Receding Horizon Implementation Research Articles

Multi-Scenario Model Predictive Control for Greenhouse Crop Production Considering Market Price Uncertainty

This paper presents a stochastic model predictive control (SMPC) strategy to maximize the economic profit of a greenhouse crop production. The strategy consists of an optimization problem that is solved with a multi-scenario MPC formulation (MS-MPC). It considers the uncertainty of market price by using its historical evolution per year as multiple price scenarios in the cost function. MS-MPC calculates a single set of dates to harvest and sell the crop production that optimizes profits for all the considered scenarios. In addition, MS-MPC determines the optimal temperature references that should be achieved inside the greenhouse for the growth of the crop. A case study for a Mediterranean tomato crop is simulated to analyze the performance of the developed MS-MPC strategy using a hierarchical control architecture with two layers. In the upper layer, MS-MPC calculations are executed following a receding horizon implementation. In the lower layer, regulatory control techniques are applied to reach the optimal temperature references by using natural ventilation and a heating system. Results show that MS-MPC can improve economic profits compared to the use of an average price scenario for the MPC calculations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the need of greenhouse farmers for strategies that maximize profit considering market prices and crop production dynamics. It is not easy for them to make decisions to achieve such long-term objectives while minimizing economic risks, because market prices are very difficult to predict. As a solution, this work presents a novel control strategy to maximize profits by means of automatic selection of the best possible dates to harvest and sell the crop production. This selection is made thanks to considering the uncertainty of market prices in the control strategy by evaluating different scenarios, which are recorded evolutions of the prices from previous years. Although the strategy was tested in simulation, results suggest that using multiple scenarios of historical prices is better for the optimization of profits than just considering an average yearly trend of prices. The more scenarios are considered, the more protection against possible evolution of market prices is obtained. In future research, this control strategy could be extended to include other uncertainties of factors affecting decision making, such as weather forecasts.

Computationally efficient infinite-horizon indefinite model predictive control with disturbance preview information

This paper proposes a model predictive control (MPC) scheme for maximising the benefit of a useful disturbance by exploiting preview information of the disturbance, in the context of goal-oriented operation. For a constrained system, subject to a persistent, bounded, and predictable disturbance, rather than attenuating the influence of disturbance, the proposed MPC aims to utilise the disturbance to optimise high-level economic criteria, e.g., profitability and productivity, which are normally represented by an indefinite cost function. For linear time-invariant systems, after examining the influence of the future disturbance profile, a computationally efficient finite-horizon convex approach is proposed to approximate the solution of the original possibly non-convex infinite-horizon optimisation problem. Then, a receding-horizon implementation is developed, taking into account the recursively updated disturbance prediction, and the recursive feasibility and input-to-state stability of the implementation are established. Numerical examples are provided to verify the efficacy of the proposed method.

Nonlinear model predictive control of salinity and water level in polder networks: Case study of Lissertocht catchment

A significant increase in surface water salinization in low-lying deltas is expected globally due to saline groundwater exfiltration driven by rising sea levels and decreasing freshwater availability. Sustaining fresh water-dependent agriculture in such areas will entail an increased demand for fresh water flushing. Unfortunately, the flushing of surface water is not operationally optimised and results in excessive use of scarce freshwater. To meet the increased demand for flushing, while minimizing the need for diverted freshwater, new operational designs are required. This paper presents a novel network model based approach that uses De Saint Venant (SV) and Advection Dispersion (AD) equations to optimize multiple objectives on water level and salinity control using a Nonlinear Model Predictive Control (NMPC). The resulting NMPC problem is solved with a receding horizon implementation, where the nonlinear program (NLP) at each iteration is solved using state-of-the-art large scale interior point solver (IPOPT). We evaluate the performance of the proposed approach and compare it to the traditional fixed flushing for a representative Dutch polder. Firstly, the approach is shown to be capable of controlling the water level and salinity level in the polder. Secondly, the results highlight that the network of canals, which were originally made for drainage, could not be made sufficiently fresh with current intake capacity. A simple design approach was used to identify appropriate new capacities for two of the gates that allow optimal flushing to guarantee the required water level and salinity constraints.

