Receding Horizon Optimal Control Research Articles

Constraint-adaptive MPC for linear systems: A system-theoretic framework for speeding up MPC through online constraint removal

Reducing the computation time of model predictive control (MPC) is important, especially for systems constrained by many state constraints. In this paper, we propose a new online constraint removal framework for linear systems, for which we coin the term constraint-adaptive MPC (ca-MPC). In so-called exact ca-MPC, we adapt the imposed constraints by removing, at each time-step, a subset of the state constraints in order to reduce the computational complexity of the receding-horizon optimal control problem, while ensuring that the closed-loop behavior is identical to that of the original MPC law. We also propose an approximate ca-MPC scheme in which a further reduction of computation time can be accomplished by a tradeoff with closed-loop performance, while still preserving recursive feasibility, stability, and constraint satisfaction properties. The online constraint removal exploits fast backward and forward reachability computations combined with optimality properties.

Model-based quantitative analysis in two-time-scale decomposed on–off optimal control of greenhouse cultivation

Greenhouse climate is crucial for crop growth. Traditional climate control techniques are carried out through on–off actuators based on growers’ experience. Advanced control algorithms usually track setpoints through continuous control inputs. These setpoints cannot guarantee maximum profit, which can be treated as the control objective of the optimal control algorithm. This paper investigated on–off optimal control algorithms based on two-time-scale decomposition. Mixed-integer nonlinear dynamic programming is used in the fast subproblem to quantify the influence of restricting different control inputs to be integers on the control objective and the CPU time. Results show that compared with continuous control inputs, a decrease of 2.21 ¥·m−2 in the control objective and an increase of 7.84·103 s in the CPU time can be found when defining all control inputs to be integers with 12 collocation points in one day. The methods of sorting and pulse width modulation are used to simulate the receding horizon optimal control in the whole growing period. Results show that compared with continuous control inputs, decreases of 83.54 ¥·m−2 and 4.45 ¥·m−2 can be found with the methods of sorting and pulse width modulation. Moreover, the method of pulse width modulation cannot guarantee state constraint satisfaction. This paper suggests modifying actuators to supply continuous control inputs before implementing optimal control algorithms for maximum profit.

Multiobjective Platooning of Connected and Automated Vehicles Using Distributed Economic Model Predictive Control

This paper considers the multi-objective platooning control problem of a group of connected and automated vehicles (CAVs) with bidirectional topologies. A new distributed economic model predictive control (DEMPC) algorithm is presented to reconcile the conflict of the control objectives of tracking, safety, stability and fuel economy of the heterogeneous vehicle platoon with guaranteed string stability. Using transient engine energy efficiency indices and cooperative performance of tracking and string stability, two distributed receding horizon optimal control problems are orderly formulated by a Lyapunov-based coupling constraint. Moreover, a new concept of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -string stability is defined for the platoon with bidirectional topologies. Some distributed terminal conditions are then derived to guarantee the recursive feasibility and asymptotic stability of the DEMPC as well as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\gamma $ </tex-math></inline-formula> -string stability of the platoon in the presence of constraints. Compared to traditional platooning control, the new DEMPC has a 4.2% energy-saving of vehicles while achieving the cooperative tasks of the platoon in several simulation scenarios.

Model predictive control for multi-zone Variable Air Volume systems based on artificial neural networks

