid alternative when other existing techniques, either deterministic or stochastic, are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance-constrained optimization problem.Comment: This manuscript is a preprint of a paper accepted for publication in the IEEE Transactions on Automatic Control, with DOI: 10.1109/TAC.2012.2203054, and is subject to IEEE copyright. The copy of record will be available at http://ieeexplore.ieee.or

Model predictive control of resistive wall mode for ITER

Active feedback stabilization of the dominant resistive wall mode (RWM) for an ITER H-mode scenario at high plasma pressure using infinite-horizon model predictive control (MPC) is presented. The MPC approach is closely-related to linear-quadratic-Gaussian (LQG) control, improving the performance in the vicinity of constraints. The control-oriented model for MPC is obtained with model reduction from a high-dimensional model produced by CarMa code. Due to the limited time for on-line optimization, a suitable MPC formulation considering only input (coil voltage) constraints is chosen, and the primal fast gradient method is used for solving the associated quadratic programming problem. The performance is evaluated in simulation in comparison to LQG control. Sensitivity to noise, robustness to changes of unstable RWM dynamics, and size of the domain of attraction of the initial conditions of the unstable modes are examined.Comment: Original manuscript as submitted to Fusion Engineering and Desig

Model predictive emissions control of a diesel engine airpath: Design and experimental evaluation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163480/2/rnc5188.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163480/1/rnc5188_am.pd

NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees

Dimensionality reduction of decision variables is a practical and classic method to reduce the computational burden in linear and Nonlinear Model Predictive Control (NMPC). Available results range from early move-blocking ideas to singular-value decomposition. For schemes more complex than move-blocking it is seemingly not straightforward to guarantee recursive feasibility of the receding-horizon optimization. Decomposing the space of decision variables related to the inputs into active and inactive complements, this paper proposes a general framework for effective feasibility-preserving dimensionality reduction in NMPC. We show how -- independently of the actual choice of the subspaces -- recursive feasibility can be established. Moreover, we propose the use of global sensitivity analysis to construct the active subspace in data-driven fashion based on user-defined criteria. Numerical examples illustrate the efficacy of the proposed scheme. Specifically, for a chemical reactor we obtain a significant reduction by factor $20-40$ at a closed-loop performance decay of less than $0.05\%$.Comment: 10 page