Norm Optimal Iterative Learning Control: A Data-Driven Approach

Iterative learning control (ILC) is a control design method that can improve the tracking performance for systems working in a repetitive manner by learning from the previous iterations. Norm optimal ILC is a well known ILC design with appealing convergence properties, e.g. monotonic error norm convergence. However, it requires an explicit system model in the design, which can be difficult or expensive to obtain in practice. To address this problem, this paper proposes a data-driven norm optimal ILC design exploiting recent development in data-driven control. A receding horizon implementation of the design is further developed to relax the requirement on data. Convergence properties of the design are analysed rigorously and simulation examples are presented to demonstrate the effectiveness of the method.

Heuristic Search and Receding-Horizon Planning in Complex Spacecraft Orbit Domains

Spacecraft missions to small celestial bodies face sensitive, strongly non-Keplerian dynamics that motivate the employment of automated sampling-based trajectory planning. However, the scarcity of onboard computing resources necessitates careful formulation of heuristics for efficiently searching the reachable sets, which exhibit complex and finely-detailed structure. We examine a global search heuristic that combines aspects of simulated annealing and hill-climbing to locate sparse regions of the planning domain that simultaneously satisfy numerous geometric and timing constraints associated with remote sensing objectives for points of interest on the central body surface. Subsequently, we demonstrate the use of a receding-horizon implementation of this maneuver-planning strategy to produce mission profiles that fulfill sets of such goals.

Coordinated charging and discharging control of electric vehicles to manage supply voltages in distribution networks: Assessing the customer benefit

Increased worldwide uptake of Electric Vehicles (EVs) accentuates the need for developing coordinated EV charging and discharging methods that mitigate detrimental and sustained under-voltage and over-voltage conditions in distribution networks. In this paper, a centrally coordinated EV charge-discharge scheduling method is proposed, referred to as Network-aware EV Charging (and Discharging) N-EVC(D), that takes into account both EV customer economics and distribution grid constraints. Specifically, N-EVC(D) is designed to maintain quasi-steady-state feeder voltages within statutory power quality limits, while minimizing EV customer operational costs associated with: (1) purchasing (or otherwise being compensated for delivering) electricity on a time-of-use tariff; and (2) battery degradation due to frequent charging and discharging. The optimization problem for N-EVC(D) is formulated as a quadratic program, with voltage constraints to limit voltage variability across a radial distribution feeder, and individual EV constraints to satisfy heterogeneous EV charge requirements. In N-EVC(D), each grid-connected EV follows an operator-specified battery schedule that is obtained by solving the proposed quadratic program. A receding horizon implementation is also proposed to support near-real-time N-EVC(D) operations while accommodating non-deterministic EV arrivals and departures. The benefits of N-EVC(D) are assessed by means of numerical simulations carried out on an IEEE test feeder populated with a real-world dataset of residential load collected from households within an Australian distribution network. The simulation results confirm that N-EVC(D) mitigates non-compliant voltage deviations that would otherwise occur when voltage constraints are not enforced. Compared to uncoordinated EV charging, N-EVC(D) offers a 92% – 111% reduction in the operational costs incurred by EV customers.

A diffusion wavelets-based multiscale framework for inverse optimal control of stochastic systems

This work presents a multiscale framework to solve a class of inverse optimal control (IOC) problems in the context of robot motion planning and control in a complex environment. In order to handle complications resulting from a large decision space and complex environmental geometry, two key concepts are adopted: (a) a diffusion wavelet representation of the Markov chain for hierarchical abstraction of the state space; and (b) a desirability function-based representation of the Markov decision process (MDP) to efficiently calculate the optimal policy. An IOC problem constructed on a ‘abstract state’ is solved, which is much more tractable than using the original bases set; moreover, the solution can be obtained recursively in the ‘coarse to fine’ direction by utilizing the hierarchical structure of basis functions. The resulting multiscale plan is utilized to finally compute a continuous-time optimal control policy within a receding horizon implementation. Illustrative numerical experiments on a robot path control in a complex environment and on a quadrotor ball-catching task are presented to verify the proposed method.