In this paper, an artificial neural network (ANN) based system-level model predictive control framework is established for a variable air volume (VAV) system to improve its robustness and energy efficiency. The VAV system consists of three processes: the zone temperature process, the damper process and the supply air volume process of the air handling unit connecting the ductwork for all of the boxes. An ANN-based predictive controller is designed for the zone temperature process, and a PI controller is used for the damper process; they operate in a cascaded manner. Another ANN predictive controller tracks the total supply air volume subject to the cooling load constraints from the lower level VAV boxes and minimizes the fan energy consumption. The ANN controllers are optimized online by the Lagrange variational approach (LVA) to minimize the system cost function and implement a feedback receding horizon optimal control. With the LVA based gradient descent training algorithm, the weight convergence of the ANN predictive controllers and stability of the control system is obtained with small computational and storage needs. The modeling methodology, based on ANNs for the above processes, is developed and calibrated with actual data measured from a site. All of the data processing and control strategy implementations are based on extensive measurements collected from a laboratory building located in the campus of Beijing University of Civil Engineering and Architecture, Beijing, China. The experimental results show that an additional 6.12% energy savings is achieved. This is accomplished by introducing the fan control signal into the system cost function as the performance index of energy consumption with a 0.2 penalty coefficient. In the presence of un-modeled disturbances and modeling errors, the framework also reduces the temperature oscillation at least by approximately 60% compared with PI control.

Motor skill learning decreases movement variability and increases planning horizon.

We investigated motor skill learning using a path tracking task, where human subjects had to track various curved paths at a constant speed while maintaining the cursor within the path width. Subjects' accuracy increased with practice, even when tracking novel untrained paths. Using a "searchlight" paradigm, where only a short segment of the path ahead of the cursor was shown, we found that subjects with a higher tracking skill differed from the novice subjects in two respects. First, they had lower movement variability, in agreement with previous findings. Second, they took a longer section of the future path into account when performing the task, i.e., had a longer planning horizon. We estimate that between one-third and one-half of the performance increase in the expert group was due to the longer planning horizon. An optimal control model with a fixed horizon (receding horizon control) that increases with tracking skill quantitatively captured the subjects' movement behavior. These findings demonstrate that human subjects not only increase their motor acuity but also their planning horizon when acquiring a motor skill.NEW & NOTEWORTHY We show that when learning a motor skill humans are using information about the environment from an increasingly longer amount of the movement path ahead to improve performance. Crucial features of the behavioral performance can be captured by modeling the behavioral data with a receding horizon optimal control model.

Receding horizon control and coordination of multi‐agent systems using polynomial expansion

AbstractThe present paper proposes a flexible and efficient methodology for constructing norm‐bounded optimal receding horizon control laws for a group of agents, each one of which is described as a repeated integrator of an arbitrary order and with a common input delay. The goal of each agent is to track the given target, while simultaneously avoiding other agents in the group. Polynomial expansion, together with appropriate subspace projection, is utilized in order to derive receding control law in the closed form. Properties of this control law have been investigated, and its link to a well‐known control strategy based on avoidance functions, which ensures collision avoidance in the case of first‐order integrator agents, has been derived.

Optimal plug-and-control of unknown nonlinear systems

Modeling and control design are typically subsequent but independent activities. Optimal control is traditionally developed on the basis of explicit models. While this usually yields good results for linear systems, the same is not as true for nonlinear ones, for which explicit solutions can be found only for few cases. In practice, in most cases receding horizon controls based on linear approximations are used. In this paper, we propose a procedure which delivers in one step both a model and an optimal receding horizon control algorithm, without requiring a linearization. Our procedure relies essentially on a system identification by a suitable class of functions which offers universal approximation properties that can be directly incorporated in the control algorithm. Using directional forgetting we show that an adaptive extension can be realized. Measurements and simulations based on a standard automotive control problem are presented to confirm the validity of our proposal.

Real-Time Ecodriving Control in Electrified Connected and Autonomous Vehicles Using Approximate Dynamic Programing

Abstract Connected and automated vehicles (CAVs), particularly those with a hybrid electric powertrain, have the potential to significantly improve vehicle energy savings in real-world driving conditions. In particular, the ecodriving problem seeks to design optimal speed and power usage profiles based on available information from connectivity and advanced mapping features to minimize the fuel consumption over an itinerary. This paper presents a hierarchical multilayer model predictive control (MPC) approach for improving the fuel economy of a 48 V mild-hybrid powertrain in a connected vehicle environment. Approximate dynamic programing (DP) is used to solve the receding horizon optimal control problem, whose terminal cost is approximated with the base policy obtained from the long-term optimization. The controller was tested virtually (with deterministic and Monte Carlo simulation) across multiple real-world routes, demonstrating energy savings of more than 20%. The controller was then deployed on a test vehicle equipped with a rapid prototyping embedded controller. In-vehicle testing confirm the energy savings obtained in simulation and demonstrate the real-time ability of the controller.

