Receding Horizon Strategy Research Articles

A Deterministic and Stochastic Petri Net Model for Traffic-Responsive Signaling Control in Urban Areas

The problem of reducing congestion within urban areas by means of a traffic-responsive control strategy is addressed in this paper. The model of an urban traffic network is microscopically represented by means of deterministic and stochastic Petri nets, which allow a compact representation of the dynamic traffic network. To properly model traffic congestion, intersections are divided into crossing sections, and roads have limited capacity. Each intersection includes a multiphase traffic signal, whose sequence of phases is given and represented by a timed Petri net. The control strategy proposed in this paper aims at minimizing queue lengths by optimizing the duration of each signal phase. This is accomplished by heuristically solving a stochastic optimization problem within a receding-horizon scheme, to take into account the actual traffic flow entering the network, thus making the proposed approach traffic-responsive. In this framework, the Petri nets play a key role, as the cost function to be minimized is a function of the marking, and the constraints include the marking state evolution. The proposed strategy is applicable to both undersaturated and oversaturated traffic conditions.

Dealing with rainfall forecast uncertainties in real-time flood control along the Demer river

Real-time Model Predictive Control (MPC) of hydraulic structures strongly reduces flood consequences under ideal circumstances. The performance of such flood control may, however, be significantly affected by uncertainties. This research quantifies the influence of rainfall forecast uncertainties and related uncertainties in the catchment rainfall-runoff discharges on the control performance for the Herk river case study in Belgium. To limit the model computational times, a fast conceptual model is applied. It is calibrated to a full hydrodynamic river model. A Reduced Genetic Algorithm is used as optimization method. Next to the analysis of the impact of the rainfall forecast uncertainties on the control performance, a Multiple Model Predictive Control (MMPC) approach is tested to reduce this impact. Results show that the deterministic MPC-RGA outperforms the MMPC and that it is inherently robust against rainfall forecast uncertainties due to its receding horizon strategy.

Near-Optimal Tracking Control of Mobile Robots Via Receding-Horizon Dual Heuristic Programming.

Trajectory tracking control of wheeled mobile robots (WMRs) has been an important research topic in control theory and robotics. Although various tracking control methods with stability have been developed for WMRs, it is still difficult to design optimal or near-optimal tracking controller under uncertainties and disturbances. In this paper, a near-optimal tracking control method is presented for WMRs based on receding-horizon dual heuristic programming (RHDHP). In the proposed method, a backstepping kinematic controller is designed to generate desired velocity profiles and the receding horizon strategy is used to decompose the infinite-horizon optimal control problem into a series of finite-horizon optimal control problems. In each horizon, a closed-loop tracking control policy is successively updated using a class of approximate dynamic programming algorithms called finite-horizon dual heuristic programming (DHP). The convergence property of the proposed method is analyzed and it is shown that the tracking control system based on RHDHP is asymptotically stable by using the Lyapunov approach. Simulation results on three tracking control problems demonstrate that the proposed method has improved control performance when compared with conventional model predictive control (MPC) and DHP. It is also illustrated that the proposed method has lower computational burden than conventional MPC, which is very beneficial for real-time tracking control.

Optimal and receding horizon control of tumor growth in myeloma bone disease

Abstract This article addresses the problem of designing therapies for the myeloma bone disease that optimize in a systematic way a compromise between drug toxicity and tumor repression. For that sake, the techniques of optimal control are applied to the dynamics of tumor growth, and the necessary conditions of Pontryagin's minimum principle are solved using a numerical relaxation algorithm. A therapy to accelerate bone mass recovery is applied in parallel, based on a PI control rule. Since the optimal controller provides an open-loop control, it is turned into a feedback law by following a receding horizon strategy. For that sake, an optimal manipulated variable profile is first computed over a time horizon, but only the initial part of this function is applied. The whole optimization procedure is then repeated starting at a time instant that corresponds to the end of the previously applied control.