The value of aggregate service levels in stochastic lot sizing problems

Dealing with demand uncertainty in multi-item lot sizing problems poses huge challenges due to the inherent complexity. The resulting stochastic formulations typically determine production plans which minimize the expected total operating cost while ensuring that a predefined service level constraint for each product is satisfied. We extend these stochastic formulations to a more general setting where, in addition to the individual service level constraints, an aggregate service level constraint is also imposed. Such a situation is relevant in practical applications where the service level aggregated from a variety of products must be collectively satisfied. These extended formulations allow the decision maker to flexibly assign different individual service levels to different products while ensuring that the overall aggregate service level is satisfied and these aggregate service level measures can be used in conjunction with the commonly adopted individual service levels. Different mathematical formulations are proposed for this problem with different types of service levels. These formulations are a piece-wise linear approximation for the β, γ, and δ service levels and a quantile-based formulation for the αc service level. We also present a receding horizon implementation of the proposed formulations which can be effectively used in a dynamic environment. Computational experiments are conducted to analyze the impact of aggregate service levels and demonstrate the value of the proposed formulations as opposed to standard service levels imposed on individual items.

Stochastic multi-period optimal dispatch of energy storage in unbalanced distribution feeders

This paper presents a convex, multi-period, AC-feasible Optimal Power Flow (OPF) framework that robustly dispatches flexible demand-side resources in unbalanced distribution feeders against uncertainty in very-short timescale solar Photo-Voltaic (PV) forecasts. This is valuable for power systems with significant behind-the-meter solar PV generation as their operation is affected by uncertainty from forecasts of demand and solar PV generation. The aim of this work is then to ensure the feasibility and reliability of distribution system operation under high solar PV penetration. We develop and present a novel, robust OPF formulation that accounts for both the nonlinear power flow constraints and the uncertainty in forecasts. This is achieved by linearizing an optimal trajectory and using first-order methods to systematically tighten voltage bounds. Case studies on a realistic distribution feeder shows the effectiveness of a receding-horizon implementation.

Conic Optimization for Electric Vehicle Station Smart Charging With Battery Voltage Constraints

This article proposes a new convex optimization strategy for coordinating electric vehicle charging, which accounts for battery voltage rise and the associated limits on maximum charging power. Optimization strategies for coordinating electric vehicle charging commonly neglect the increase in battery voltage, which occurs as the battery is charged. However, battery voltage rise is an important consideration since it imposes limits on the maximum charging power. This is particularly relevant for dc fast charging, where the maximum charging power may be severely limited, even at the moderate state of charge levels. First, a reduced-order battery circuit model is developed, which retains the nonlinear relationship between the state of charge and maximum charging power. Using this model, limits on the battery output voltage and battery charging power are formulated as the second-order cone constraints. These constraints are integrated with a linearized power flow model for three-phase unbalanced distribution networks. This provides a new multiperiod optimization strategy for electric vehicle smart charging. The resulting optimization is a second-order cone program and, thus, can be solved in polynomial time by standard solvers. A receding horizon implementation allows the charging schedule to be updated online, without requiring prior information about when vehicles will arrive.

Positive Invariant Sets for Safe Integrated Vehicle Motion Planning and Control

This article describes a method for real-time integrated motion planning and control aimed at autonomous vehicles. Our method leverages feedback control, positive invariant sets, and equilibrium trajectories of the closed-loop system to produce and track trajectories that are collision-free with guarantees according to the vehicle model. Our method jointly steers the vehicle to a target region and controls the velocity while satisfying constraints associated with future motion of surrounding obstacles. We develop a receding-horizon implementation of the control policy and verify the method in both a simulated road scenario and an experimental validation using a scaled mobile robot with car-like dynamics using only onboard sensing. The results show that our method generates dynamically feasible and safe (i.e., collision-free) trajectories in real time, and indicate that the proposed planner is robust to sensing and mapping errors.