An Algorithm to Warm Start Perturbed (WASP) Constrained Dynamic Programs

Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the objective function, vary only marginally from one time step to the next. In this case, recomputing the optimal solution at each time represents a significant burden for real-time applications. This paper proposes a novel algorithm to approximately solve a perturbed constrained dynamic program that significantly improves the computational burden when the objective function and the constraints are perturbed slightly. The method hinges on determining closed-form expressions for first-order perturbations in the optimal strategy and the Lagrange multipliers of the perturbed constrained dynamic programming problem. This information can be used to initialize any algorithm (such as the method of Lagrange multipliers, or the augmented Lagrangian method) to solve the perturbed dynamic programming problem with minimal computational resources.

Fruit development modelling and performance analysis of automatic greenhouse control

This paper presents a receding horizon optimal control (RHOC) method with an economic objective function for balancing the cost of resources ( resource use × cost ) with income through yield ( yield × product price ). This paper considers the two elements that determine the income through yield. The first element is yield and associated fruit development. A new, computationally viable, approach to model the income through yield is proposed and its prediction accuracy with respect to the original model is evaluated. The new approach employs a model that predicts at each time step, the future income through yield based on the assimilates partitioned to the fruits at the current time step. Simulations suggest that the assumptions made to arrive at the model for the new approach, do not significantly affect the accuracy of the predictions. The second element considered in this paper is the product price and the uncertainty inherent in its forecasts. Historical product price data are used to generate artificial product price forecasts. An uncertainty analysis, in combination with the artificial product price forecasts, showed that the product price forecast error does not considerably affect the optimised control strategy. Season-wide simulations with RHOC suggest that the product price forecast error does not considerably affect the value of the economic objective function. • A computationally viable approach to model the income through yield is proposed. • The new approach to model income through yield allows for RHOC with a short horizon. • Historical product price data are used to create artificial product price forecasts. • Product price forecast errors do not considerably affect the control strategy.

Prioritized multi‐objective model predictive control without terminal constraints and its applications to nonlinear processes

AbstractMany process control problems encapsulate multiple and often conflicting objective criteria spanning different levels of relative importance. In this paper, we consider a class of multi‐objective receding horizon optimal control problems and propose a novel multi‐objective model predictive control (MO‐MPC) scheme for nonlinear systems subject to constraints and several prioritized (economic) criteria. Combining the lexicographic optimization and the receding horizon principle, a prioritized MO‐MPC scheme without terminal constraints is presented to solve economically optimal control problems of the constrained nonlinear system. The results on recursive feasibility and stability of the MO‐MPC are established in the context of economy optimization and no terminal constraints. Particularly, for the systems without state constraints, the computational burden of the MO‐MPC is reduced due to the removal of terminal constraints. Using an intuitive optimizaiton, the feasible set of initial states is offline estimated to move out the initial feasibility condition. The proposed MO‐MPC strategy is verified by the multiple control problems of a coupled‐tank system and a six‐order fluidized bed combustion process.

Lexicographic multi-objective MPC for constrained nonlinear systems with changing objective prioritization

This paper proposes a new lexicographic multi-objective model predictive control (MoMPC) scheme for constrained nonlinear systems with changing objective prioritization. The lexicographic optimization-based receding horizon optimal control problem is firstly formulated to accommodate the concern on prioritized control of multiple (economic) objectives. Then an elaborate generic function and the notion of general terminal constraints are introduced to regain feasibility of lexicographic MoMPC in the presence of constraints and changing objective prioritization. Moreover, the LaSalle invariance set theorem is used to establish stability of the closed-loop system with the lexicographic MoMPC. An example of a coupled-tank level control problem with three conflicting objectives is adopted to demonstrate the effectiveness of the proposed scheme.

