Receding Horizon Formulation Research Articles

MILP-based model predictive control for home energy management systems: A real case study in Algarve, Portugal

This paper addresses the development of an innovative home energy management system (HEMS). The presented HEMS relies on a mixed-integer linear programming (MILP)-based model predictive control. The system takes advantage of the powerful formulation capabilities of a MILP-based mathematical programming problem with the capabilities of model predictive control to optimize, at each sample instant the HEMS operation using a receding-horizon formulation. The system is designed for a residence located in Algarve, Portugal. The results of the presented system are compared with the real experimental results obtained by a commercial PV-battery management system. Additionally, an analysis of the system's performance is conducted, in terms of operation planning for 2021 market prices compared to 2022 prices, where there was a significant rise of buying price due to the energy world context. In all simulations performed, it is verified that the MILP-based model predictive control presents better results, with statistical relevance.

Flexible-Time Receding Horizon Iterative Learning Control With Application to Marine Hydrokinetic Energy Systems

This brief presents an iterative learning control (ILC) framework for a class of repetitive control (RC) applications characterized by: 1) continuous operation; 2) flexible iteration time; and 3) an economic performance metric. Specifically, the effect of iteration-varying initial conditions, resulting from the continuous nature of the operation, is accounted for through an iteration domain receding horizon formulation. To address the need for flexible iteration times, the time-domain dynamics are transformed into path-domain dynamics characterized by a non-dimensional parameter spanning an iteration-invariant range. The resulting model is used to derive learning filters that minimize a multi-objective economic cost. The proposed methodology is applied to the control a kite-based marine hydrokinetic (MHK) system, which executes high-speed, repetitive flight paths with the objective of maximizing its lap-averaged power output. The proposed approach is validated via simulations of a medium-fidelity nonlinear model of a kite-based MHK system, and the results demonstrate robust and fast convergence of the kite to power-optimal flight patterns.

Polyhedral potential field constructions for obstacle avoidance in a receding horizon formulation

We revisit and enhance previous work pertaining to the use of polyhedral potential fields for motion planning in a receding horizon framework. We adapt the standard vertex-based mixed-integer (MI) representations of piecewise affine functions and propose three equivalent formulations which balance the complexity of the geometric representation with the size of the associated MI representation. In all cases, we arrive at formulations whose polyhedral support comes (either directly or as a refinement of it) from an associated hyperplane arrangement induced by the hyperplanes bounding the polyhedral obstacles.

Hybrid output regulation for nonlinear systems: Steady-state vs receding horizon formulation

The hybrid output regulation problem in the presence of periodic jumps is approached in this paper for a class of nonlinear hybrid systems satisfying rather mild assumptions. We provide sufficient conditions that characterize steady-state trajectories achieving output regulation that are defined, mimicking the linear case, in terms of two equations: the first one describes the solution of a flow-only output regulation problem, while the second is associated to an auxiliary output regulation problem concerning the monodromy equivalent system of the flow zero-dynamics. Such conditions are then revisited and a receding-horizon, steady-state-less, solution to the (hybrid) output regulation problem is suggested, based on the solution of a sequence of two-point boundary value problems.

Learning and Verification of Feedback Control Systems using Feedforward Neural Networks

We present an approach to learn and formally verify feedback laws for data-driven models of neural networks. Neural networks are emerging as powerful and general data-driven representations for functions. This has led to their increased use in data-driven plant models and the representation of feedback laws in control systems. However, it is hard to formally verify properties of such feedback control systems. The proposed learning approach uses a receding horizon formulation that samples from the initial states and disturbances to enforce properties such as reachability, safety and stability. Next, our verification approach uses an over-approximate reachability analysis over the system, supported by range analysis for feedforward neural networks. We report promising results obtained by applying our techniques on several challenging nonlinear dynamical systems.

Distributed Augmentation-Regularization for Robust Online Convex Optimization

Abstract This paper studies the use of distributed, primal-dual dynamics to solve continuous, time-dependent optimization problems on the fly. When using primal-dual dynamics, the availability of a strongly convex-strongly concave Lagrangian is desirable, but this is a strong assumption not satisfied in many applications. To deal with this, we develop a new Lagrangian regularization technique that seeks to minimize the perturbation to the original solutions and is compatible with the distributed nature of the optimization problem. We provide analytic bounds of the tracking error of the optimal solution using standard Lyapunov stability analysis techniques. As an application, we consider a receding horizon formulation of a dynamic traffic assignment problem and illustrate the performance of our approach in simulation.

An Efficient Game for Coordinating Electric Vehicle Charging

A novel class of auction-based games is formulated to study coordination problems arising from charging a population of electric vehicles (EVs) over a finite horizon. To compete for energy allocation over the horizon, each individual EV submits a multidimensional bid, with the dimension equal to two times the number of time-steps in the horizon. Use of the progressive second price (PSP) auction mechanism ensures that incentive compatibility holds for the auction games. However, due to the cross elasticity of EVs over the charging horizon, the marginal valuation of an individual EV at a particular time is determined by both the demand at that time and the total demand over the entire horizon. This difficulty is addressed by partitioning the allowable set of bid profiles based on the total desired energy over the entire horizon. It is shown that the efficient bid profile over the charging horizon is a Nash equilibrium of the underlying auction game. An update mechanism for the auction game is designed. A numerical example demonstrates that the auction process converges to an efficient Nash equilibrium. The auction-based charging coordination scheme is adapted to a receding horizon formulation to account for disturbances and forecast uncertainty.

