A receding horizon control approach to sampled-data implementation of continuous-time controllers

We propose a novel way for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller. Our approach exploits a model predictive control (MPC) strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We propose a control law and present conditions under which stability and sub-optimality of the closed loop can be proved. We only consider the case of unconstrained MPC. We show that the recent results in [G. Grimm, M.J. Messina, A.R. Teel, S. Tuna, Model predictive control: for want of a local control Lyapunov function, all is not lost, IEEE Trans. Automat. Control 2004, to appear] can be directly used for analysis of stability of our closed-loop system.     

Move blocking strategies in receding horizon control

In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as ‘move blocking’. This paper will address two issues. First, a survey of various move blocking strategies is presented and the shortcomings of these blocking policies, such as the lack of stability and constraint satisfaction guarantees, will be illustrated. Second, a novel move blocking scheme, ‘Moving Window Blocking’ (MWB), will be presented. In MWB, the blocking strategy is time-dependent such that the scheme yields stability and feasibility guarantees for the closed-loop system. Finally, the results of a large case study that illustrate the advantages and drawbacks of the various control strategies discussed in this paper and the implementation of the MWB scheme on a mechanical system are presented.     

Distributed receding horizon control for multi-vehicle formation stabilization

We consider the control of interacting subsystems whose dynamics and constraints are decoupled, but whose state vectors are coupled non-separably in a single cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon control implementation is stabilizing to a neighborhood of the objective state. The implementation requires synchronous updates and the exchange of the most recent optimal control trajectory between coupled subsystems prior to each update. The key requirements for stability are that each subsystem not deviate too far from the previous open-loop state trajectory, and that the receding horizon updates happen sufficiently fast. The venue of multi-vehicle formation stabilization is used to demonstrate the distributed implementation.     

On receding horizon feedback control

Receding horizon feedback control (RHFC) was originally introduced as an easy method for designing stable state-feedback controllers for linear systems. Here those results are generalized to the control of nonlinear autonomous systems, and we develop a performance index which is minimized by the RHFC (inverse optimal control problem). Previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the RHFC horizon distance a function of the state. That functional dependence was implicit and difficult to implement on-line. Here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state.     

Decentralized receding horizon control for large scale dynamically decoupled systems

We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.     

Event-based receding horizon control for two-stage multi-product production plants

In this paper a receding horizon control approach for multi-product production plants is presented. Specifically two-stage plants are considered. In the first stage, a set of parallel production lines generates intermediate products from raw materials. In the second stage, the intermediate products are assembled into final products. A set of buffers for the intermediate products connects the production lines and the assembly line thus allowing a continuous production flow.

The focus is on plants where the switch between product types is less frequent than in the assembly line. The latter is mostly dictated by the external demand, while the first one is the main scheduling variable. A systematic event-based control approach using receding horizon control (RHC) techniques is proposed; specifically the production line flow is controlled in order to satisfy the time-varying request from the assembly line while minimizing the intermediate products storage and processing time. Experimental results underline the benefits resulting from the application of the proposed approach to a car engine manufacturing process.     

Broadcast stochastic receding horizon control of multi-agent systems

Optimal regulation of stochastically behaving agents is essential to achieve a robust aggregate behavior in a swarm of agents. How optimally these behaviors are controlled leads to the problem of designing optimal control architectures. In this paper, we propose a novel broadcast stochastic receding horizon control architecture as an optimal strategy for stabilizing a swarm of stochastically behaving agents. The goal is to design, at each time step, an optimal control law in the receding horizon control framework using collective system behavior as the only available feedback information and broadcast it to all agents to achieve the desired system behavior. Using probabilistic tools, a conditional expectation based predictive model is derived to represent the ensemble behavior of a swarm of independently behaving agents with multi-state transitions. A stochastic finite receding horizon control problem is formulated to stabilize the aggregate behavior of agents. Analytical and simulation results are presented for a two-state multi-agent system. Stability of the closed-loop system is guaranteed using the supermartingale theory. Almost sure (with probability 1) convergence of the closed-loop system to the desired target is ensured. Finally, conclusions are presented.     

Enlarged terminal sets guaranteeing stability of receding horizon control

The purpose of this paper is to relax the terminal conditions typically used to ensure stability in model predictive control, thereby enlarging the domain of attraction for a given prediction horizon. Using some recent results, we present novel conditions that employ, as the terminal cost, the finite-horizon cost resulting from a nonlinear controller u=−sat(Kx) and, as the terminal constraint set, the set in which this controller is optimal for the finite-horizon constrained optimal control problem. It is shown that this solution provides a considerably larger terminal constraint set than is usually employed in stability proofs for model predictive control.     

Event-driven receding horizon control for energy-efficient container handling

The performance of container terminals needs to be improved to adapt the growth of containers while maintaining sustainability. This paper provides a methodology for determining the trajectory of interacting machines that transport containers between the quayside area and the stacking area in an automated container terminal. The behaviors of the interacting machines are modeled as a combination of discrete-event dynamics and continuous-time dynamics. An event-driven receding horizon controller (RHC) is proposed for achieving energy efficient container handling. The underlying control problems are hereby formulated as a collection of small optimization problems that are solved in a receding horizon way. Simulation studies illustrate that energy consumption of container handling can indeed be reduced by the proposed methodology. Moreover, an assessment is made of performance of the proposed RHC controller under different types of uncertainties.     

Receding horizon control applied to optimal mine planning

In this paper we show that the problem of optimal mine planning can be cast in the framework of receding horizon control. Traditional formulations of this problem have cast it in the framework of mixed integer linear programming. In this paper, we present an alternative formulation of the mine planning problem using the “language” of control engineering. We show that this alternative formulation gives rise to new insights which have the potential to lead to improved computational procedures. The advantages are illustrated by an example incorporating many practical features of an actual mine planning problem.