MPC-based 3-D trajectory tracking for an autonomous underwater vehicle with constraints in complex ocean environments

This paper presents a novel three-dimension (3-D) underwater trajectory tracking method for an autonomous underwater vehicle (AUV) using model predictive control (MPC). First, the 6-degrees of freedom (DoF) model of a fully-actuated AUV is represented by both kinematics and dynamics. After that, the trajectory tracking control is proposed as an optimization problem and then transformed into a standard convex quadratic programming (QP) problem which can be readily computed online. The practical constraints of the system inputs and states are considered effectively in the design phase of the proposed control strategy. To make the AUV move steadily, the control increments are considered as the system input and optimized. The receding horizon implementation makes the optimal control inputs be recalculated at each sampling instant, which can improve the robustness of the tracking control under the model uncertainties and time-varying disturbances. Simulations are carried out under two different 3-D trajectories to verify the performance of trajectory tracking under random disturbances, ocean current disturbances, and ocean wave disturbances. The simulation results are given to show the feasibility and robustness of the MPC-based underwater trajectory tracking algorithm.

Motion Planning of Autonomous Road Vehicles by Particle Filtering

This paper describes a probabilistic method for real-time decision making and motion planning for autonomous vehicles. Our approach relies on the fact that driving on road networks implies a priori defined requirements that the motion planner should satisfy. Starting from an initial state of the vehicle, a map, the obstacles in the region of interest, and a goal region, we formulate the motion-planning problem as a nonlinear non-Gaussian estimation problem, which we solve using particle filtering. We assign probabilities to the generated trajectories according to their likelihood of obeying the driving requirements. Decision making and collision avoidance is naturally integrated in the approach. We develop a receding-horizon implementation and verify the method in simulated real road scenarios and in an experimental validation using a scaled mobile robot setup with car-like dynamics. The results show that the method generates dynamically feasible trajectories for a number of scenarios, such as collision avoidance, overtaking, and traffic-jam scenarios. In addition, the computation times and memory requirements indicate that the method is suitable for real-time implementation.

4-D Flight Trajectory Tracking: A Receding Horizon Approach Integrating Feedback Linearization and Scenario Optimization

This paper proposes a control strategy to steer an aircraft along a given reference 4-D trajectory. The aircraft has a nonlinear dynamics and is subject to constraints related to its maneuverability and to passengers comfort. Feedback linearization of the aircraft dynamics and convex relaxation of the constraints allow for a reformulation of the trajectory tracking problem that is suitable for a receding horizon implementation. Uncertainty is affecting the aircraft motion, mainly through wind, which is described as a Gaussian random field and approximated on-the-fly by a local autoregressive model. The adoption of a scenario-based minimization of the tracking error introduced by the stochastic wind disturbance preserves the problem convexity and allows obtaining a program that can be solved with limited computational effort. The wind model update jointly with the recomputation of the control action at each time step allow to account for the spatial variability of the random field and to obtain recursive feasibility of the receding horizon solution.

Receding horizon guidance and control using sequential convex programming for spacecraft 6-DOF close proximity