Receding Horizon Pseudospectral Control for Energy Maximization With Application to Wave Energy Devices

This paper addresses the issue of real-time control for applications, subject to physical constraints, involving an energy maximization objective. Typical application areas include renewable energy systems where, in spite of the fact that the raw energy resource is free, the capital and operational costs associated with the energy conversion process are not. In addition, economic energy delivery can only be achieved if the conversion device is operated efficiently. Previous approaches to this problem include model predictive control (MPC), but the computational cost associated with MPC can be high. Pseudospectral solutions show considerable promise in achieving a good balance between performance and computation, but currently available solutions deal with fixed-period optimization. In this paper, a receding horizon real-time pseudospectral control is developed, based on half-range Chebyshev Fourier basis functions, which can accurately represent harmonic signals in the application domain, while also efficiently dealing with the signal truncation effects associated with a receding horizon formulation. An application example, based on a wave energy converter, is used to illustrate the new control algorithm.

Optimization of Taxiway Routing and Runway Scheduling

This paper describes a mixed-integer linear programming optimization method for the coupled problems of airport taxiway routing and runway scheduling. The receding-horizon formulation and the use of iteration in the avoidance constraints allows the scalability of the baseline algorithm presented, with examples based on Heathrow Airport, London, U.K., which contains up to 240 aircraft. The results show that average taxi times can be reduced by half, compared with the first-come-first-served approach. The main advantage is shown with the departure aircraft flow. Comparative testing demonstrates that iteration reduces the computational demand of the required separation constraints while introducing no loss in performance.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

Boolean-controlled systems via receding horizon and linear programing

We consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programing by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively controlled systems.

Stochastic Receding Horizon Control of Constrained Linear Systems With State and Control Multiplicative Noise

We develop a receding horizon control approach to stochastic linear systems with control and state multiplicative noise that also contain constraints. Our receding horizon formulation is based upon an on-line optimization that utilizes open-loop plus linear feedback and is solved as a semi-definite programming problem. We also provide a characterization of stability, performance, and constraint satisfaction properties of the receding horizon controlled system under a specific choice of terminal weight and terminal constraint. A simple numerical example is used to illustrate the approach.

Model predictive control strategies for supply chain management in semiconductor manufacturing

This paper examines the application of model predictive control (MPC), an advanced control technique originating from the process industries, to supply chain management (SCM) problems arising in semiconductor manufacturing. The main goal of this work is to demonstrate the usefulness of MPC as a tactical decision policy that is an integral part of a comprehensive hierarchical decision framework aimed at achieving operational excellence. A fluid analogy is used to describe the dynamics of the supply chain. Compared to traditional flow control problems, challenges of SCM in semiconductor manufacturing result from high stochasticity and nonlinearity in throughput times, yields and customer demands. The advantages of the control-oriented receding horizon formulation behind MPC are presented for three benchmark problems which highlight distinguishing features of semiconductor manufacturing. The effects of tuning, model parameters, and capacity are shown by comparing system robustness and multiple performance metrics in each case study.

Hybrid Model for Receding Horizon Guidance of Agile Autonomous Rotorcraft

This paper presents a novel framework for full-envelope guidance of agile, autonomous rotorcraft. A velocity control mode is combined with a maneuver scheduler that enables execution of pre-programmed, agile maneuvers. The closed-loop dynamics in the body-axis frame are described by a hybrid model, consisting of a set of constrained, linear, time-invariant modes and discrete transitions in the state space. Optimal trajectories through cluttered environments are then computed using mixed integer linear programming. A receding horizon formulation is presented that is feasible for real-time guidance.

New path-generation based receding-horizon formulation for constrained stabilization of nonlinear systems

In this paper, a new formulation of constrained stabilizing receding-horizon control is proposed. This formulation is based on the use of open-loop steering path generators. The open-loop optimization problem associated to the proposed receding-horizon formulation is scalar in which the optimization variable is the prediction horizon length. Stability is proved in a sampling control scheme. A simple example is given to illustrate the main concepts.

High-fidelity control of a seismic shake table

A high-fidelity PC-based control system has been developed to improve the tracking characteristics of a small-scale seismic motion simulator used for testing structural control designs. This work outlines the development and testing of the control system. First, the simulator hardware is described in detail. The process of constructing a mechanistic model of the system and identifying model parameters is then described. Next, a closed-loop feedback/feed-forward control algorithm, based on an optimal receding horizon formulation, is developed. The control design was tested and the results indicate that the seismic shake table precisely tracked reference seismic motions. Copyright © 1999 John Wiley & Sons, Ltd.

Stability of a truncated infinite constrained receding horizon scheme: the general discrete nonlinear case

Some results concerning the constrained receding horizon formulation with infinite and truncated prediction horizon are presented. In this formulation a distinction is made between prediction and control horizons. The main result is a generalization of a known fact for linear systems, namely that, under certain technical requirements, the asymptotic stability of the above formulation holds for a sufficiently large finite prediction horizon. Existence results are also provided under stabilizability assumptions.