Sampled-data Model Predictive Control Research Articles

Sampled-Data Model Predictive Control

This paper focus on model predictive control (MPC) design in the context of sampled-data control systems with full-state measurements. It is shown that recent results on this area can be successfully generalized to cope with sampled-data MPC. The open-loop plant is subjected to polytopic parameter uncertainty and at sampling times a controlled output variable satisfies a set of convex constraints. A guaranteed H2 performance index with infinity horizon is minimized such as the feedback control preserves asymptotic stability and feasibility. The design conditions are expressed though differential linear matrix inequalities (DLMIs). Continuous-time systems are treated with no kind of discrete-time modeling approximation. Comparisons with classical methods from the literature dealing with continuous-time systems are presented and discussed. Examples are included for illustration.

Aperiodic sampled-data MPC strategy for LPV systems

This paper addresses the design of a sampled-data model predictive control (MPC) strategy for linear parameter-varying (LPV) systems. A continuous-time prediction model, which takes into account that the samples are not necessarily periodic and that plant parameters vary continuously with time, is considered. Moreover, it is explicitly assumed that the value of the parameters used to compute the optimal control sequence is measured only at the sampling instants. The MPC approach proposed by Kothare et al. [1], where the basic idea consists in solving an infinite horizon guaranteed cost control problem at each sampling time using linear matrix inequalities (LMI) based formulations, is adopted. In this context, conditions for computing a sampled-data stabilizing LPV control law that provides a guaranteed cost for a quadratic performance criterion under input saturation are derived. These conditions are obtained from a parameter-dependent looped-functional and a parameter-dependent generalized sector condition. A strategy that consists in solving convex optimization problems in a receding horizon policy is therefore proposed. It is shown that the proposed strategy guarantees the feasibility of the optimization problem at each step and leads to the asymptotic stability of the origin. The conservatism reduction provided by the proposed results, with respect to similar ones in the literature, is illustrated through numerical examples.

Robust model predictive control with sliding mode for constrained non‐linear systems

This study proposes a tractable robust non-linear model predictive control for constrained continuous-time uncertain systems with stability guarantees. First, a sampled-data model predictive control for the nominal system is designed to provide a desired performance. Then, a sliding mode control is designed to recover the nominal performance for the uncertain system. The sampled-data model predictive control that is solved online includes the initial state of the model employed in the problem as a decision variable. By merging sampled-data model predictive control and sliding mode control in between samples, the effect of the uncertainty, which is matched with the input, is reduced efficiently. The computational complexity of the proposed robust model predictive control is the same as for the model predictive control while the input and state constraints satisfaction and asymptotic stability of the closed-loop system are achieved. To illustrate the effectiveness of the proposed approach, the controller is applied to a vehicle platooning system.

Tractable robust model predictive control with adaptive sliding mode for uncertain nonlinear systems

This paper proposes a tractable robust nonlinear model predictive control for continuous-time uncertain systems with stability guaranteed. The uncertainty is considered in parameters or additive form. First, a sampled-data model predictive control for the nominal system is designed to provide the desired performance. Then, an adaptive sliding mode control is designed to recover the nominal performance for the uncertain system. By merging sampled-data model predictive control and sliding mode control in-between samples, the effect of the uncertainty is reduced efficiently. The computational complexity of the proposed robust model predictive control is the same as for the model predictive control while asymptotic stability of the closed-loop system is achieved. The simulation results illustrate the effectiveness of the proposed approaches.

Recursive Feasibility of Continuous-Time Model Predictive Control Without Stabilising Constraints

We consider sampled-data Model Predictive Control (MPC) of nonlinear continuous-time control systems. We derive sufficient conditions to guarantee recursive feasibility and asymptotic stability without stabilising costs and/or constraints. Moreover, we present formulas to explicitly estimate the required length of the prediction horizon based on the concept of (local) cost controllability. For the linear-quadratic case, cost controllability can be inferred from standard assumptions. In addition, we extend results on the relationship between the horizon length and the distance of the initial state to the boundary of the viability kernel from the discrete-time to the continuous-time setting.

Sampled–data model predictive control: Adaptive time–mesh refinement algorithms and guarantees of stability

This article addresses the problem of controlling a constrained, continuous–time, nonlinear system through Model Predictive Control (MPC). In particular, we focus on methods to efficiently and accurately solve the underlying optimal control problem (OCP). In the numerical solution of a nonlinear OCP, some form of discretization must be used at some stage. There are, however, benefits in postponing the discretization process and maintain a continuous-time model until a later stage. This is because that way we can exploit additional freedom to select the number and the location of the discretization node points.We propose an adaptive time–mesh refinement (AMR) algorithm that iteratively finds an adequate time–mesh satisfying a pre–defined bound on the local error estimate of the obtained trajectories. The algorithm provides a time–dependent stopping criterion, enabling us to impose higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. Additionally, we analyze the conditions to guarantee closed–loop stability of the MPC framework using the AMR algorithm. The numerical results show that the proposed AMR strategy can obtain solutions as fast as methods using a coarse equidistant–spaced mesh and, on the other hand, as accurate as methods using a fine equidistant–spaced mesh. Therefore, the OCP can be solved, and the MPC law obtained, faster and/or more accurately than with discrete-time MPC schemes using equidistant–spaced meshes.