Eco-Driving of Connected and Autonomous Vehicles with Sequence-to-Sequence Prediction of Target Vehicle Velocity

The Eco-Driving control problem seeks to perform fuel efficient speed planning for a Connected and Autonomous Vehicle (CAV) that can exploit information available from advanced mapping, and from Vehicle-to-Everything (V2X) communication. The ability of an Eco-Driving strategy to adapt in real time to variable traffic scenarios where surrounding vehicles can be either connected or unconnected is critical for further development and deployment of this technology in the transportation sector. In this work, the Eco-Driving strategy, formulated as a receding-horizon optimal control problem, is integrated with a target vehicle speed prediction model and solved via Dynamic Programming (DP) to determine the optimal speed trajectory in the presence of a human-driven target vehicle. An encoder-decoder architecture analyzes the patterns in the target vehicle velocity recorded over a historic window using a Gated-Recurrent-Unit (GRU) based encoder and generates an estimate of the future velocity trajectory using the GRU based decoder. A sensitivity study is done to analyze the effect of the historical and prediction windows on the accuracy of the velocity predictor. The proposed Eco-Driving controller is evaluated through microscopic simulations using a traffic simulator.

Receding horizon optimal control of HEVs with on‐board prediction of driver's power demand

To improve a parallel hybrid electric vehicle's (HEV's) fuel economy, this study develops a real-time optimisation strategy with a learning-based method that predicts the driver's power demand under the connected environment. This demand is strongly constrained by the total power generated by the energy sources. Therefore, a key issue of solving the energy management problem in real time by model-based predictive optimisation is to predict the power demand of each receding horizon. The proposed optimisation strategy consists of two layers. The upper layer provides the prediction of the driver's torque demand. Gaussian process regression (GPR) is used to predict the driver's demand with the uncertain and stochastic estimation between the traffic environment and torque demand. Vehicle-to-vehicle and vehicle-to-infrastructure data are used as the inputs of the GPR model. The lower layer performs finite-horizon optimisation based on the cost function of energy consumption. A receding horizon control (RHC) problem is formulated, and optimisation is achieved by a sequential quadratic programming algorithm. To validate the proposed optimisation strategy, a powertrain control co-simulation platform with a traffic-in-the-loop environment is constructed, and results validation with the platform is demonstrated. The comparisons with the dynamic programming and no-prediction RHC results show that the proposed strategy can improve fuel economy.

Receding-Horizon Energy-Maximising Optimal Control of Wave Energy Systems Based on Moments

In this study, we address the issue of real-time energy-maximising control for wave energy converters (WECs), by proposing a receding-horizon optimal control framework based on the concept of a moment. This approach is achieved by extending the so-called moment-based framework, recently published in the WEC literature, to effectively solve the associated optimal control problem within a finite time-horizon, allowing for real-time performance, and a straightforward inclusion of the wave excitation force F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> estimation and forecasting requirements, which are intrinsic to the wave energy control application. We present a case study, based on a CorPower-like device, subject to both state and input constraints. We show that the proposed strategy can perform almost identically to the ideal performance case, where full knowledge of F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> over the time-horizon is assumed available. Moreover, a sensitivity analysis is provided, addressing the impact of wave excitation force estimation and forecasting errors in the computation of the moment-based control input. Two main conclusions can be drawn from this analysis: Forecasting mismatch has a negligible impact on the overall performance of the strategy, while potential differences arising from estimating F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> , in particular, phase errors, can substantially impact total energy absorption.