Advanced building energy management based on a two-stage receding horizon optimization

The continuous increase in energy demand and the integration of a large number of renewable energy sources with intermittent production require an advanced energy management to guarantee an uninterrupted supply. Deployment of smart meters in wide areas of power networks and availability of affordable storage systems encourage development and implementation of local energy management systems. Local energy management is considered a feasible and inexpensive approach to reduce the impact of load variations and intermittent generation. Demand response and load shaping techniques provide customers with the facility to contribute to system balancing and improve power quality. This paper presents a building energy management which determines the optimal scheduling of the components of the local energy system. The developed two-stage optimization is based on a receding horizon strategy and minimizes the energy costs under consideration of the physical system constraints. The proposed building energy management has been implemented and tested with a medium-size hotel emulated in a microgrid testbed using power-hardware-in-the-loop techniques. The obtained results underline that energy management strategies can be validated under realistic conditions using flexible power scenarios.

A networked-based receding horizon scheme for constrained LPV systems

This paper deals with control problems for networked constrained polytopic Linear Parameter Varying (LPV) systems. A novel LPV customization of a recent Receding Horizon robust Control (RHC) scheme developed for polytopic uncertainty systems is here proposed for the case where command inputs and state measurement are subject to time-varying delays. By taking advantage of the flexibility of the LPV structure, families of precomputed one-step controllable sets are off-line computed which result less conservative with respect to their robust counterparts. Finally, simulation results involving the constrained tracking problem of an unicycle-type mobile robot are reported to show the effectiveness and the benefits of the proposed control scheme.

Robust Model Predictive Flight Control of Unmanned Rotorcrafts

This paper addresses the problem of robust flight control of unmanned rotorcrafts, by proposing and experimentally evaluating a real---time robust model predictive control scheme in various challenging conditions, aiming to capture the demanding nature of the potential requirements for their efficient and safe integration in real---life operations. The control derivation process is based on state space representations applicable in most rotorcraft configurations and incorporate the effects of external disturbances. Exploiting this modeling approach, two different unmanned rotorcraft configurations are presented and experimentally utilized. The formulated control strategy consists of a receding horizon scheme, the optimization process of which employs the minimum peak performance measure, while incorporating and accounting for the modeled dynamics and input and state constraints. This strategy aims to ensure the minimum possible deviation subject to the worst---case disturbance, while robustly respecting and satisfying the physical limitations of the system, or a set of mission-related requirements, as encoded in the constraints. The proposed framework is further augmented in order to provide obstacle avoidance capabilities into a unified scheme. Multiparametric methods were utilized in order to provide an explicit solution to the controller computation optimization problem, therefore allowing for fast real---time execution and seamless integration into any digital avionics system. The efficiency of the proposed strategy is validated via several experimental case studies on the two unmanned rotorcraft platforms. The experiments set consists of: trajectory tracking subject to atmospheric disturbances, slung load operations, fast highly disturbed maneuvers, collisions handling, as well as avoidance of known obstacles.

Receding horizon trajectory optimization in opportunistic navigation environments

Receding horizon trajectory optimization for optimal information gathering in opportunistic navigation environments is considered. A receiver is assumed to be dropped in an environment consisting of multiple signals of opportunity (SOPs) transmitters. The receiver has minimal a priori knowledge about its own states and the SOPs’ states. The receiver draws pseudorange observations from the SOPs. The receiver’s objective is to build a high-fidelity signal landscape map while simultaneously localizing itself within this map in space and time. Assuming that the receiver can control its maneuvers, the following two problems are considered. First, the minimal conditions under which the environment is completely observable are established. It is shown that receiver-controlled maneuvers reduce the minimal a priori information about the environment required for complete observability. Second, the trajectories that the receiver should traverse are prescribed. To this end, a one-step look-ahead (greedy) strategy is compared with a multistep look-ahead (receding horizon) strategy. The limitations and achieved improvements in the map quality and space-time localization accuracy due to the receding horizon strategy are quantified. The computational burden associated with the receding horizon strategy is also discussed.

Model predictive control for constrained networked systems subject to data losses

The paper addresses the stabilization problem for constrained control systems where both plant measurements and command signals in the loop are sent through communication channels subject to time-varying delays and data losses. A novel receding horizon strategy is proposed by resorting to an uncertain polytopic linear plant framework. Sequences of pre-computed inner approximations of the one-step controllable sets are on-line exploited as target sets for selecting the commands to be applied to the plant in a receding horizon fashion. The communication channel effects are taken into account by resorting to both Independent-of-Delay and Delay-Dependent stability concepts that are used to initialize the one-step controllable sequences. The resulting framework guarantees Uniformly Ultimate Boundedness and constraints fulfilment of the regulated trajectory regardless of plant uncertainties and data loss occurrences.