This paper presents a receding horizon implementation of sequential convex programming for the spacecraft six-degree-of-freedom close proximity to a non-cooperative target satellite. With linearized relative translational dynamics and newly derived discrete rotational equations in terms of modified Rodrigues parameters, nonlinear system dynamics of the original optimal guidance and control problem for proximity are converted into convex ones for sequentially planning. The nonconvex constraint on field-of-view of the visual sensor pointing with coupled attitude and relative position is then approximately relaxed as a convex standard second-order cone, and concave spherical and ellipsoidal obstacle regions respectively around the target's body and solar arrays are convexified by affine constraints in terms of tangent planes. The original nonlinear optimal guidance and control problem is accordingly transformed into a series of second-order cone programming sub-problems via iteratively successive convexification with the trust region constraints, and sequentially solved using disciplined convex programming method. A close-loop guidance and control using the proposed sequential convex programming scheme is then demonstrated by means of receding horizon to robustly drive the spacecraft maneuvering close to the target. Numerical simulations and results reveal that the proposed method provides rapid and reliable guidance and control performance for six-degree-of-freedom close proximity and shows the potential for on-board implementations in real-time applications.

Trajectory Tracking Control of an Autonomous Underwater Vehicle Using Lyapunov-Based Model Predictive Control

This paper studies the trajectory tracking control problem of an autonomous underwater vehicle (AUV). We develop a novel Lyapunov-based model predictive control (LMPC) framework for the AUV to utilize computational resource (online optimization) to improve the trajectory tracking performance. Within the LMPC framework, the practical constraints, such as actuator saturation, can be explicitly considered. Also, the thrust allocation subproblem can be addressed simultaneously with the LMPC controller design. Taking advantage of a nonlinear backstepping tracking control law, we construct the contraction constraint in the formulated LMPC problem so that the closed-loop stability is theoretically guaranteed. Sufficient conditions that ensure the recursive feasibility, and hence the closed-loop stability, are provided analytically. A guaranteed region of attraction is explicitly characterized. In the meantime, the robustness of the tracking control can be improved by the receding horizon implementation that is adopted in the LMPC control algorithm. Simulation results on the Saab SeaEye Falcon model AUV demonstrate the significantly enhance trajectory tracking control performance via the proposed LMPC method.

Sparse and constrained stochastic predictive control for networked systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission.

Dropout feedback parametrized policies for stochastic predictive controller

Abstract: This article presents a novel control policy class for the networked control of linear dynamical systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts. Our proposed class of policies is parametrized relative to the past dropouts. We show how to augment the underlying optimization problem with a constant negative drift constraint in order to ensure mean-square boundedness of the closed-loop states. The resulting convex quadratic program can be solved periodically online. The states of the closed loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control.

LatchingDeclutching Control of Wave Energy Converters Using Derivative-Free Optimization

We consider predictive control of a wave energy converter (WEC) that can switch between three modes: 1)power generation; 2)declutched with no power generation; or 3)latched with zero velocity. We propose a formulation that turns the optimal control problem into a small dimensional discrete optimization problem, where the only decision variables are bounds on the latching time and power take-off (PTO) time, whereas the objective function is computed from the trajectory of a hybrid system with linear dynamics in each sample interval. The optimization problem is solved using a novel derivative-free algorithm that exploits the quantization of the decision variables in order to reduce the number of function evaluations. Two closed-loop formulations are also studied within a receding horizon implementation: the first one uses past wave information and can double the energy generation compared to the uncontrolled case, while the second formulation uses predictions of future waves and is able to result in a further increase in energy generation. The benefits of codesigning the physical system and controller is compared to the sequential approach of first optimizing the physical system without control, followed by controller design.

Heuristic Search and Receding-Horizon Planning in Complex Spacecraft Orbit Domains

Spacecraft missions to small celestial bodies face sensitive, strongly non-Keplerian dynamics that motivate the employment of automated sampling-based trajectory planning. However, the scarcity of onboard computing resources necessitates careful formulation of heuristics for efficiently searching the reachable sets, which exhibit complex and finely-detailed structure. We examine a global search heuristic that combines aspects of simulated annealing and hill-climbing to locate sparse regions of the planning domain that simultaneously satisfy numerous geometric and timing constraints associated with remote sensing objectives for points of interest on the central body surface. Subsequently, we demonstrate the use of a receding-horizon implementation of this maneuver-planning strategy to produce mission profiles that fulfill sets of such goals.