Explicit stochastic Nonlinear Predictive Control based on Gaussian process models

Nonlinear model predictive control of the Tennessee Eastman challenge process

We propose a robust nonlinear model predictive control (NMPC) algorithm based on multi-scenario nonlinear programming (NLP). We show that this multi-scenario formulation is Input-to-State practical stable (ISpS). Moreover, the proposed algorithm yields less steady-state offset than the minmax strategy.

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Batch processes are ubiquitous in the chemical industry and difficult to control, such that nonlinear model predictive control is one of the few promising control techniques. Many chemical process models however are affected by various uncertainties, which can lower the performance and lead to constraint violations. In this paper we propose a framework for output feedback stochastic nonlinear model predictive control (SNMPC) to consider the uncertainties explicitly, which are assumed to follow known probability distributions. Polynomial chaos expansions are employed both for the formulation of the SNMPC algorithm and a nonlinear filter for the estimation of the uncertain parameters online given noisy measurements. The effectiveness of the proposed SNMPC scheme was verified on an extensive case study involving the production of the polymer polypropylene glycol in a semi-batch reactor.

We propose two different nonlinear model predictive control (NMPC) schemes (with and without terminal cost and constraints) for stabilizing the translational dynamics of thrust-propelled vehicles. Both approaches make use of an elaborated nonlinear feedback linearization controller and its associated ellipsoidal invariant set under restrictive input constraints, hence guaranteeing the closed-loop asymptotic stability. The terminal constraint set of the corresponding NMPC design is easy to tune due to its clear formulation expressed directly in terms of the tuning variables, while for the NMPC scheme without terminal constraint, the design allows to stabilize the system with a significantly shorter prediction horizon in comparison with the existing method in the literature. Simulation and experimental tests over a nano-drone platform validate the proposed approaches.

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.

Stochastic Nonlinear Model Predictive Control with Active Model Discrimination: A Closed-Loop Fault Diagnosis Application

Air-Handling or Air-handler Units (AHUs) as a section of a Heating, Ventilating, and Air-Conditioning (HVAC) system are used for refrigerating and filtering the environment. AHU provides comfortable conditions by adjusting the control actuators of the air and water in a field-level of industrial automation. This device has strong interacting nonlinearities characteristics with complicated coupling between states and variable parameters. Thus, designing a controller has been always a challenging issue. In this work, a multivariable Nonlinear Model Predictive Controller (NMPC) centered on fmincon algorithm for AHU with a single zone in a Variable Air Volume (VAV) is pro-posed. The NMPC structure is focused on iterative optimization (online) of a cost function with a finite horizon of operating performance and using the future behavior of air-handler to generate the control effort without considering the past error. Simulation results indicate good efficiency of the NMPC approach in estimation and tracking the desired set-point compared to Linear Quadratic Regulator (LQR).

This paper presents the main principles of a stochastic nonlinear model predictive control (NMPC) novel approach for imperfectly observed discrete time systems described by time varying nonlinear non-Gaussian state space models with unknown parameters. A convergent particle estimator of the conditional expectation of a chosen cost function on a given receding control horizon is built, leading to an almost sure (a.s.) epi-convergent estimator of the NMPC cost-to-go criterion. The estimator of the expected cost function relies upon simulations and on a recently developed nonparametric convergent particle estimator of a multi-step ahead conditional probability density function (pdf) of the state variables. The theory of stochastic epi-convergence is applied to the estimated cost-to-go criterion to prove the almost sure convergence of the optimal solutions of the approximated NMPC problem to their true counterparts, when both simulation and particle numbers grow to infinity.

Real-time random reference tracking nonlinear model predictive control: a case study on wind turbines.

The development of schemes for effectively examining unmeasured disturbances and plant-model mismatch in nonlinear model predictive control (NMPC) is an important area, which has attracted considerable attention over the past decade. In this work, we propose NMPC formulations for improving regulatory performance using nonlinear state space models identified from input-output data. The NARX-type MISO and MIMO nonlinear models identified in Srinivasarao et al.(17) are used to develop the state estimators and the predictors in the proposed NMPC formulations. We show that these models provide information about the covariances of the fast changing disturbances that are necessary for developing an extended Kalman filter (EKF) used in an NMPC scheme (EKF-NMPC). Rather than formulating an EKF to reject these disturbances, which we show has certain drawbacks, we proceed to propose an alternate prediction scheme based on the direct use of the identified noise model for future trajectory predictions. We show that the resulting NMPC formulation (DC-NMPC) is relatively easy to tune to achieve disturbance rejection as well as offset removal. The efficacy of the proposed control schemes is demonstrated using simulation studies on two benchmark control problems: (a) regulatory control of a continuously stirred tank reactor (CSTR) exhibiting input multiplicity at a singular point, and (b) servo control of a CSTR exhibiting output multiplicities. The analysis of simulation results reveals that the proposed EKF-NMPC and DC-NMPC schemes consistently generate significantly better regulatory performances, when compared to the performance of a conventional NDMC-type formulation, even in the presence of significant plant-model mismatch. In particular, the DC-NMPC performs significantly better than the EKF-NMPC formulation and can be tuned to achieve excellent regulatory performance without causing excessive input variability using parameters of a single disturbance filter. The conclusions reached through simulation studies are validated by conducting servo and regulatory control experiments on a laboratory-scale heater-mixer setup.

Multi-objective nonlinear predictive control of process systems: A dual-mode tracking control approach

This paper discusses the robustness of nonlinear model predictive control (NMPC) based on sub-optimal solution obtained under reduced precision solution (RPS) criteria. NMPC needs to solve the optimal control problem (OCP) quickly and the input is injected to the controlled plant in time. Traditional convergence criteria in optimization algorithms usually cost excessive long computation time with little improvement of solution, which results in degradation of control performance eventually. RPS criteria are new convergence criteria for deciding whether the current iterate is good enough and whether the optimization procedure should be terminated. It can terminate the optimization process timely. This work pays special attention to robustness of the closed-loop system controlled by NMPC with RPS criteria when model plant mismatch exists. Simulations demonstrate that the proposed algorithm owns good robustness and stability.

Computationally efficient nonlinear predictive control based on neural Wiener models

This letter presents the modeling, system identification and nonlinear model predictive control (NMPC) design for longitudinal, full envelope velocity control of a small tiltwing hybrid unmanned aerial vehicle (H-UAV). A first-principles based dynamics model is derived and identified from flight data. It captures important aerodynamic effects including propeller-wing interaction and stalled airfoils, but is still simple enough for on-board online trajectory optimization. Based on this model, a high-level NMPC is formulated which optimizes throttle, tilt-rate and pitch-angle setpoints in order to track longitudinal velocity trajectories. We propose and investigate different references suitable to regularize the optimization problem, including both offline generated trims as well as preceding NMPC solutions. In simulation, we compare the NMPC with a frequently reported dynamic inversion approach for H-UAV velocity control. Finally, the NMPC is validated in flight experiments through a series of transition maneuvers, demonstrating good tracking capabilities in the full flight envelope.