Multirobot Rendezvous Planning for Recharging in Persistent Tasks

This paper addresses a multirobot scheduling problem in which autonomous unmanned aerial vehicles (UAVs) must be recharged during a long-term mission. The proposal is to introduce a separate team of dedicated charging robots that the UAVs can dock with in order to recharge. The goal is to schedule and plan minimum cost paths for charging robots such that they rendezvous with and replenish the UAVs, as needed, during the mission. The approach is to discretize the 3-D UAV flight trajectories into sets of projected charging points on the ground, thus allowing the problem to be abstracted onto a partitioned graph. Solutions consist of charging robot paths that collectively charge each of the UAVs. The problem is solved by first formulating the rendezvous planning problem to recharge each UAV once using both an integer linear program and a transformation to the Travelling Salesman Problem. The methods are then leveraged to plan recurring rendezvous’ over longer horizons using fixed horizon and receding horizon strategies. Simulation results using realistic vehicle and battery models demonstrate the feasibility and robustness of the proposed approach.

Non-smooth Predictive Control for Wiener Systems with Backlash-Like Hysteresis

In this paper, a nonsmooth predictive control method for Wiener systems with backlash-like hysteresis is proposed. In this type of system, the backlash-like hysteresis is connected in series with a preceded linear dynamic subsystem. A backlash-like hysteresis is modeled as a nonsmooth function with multivalued mapping; the corresponding objective function of the control system is also defined as being nonsmooth. In this case, the implementation of conventional model predictive control for such systems will encounter a challenge, since the gradients of the control criterion function with respect to control variables do not exist at nonsmooth points. In order to solve this problem, a nonsmooth receding horizon strategy based on Clarke subgradients is proposed. Moreover, the robust stability of the predictive control of such nonsmooth Wiener systems is analyzed. Finally, a numerical example and a simulation study on a mechanical transmission system are implemented to validate the proposed method.

A receding horizon scheme for discrete-time polytopic linear parameter varying systems in networked architectures

This paper proposes a Model Predictive Control (MPC) strategy to address regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to input and state constraints in which both plant measurements and command signals in the loop are sent through communication channels subject to time-varying delays (Networked Control System (NCS)). The results here proposed represent a significant extension to the LPV framework of a recent Receding Horizon Control (RHC) scheme developed for the so-called robust case. By exploiting the parameter availability, the pre-computed sequences of one- step controllable sets inner approximations are less conservative than the robust counterpart. The resulting framework guarantees asymptotic stability and constraints fulfilment regardless of plant uncertainties and time-delay occurrences. Finally, experimental results on a laboratory two-tank test-bed show the effectiveness of the proposed approach.

Shale-gas scheduling for natural-gas supply in electric power production

This paper describes a novel integration of shale-gas supply in geographical proximity to natural-gas power production. Shale-gas reservoirs hold special properties that make them particularly suited for intermittent shut-in based production schemes. The proposed scheme argues that shale-gas reservoirs can be used to shift storage of gas used for meeting varying demands, from separate underground storage units operated by local distribution companies to the gas producers themselves. Based on this property, we present an economical attractive option for generating companies to increase their use of firm gas–supply contracts to the natural-gas power plants in order to secure a sufficient gas supply. The shale-well scheduling is formulated as profit-maximization model for well operators, in which we seek to include their main operational challenges, while preserving an economic incentive for the operators to adopt the proposed scheme. The resulting large-scale mixed integer linear program is solved by a Lagrangian relaxation scheme, with a receding horizon strategy implemented to handle operational uncertainties. We present the proposed optimization framework by illustrative case studies. The numerical results show a significant economic potential for the shale-well operators, and a viable approach for generating companies to secure a firm gas supply for meeting varying seasonal electricity demands.

Optimal control of the temperature in a solar furnace

SummaryThis article describes the application of optimal control to a solar furnace that is used to perform temperature stress cycling tests in material samples. This process is characterized by having nonlinearities that depend on the sample properties and relate the temperature of the sample with the solar energy fluctuations and the position of the furnace shutter. An optimal control problem with fix terminal time and free terminal state and control constraints is addressed in continuous time domain. The solution is approximated using discretized state and costate equations and applied to the furnace according to a receding horizon strategy. The performance of the overall system is evaluated from computer simulations which show that the controller is able to tolerate, up to some degree, the presence of parameter uncertainty. Copyright © 2014 John Wiley & Sons, Ltd.