Gaussian learning‐based fuzzy predictive cruise control for improving safety and economy of connected vehicles

This study considers an adaptive cruise control problem of connected vehicles in the vehicular ad-hoc network and proposes a Gaussian learning-based fuzzy predictive cruise control approach to enhance the fuel efficiency and safety of the connected vehicles in a vehicle-following scenario. First, a Gaussian process regression model is introduced and trained with real data to estimate the future acceleration of the preceding vehicle over the prediction horizon. Moreover, with assessing traffic scenarios, the weights characterising the importance of individual performance are adjusted by a fuzzy decision method in real time. Then a fuzzy predictive cruise controller is obtained by online solving a constrained receding horizon optimal control problem with a changing cost function and acceleration prediction of the preceding vehicle. Finally, through CarSim/Simulink co-simulation, it is shown that the proposed approach has an improvement in fuel economy and safety compared with conventional predictive cruise control algorithms.

Design of an eco-gearshift control strategy under a logic system framework

Good access to traffic information provides enormous potential for automotive powertrain control. We propose a logical control approach for the gearshift strategy, aimed at improving the fuel efficiency of vehicles. The driver power demand in a specific position usually exhibits stochastic features and can be statistically analyzed in accordance with historical driving data and instant traffic conditions; therefore, it offers opportunities for the design of a gearshift control scheme. Due to the discrete characteristics of a gearshift, the control design of the gearshift strategy can be formulated under a logic system framework. To this end, vehicle dynamics are discretized with several logic states, and then modeled as a logic system with the Markov process model. The fuel optimization problem is constructed as a receding-horizon optimal control problem under the logic system framework, and a dynamic programming algorithm with algebraic operations is applied to determine the optimal strategy online. Simulation results demonstrate that the proposed control design has better potential for fuel efficiency improvement than the conventional method.

Nonlinear Noncausal Optimal Control of Wave Energy Converters Via Approximate Dynamic Programming

This article proposes a novel nonlinear receding horizon optimal control algorithm for wave energy converter (WECs) with nonlinear dynamics. It is well accepted that the WEC control problem is essentially a noncausal constrained optimal control problem, where the energy output can be improved by incorporating the short-term wave prediction into the control synthesis. Inspired by this fact, we suggest a new nonlinear noncausal optimal control (NNOC) for WECs based on the principle of approximate dynamic programming, which can, first, explicitly use the wave prediction to improve the energy conversion efficiency; second, handle the state and control input constraints; third, reduce the computational burden. Different to the existing linear noncausal optimal control, the derived Hamilton-Jacobi-Bellman equation for NNOC does not have an analytic solution. To tackle this problem, a critic neural network (NN) is adopted to approximate its solution in a receding horizon manor. The weights of NN are determined via a policy iteration algorithm. The resulting NNOC consists of a causal state feedback part and a noncausal feedforward part to explicit incorporate wave prediction information. Numerical simulations are provided to verify the efficacy of the proposed NNOC method.

Platooning Control for Heterogeneous Sailboats Based on Constant Time Headway

This paper addresses the problem of platooning control for a fleet of heterogeneous sailboats. The platooning maintains a constant time headway (CTH) between sailboats following a circular path, a complex problem for sailboats due to the influence of wind direction. First, the desired acceleration based on the CTH and the sailboat velocity needed to converge to the platooning is defined. Second, a control of sailboat orientation to manage the sailboat acceleration is proposed. The proposed platooning strategy adapts to the specific characteristics of sailboats, which are different from other motorized marine vehicles. Two tack strategies can be used for the method: the first is to regulate the sailboat velocity; the second is to go front of the wind while staying in a short corridor. The desired acceleration for fulfilling the platooning has been derived and validated. The simulation results demonstrate the effectiveness of the proposed approach in comparison with an optimal receding horizon control algorithm.

Double closed-loop optimal control of greenhouse cultivation

Two time-scale receding horizon optimal control (TTRHOC) of greenhouse cultivation is investigated. Recent developments enable closure of the outer-loop of this control system because they facilitate on-line recomputation of the optimal control of the slow dynamics on a daily basis. This paper quantifies the benefits obtained from having an outer closed-loop that counteracts errors and changes concerning predictions of crop growth, long-term weather, revenues obtained from selling crops and costs to control greenhouse climate. As a special, important case LED lighting is considered which increases both crop growth and profit. Having an outer closed-loop is especially beneficial in this case.