Robust one-step receding horizon control for constrained systems

This paper proposes a robust receding horizon control scheme for discrete-time uncertain linear systems with input and state constraints. The control scheme is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix. It is shown that the proposed receding horizon control robustly asymptotically stabilizes uncertain constrained systems under some matrix inequality conditions on the terminal weighting matrices. This robust receding horizon control scheme has a larger feasible initial-state set and a more general structure than existing robust receding horizon controls for uncertain constrained systems under the same design parameters. The proposed controller is obtained using semidefinite programming. Copyright © 1999 John Wiley & Sons, Ltd.     

LTL receding horizon control for finite deterministic systems

This paper considers receding horizon control of finite deterministic systems, which must satisfy a high level, rich specification expressed as a linear temporal logic formula. Under the assumption that time-varying rewards are associated with states of the system and these rewards can be observed in real-time, the control objective is to maximize the collected reward while satisfying the high level task specification. In order to properly react to the changing rewards, a controller synthesis framework inspired by model predictive control is proposed, where the rewards are locally optimized at each time-step over a finite horizon, and the optimal control computed for the current time-step is applied. By enforcing appropriate constraints, the infinite trajectory produced by the controller is guaranteed to satisfy the desired temporal logic formula. Simulation results demonstrate the effectiveness of the approach.     

Stochastic model predictive control for constrained discrete-time Markovian switching systems

In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the SMPC law under very weak assumptions. In the special but important case of constrained MJLS we present an algorithm for computing explicitly the SMPC control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization.     

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. This work was supported by MURST-PRIN 2007ZMZK5T “Decisional model for the design and the management of logistics networks characterized by high interoperability and information integration”.     

Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

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.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Nonlinear sampled-data output feedback receding horizon control

In this paper, we present an output feedback receding horizon control for a class of SISO nonlinear systems. A globally stabilizing state feedback receding horizon control scheme is combined with a discretized high gain observer. This is motivated by the fact that measurable system’s outputs are only available at specific sampling intervals. Our result follows from the application of a separation principle applicable to a class of sampled-data nonlinear systems. It is shown that the output-feedback scheme recovers the performance (rate of convergence) achieved under state feedback receding horizon control for a sufficiently large observer gain and sampling frequency.     

Modified reference tracking MPC for constrained linear systems

This article presents a model predictive control for tracking piecewise constant references with a new steady-state parametrisation. The modified algorithm is based on the artificial reference idea, but the number of decision variables is equal to the standard MPC for regulation. The proposed strategy is able to track admissible constant references with an admissible evolution. If the reference is not admissible, the system is steered to the closest admissible stationary point. A modified initialisation algorithm is proposed to recover the enlarged domain of attraction provided by related artificial reference-based strategies. Simulation examples are presented to illustrate the benefits of the proposed strategy.     

Approximate explicit receding horizon control of constrained nonlinear systems

An algorithm for the construction of an explicit piecewise linear state feedback approximation to nonlinear constrained receding horizon control is given. It allows such controllers to be implemented via an efficient binary tree search, avoiding real-time optimization. This is of significant benefit in applications that requires low real-time computational complexity or low software complexity. The method has a priori guarantee of asymptotic stability with region of attraction being a close inner approximation to the stabilizable set. This is achieved by ensuring that the approximation error does not exceed the stability margin.     

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.     

Receding horizon time-optimal control for a class of differentially flat systems

A closed-loop, time-optimal path-following control scheme is proposed for a class of constrained differentially flat systems. Within a receding horizon framework, a finite horizon optimisation problem is solved at each sample, using available state feedback and feedforward path information. Irrespective of horizon length, the proposed formulation guarantees exact path-following. Moreover, the requirements under which the proposed algorithm achieves minimum-time path-following are established. Simulations conducted with a rigid X–Y table model confirm the theoretical results.     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

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.     

Resource-aware MPC for constrained nonlinear systems: A self-triggered control approach

In systems with resource constraints, such as actuation limitations or limited communication bandwidth, it is desired to obtain control signals that are either sparse or sporadically changing in time to reduce resource utilization. In this paper, we propose a resource-aware self-triggered MPC strategy for discrete-time nonlinear systems subject to state and input constraints that has three important features: Firstly, significant reductions in resource utilization can be realized without modifying the cost function by input regularization or explicitly penalizing resource usage. Secondly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels (in terms of the original cost function) are guaranteed by design next to asymptotic stability and constraint satisfaction. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of numerical examples, we show the effectiveness of this novel strategy.     

Reduced order model predictive control for constrained discrete‐time linear systems

A reduced order model predictive control (MPC) is discussed for constrained discrete‐time linear systems. By employing a decomposition method for finite‐horizon linear systems, an MPC law is obtained from a reduced order optimization problem. The decomposition enables us to construct pairs of initial state and control sequence which have large influence on system responses, and it also characterizes the standard LQ control. The MPC law is obtained based on a combination of the LQ control and dominant input sequences over the prediction horizon. The proposed MPC method is illustrated with numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Periodic event-triggering in distributed receding horizon control of nonlinear systems

How to efficiently use limited system resources in distributed receding horizon control (DRHC) is an important issue. This paper studies the DRHC problem for a class of dynamically decoupled nonlinear systems under the framework of event-triggering, to efficiently make use of the computation and communication resources. To that end, a distributed periodic event-triggered strategy is designed and a detailed DRHC algorithm is presented. The conditions for ensuring feasibility of the designed algorithm and stability of the closed-loop system are developed, respectively. We show that the closed-loop system is input-to-state stable if the energy bound of the disturbances, the triggering condition and the cooperation matrices fulfill the proposed conditions.