An Event-Triggered Receding-Horizon Scheme for Planning Rail Operations in Maritime Terminals

This paper proposes a planning approach to optimize railway operations in seaport terminals by adopting a queue-based discrete-time model of the considered system. First, a mixed-integer linear mathematical programming problem is defined in order to optimize the timing of import trains and the use of the handling resources devoted to rail port operations. Second, in order to deal with unexpected situations or uncertainty in estimating some data necessary to the planning, an event-triggered receding-horizon planning approach is proposed, in which the finite horizon optimization problem is solved whenever a critical event happens or the real values of some problem data significantly differ from the predicted ones. Both these planning approaches are tested on data referred to a real terminal and deeply discussed in this paper.

Distributed mixed continuous‐discrete receding horizon filter for multisensory uncertain active suspension systems with measurement delays

This study presents a new robust filtering method in modelling an active multisensory suspension system with measurement delays and parameteric uncertainties in a state-space dynamical model. To achieve good performance of the system, a new distributed fusion receding horizon filtering frameworks are constructed to couple the continuous dynamics with the multisensory discrete measurements, and to coordinately deal with the parametric uncertainty and time-delays. The novel filtering algorithm is proposed based on the receding horizon strategy, standard mixed continuous-discrete Kalman filtering and discrete Kalman filtering for systems with time-delays in order to achieve high estimation accuracy and stability under parametric uncertainties. The key theoretical contributions of this study are the derivation of the error cross-covariance equations between the local receding horizon filters in order to compute the optimal matrix fusion weights. The high accuracy and efficiency of the new filter are demonstrated through its implementation and performance and then compared to the existing vehicle active suspension system.

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.

Square Root Receding Horizon Information Filters for Nonlinear Dynamic System Models

New nonlinear filtering algorithms are designed based on a receding horizon strategy, i.e., a finite impulse response (FIR) structure, and square root information filtering to achieve high accuracy and good performance in empirical error covariance tests. The new nonlinear receding horizon filters reduce approximation errors in nonlinear filtering by considering a set of recent observations with non-informative initial conditions. By applying information filtering, we are able to manage the non-informative initial conditions, and thus propose the square root version of the algorithm as a means of retaining the positive definiteness of the error covariance. Based on the proposed strategy, we then implement known nonlinear filtering frameworks. Simulation results confirm that the new nonlinear receding horizon filters outperform existing nonlinear filters in well-known nonlinear examples.

Collision avoidance command governor for multi-vehicle unmanned systems

SUMMARY In this paper, we consider the problem of coordinating a collection of autonomous unmanned vehicles while guaranteeing collision avoidance. Each vehicle is regulated by a local controller that ensures stability and provides desired path tracking performance in the absence of constraints. The fulfillment of coordination tasks (e.g., collision avoidance) and local constraints (e.g., input saturation constraints) is achieved through a command governor (CG) strategy that, whenever necessary, modifies the nominal paths of the vehicles. First, a centralized CG approach is proposed and fully analyzed. Then, a more interesting distributed implementation requiring low communication rates is discussed. Both approaches make use of a receding horizon strategy and require the on-line solution of mixed-integer optimization programs. Finally, an example is given for illustration purposes. Copyright © 2013 John Wiley & Sons, Ltd.

Stochastic model predictive control of LPV systems via scenario optimization

A stochastic receding-horizon control approach for constrained Linear Parameter Varying discrete-time systems is proposed in this paper. It is assumed that the time-varying parameters have stochastic nature and that the system’s matrices are bounded but otherwise arbitrary nonlinear functions of these parameters. No specific assumption on the statistics of the parameters is required. By using a randomization approach, a scenario-based finite-horizon optimal control problem is formulated, where only a finite number M of sampled predicted parameter trajectories (‘scenarios’) are considered. This problem is convex and its solution is a priori guaranteed to be probabilistically robust, up to a user-defined probability level p. The p level is linked to M by an analytic relationship, which establishes a tradeoff between computational complexity and robustness of the solution. Then, a receding horizon strategy is presented, involving the iterated solution of a scenario-based finite-horizon control problem at each time step. Our key result is to show that the state trajectories of the controlled system reach a terminal positively invariant set in finite time, either deterministically, or with probability no smaller than p. The features of the approach are illustrated by a numerical example.