Guaranteed Constraint Satisfaction in Continuous-Time Control Problems

In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is used with a digital device, such as in sampled-data model-based control, in an optimal control solver, or in sampled-data model predictive control. In this letter, we establish a condition that when verified on a finite set of time instants (using limited computational power) can guarantee that the trajectory constraints are satisfied on an uncountable set of times. The case of constrained optimal control problems is further explored here. We develop an algorithm for the numerical solution of constrained nonlinear optimal control problems that combines a guaranteed constraint satisfaction strategy with an adaptive mesh refinement strategy.

Cooperative Path Following of Autonomous Vehicles with Model Predictive Control and Event Triggered Communications

This paper presents a solution to the problem of multiple vehicle cooperative path following (CPF) that takes explicitly into account the constraints on the vehicles inputs and the topology of the inter-vehicle communications network. The solution involves decoupling the original constrained CPF problem into two sub-problems: i) single vehicle constrained path following and ii) multi-agent system (MAS) coordination. The first is solved by adopting a sampled-data model predictive control (MPC) scheme, whereas the latter is tackled by using a distributed control law with an event triggered communication (ETC) mechanism. We show that this design methodology yields a stable closed-loop CPF system: the path following error for each vehicle is globally asymptotically stable (GAS) and the coordination errors between the vehicles are bounded. A simulation example consisting of three autonomous vehicles following a given 2D- desired formation illustrates the efficacy of the CPF strategy proposed.

Quantised MPC for LPV systems by using new Lyapunov–Krasovskii functional

This study deals with the problem of sampled-data model predictive control (MPC) for linear parameter varying (LPV) systems with input quantisation. The LPV systems under consideration depend on a set of parameters that are bounded and available online. To deal with a piecewise constant sampled-data and quantisation of the control input, the closed-loop system is modelled as a continuous-time impulsive dynamic model with sector non-linearity. The control problem is formulated as a minimisation of the upper bound of infinite horizon cost function subject to a sufficient condition for stability. The stability of the proposed MPC is guaranteed by constructing new Lyapunov–Krasovskii functional. Finally, a numerical example is provided to illustrate the effectiveness and benefits of the proposed theoretical results.

On convergence and performance certification of a continuous-time economic model predictive control scheme with time-varying performance index

This paper addresses the design of convergence and performance certified sampled-data model predictive control (MPC) laws with a time-dependent economic performance index. More precisely, using a dissipativity property of the system, we provide a set of sufficient conditions that guarantee convergence of the closed-loop state trajectory to a, possibly time-varying, average economically optimal state trajectory. Moreover, the average performance of the closed-loop system is shown to be no worse than the one obtained by operating the system at the average economically optimal state trajectory. Constructive methods to design an appropriate terminal set and terminal cost that satisfy the proposed sufficient conditions are presented and illustrated with numerical examples.

Event-Based Robust Sampled-Data Model Predictive Control: A Non-Monotonic Lyapunov Function Approach

In this paper, two event-based robust sampled-data model predictive control (MPC) strategies are proposed based on the non-monotonic Lyapunov function approach for continuous-time systems with disturbances. Each event-triggering mechanism consists of the event-based MPC law and the triggering conditions. We show that although the proposed event-triggering conditions are only checked at the sampling instants and the control law is piecewise constant, the feasibility of the event-based sampled-data MPC algorithm and the stability of the closed-loop system are guaranteed in continuous time. Besides, the implementation issue is discussed, and we show that the proposed triggering conditions can be checked rapidly without obviously increasing the computational burden. Finally, an application to a nonholonomic robot system is provided to illustrate the effectiveness of the proposed results.

Sampled‐data MPC for LPV systems with input saturation

In this work, a sampled-data model predictive control (MPC) design method is proposed for continuous-time linear parameter varying (LPV) systems. The input saturation and parameter uncertainties are both considered. Using a method to deal with actuator saturation, the MPC controller is permitted to saturate. Using the measurable parameter vector, a scheduled state-feedback MPC controller is computed at each time instant which fully exploits the real-time information on the variations of the plant characteristics. By modelling the closed-loop systems of the continuous-time LPV systems with a piecewise constant sampled-data control input as linear impulsive systems, the stability properties of the proposed MPC are studied. The sampling interval in this work is not required to be periodic. The proposed MPC design method is expected to further reduce the conservativeness. The improvements of the proposed sampled-data MPC method w.r.t. other existing MPC techniques are demonstrated by an example.

Sampled Data Model Predictive Control of a Voltage Source Inverter for Reduced Harmonic Distortion

This brief considers model predictive control of switched mode power converters using a hybrid sampled data model. The goal of the approach is to synthesize a controller that achieves both good dynamic performance and low harmonic distortion at steady state. The suggested control approach takes the switched nature of the converter into account in both the system model and the control objective. This has two main advantages. First, it removes the need for the low-pass filters which are conventionally applied to the state measurements to attenuate the switching ripple. This implies that improved dynamic performance can be obtained. Second, it penalizes the ripple deviation from the reference, which means that reduced harmonic distortion can be obtained at steady state.

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Raković (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.